American Political Science Review (2018)112.4,844-859 doi:10.1017/S0003055418000229 American Political Science Association 2018 Leadership with Trustworthy Associates TORUN DEWAN London School of Economics and Political Science FRANCESCO SOUINTANI Warwick University roup members value informed decisions and hold ideological preferences.A leader takes a de- cision on their behalf Good leadership depends on characteristics of moderation and judgment. The latter emerges (endogenously)via advice communicated by "trustworthy associates."Trust- worthy advice requires ideological proximity to the leader.A group may choose a relatively extreme leader with a large number of such associates.Paradoxically,this can happen though it is in the group's collective interest to choose a moderate leader.To assess whether these insights persist when political groups compete,we embed our analysis in a model of elections.Each of two parties chooses a leader who implements her preferred policy if elected.We find that a party may choose an extreme leader who defeats a moderate candidate chosen by the opposing party.Our results highlight the importance of party cohesion and the relations between a leader and her party.These can be more important to electoral success than proximity of a leader's position to the median voter. E la prima coniettura che si fa del cervello d'uno signore, relations a leader enjoys with others in the governance e vedere li uomini che lui ha d'intorno. process and the advice that she obtains from them.We Niccolo'Machiavelli,Il Principe,Ch.22. find this perspective in Aristotle who,in Politics III.16 1287 27-35,argues that advice from friends is central INTRODUCTION to a leader's judgment: ho should rule?Which individual characteris. "It would perhaps be accounted strange if someone,when tics are required for good and successful lead- judging with one pair of eyes and one pair of ears,and act- ership?These questions are central to politi- ing with one pair of feet and hands,could see better than cal writing and thought.They are addressed in Plato's many people with many pairs,since,as things stand,monar- Republic and,perhaps most famously,in Machiavelli's chs provide themselves with many eyes,ears,hands and feet.For they appoint as co-rulers those who are friends masterpiece I Principe.A central contention of Machi- to themselves and to their rule.If they are not his friends. avelli is that good governance stems from the charac- they will not do as the monarch chooses.But suppose they teristics of a ruler and that these determine political are friends to him and to his rule-well.a friend is someone success.This view is shared by contemporary political similar and equal,so if he thinks they should rule,he must scientists.Since Stokes(1963),studies have recognized think that those who are equal and similar to her should 是 the importance to electoral success of a candidates rule like him." valence-a term used to describe competence,talent and good judgment,which are generally desirable qual- A related theme emerges in Machiavelli's Il Principe. ities of a leader. Our opening quote comes from chapter 22,where he The personal attributes that contribute toward writes on knowledge acquisition and making use of good leadership might be innate,as in the "great trusted advisers,and is translated as man"theory espoused by the social historian Thomas "The first opinion that one forms of a prince,and of his un- Carlyle (1841).Alternatively,they might be the derstanding,is by observing the men he has around him." product of education and training.Plato,for example, believed the education of future leaders to be a core One interpretation,according to the idiom "a person function of the state.There is,however,a different is known for the company she seeks,"suggests that we view.Leadership characteristics may stem from the infer a leader's quality from the type of person she as- sociates with.Another,perhaps more intriguing inter- pretation,is that a leader's qualities arise because of Torun Dewan is a Professor of Government London School of Eco- nomics and Political Science.Houghton Street,London,UK.WC2A those she associates with.?Machiavelli entertains this 2AE (t.dewan@lse.ac.uk) second interpretation,attributing the greatness of Pan- Francesco Squintani is a Professor of Economics Warwick dolfo Petrucci,Prince of Siena,to the relationship he University,Coventry,UK,CV4 7AL (F.Squintani@Warwick. enjoyed with his valent minister Antonio da Venafro. ac.uk) We thank for their comments audiences at several seminars. Indeed,Machiavelli highlights that Pandolfo's ability as including Harvard University,Stanford University,University of a ruler depended upon the information and good judg- Chicago,Berkeley University,Princeton University,University of ment provided by Antonio.3 Rochester,and Washington University in St.Louis,and at several conferences,and Melissa Schwartzberg. 2 A different interpretation is that an intrinsically good leader is not Received:May 23,2017;revised:December 3,2017;accepted:April threatened even when surrounded by highly capable,if potentially 4,2018.First published online:June 21,2018. hostile,associates.For example,Kearns Goodwin(2005)relates the political genius of Abraham Lincoln to his ability in forming a cabi- /:sony 1 See McCurley and Mondak (1995):Ansolabehere.Snyder,and net consisting of erstwhile rivals to his presidency. Stewart (2001):Burden (2004);Stone and Simas (2010);amongst These two prominent examples develop the theme that reliable ad- others vice from friends,allies,and associates leads to better judgment and 844
American Political Science Review (2018) 112, 4, 844–859 doi:10.1017/S0003055418000229 © American Political Science Association 2018 Leadership with Trustworthy Associates TORUN DEWAN London School of Economics and Political Science FRANCESCO SQUINTANI Warwick University Group members value informed decisions and hold ideological preferences. A leader takes a decision on their behalf. Good leadership depends on characteristics of moderation and judgment. The latter emerges (endogenously) via advice communicated by “trustworthy associates.” Trustworthy advice requires ideological proximity to the leader. A group may choose a relatively extreme leader with a large number of such associates. Paradoxically, this can happen though it is in the group’s collective interest to choose a moderate leader. To assess whether these insights persist when political groups compete, we embed our analysis in a model of elections. Each of two parties chooses a leader who implements her preferred policy if elected. We find that a party may choose an extreme leader who defeats a moderate candidate chosen by the opposing party. Our results highlight the importance of party cohesion and the relations between a leader and her party. These can be more important to electoral success than proximity of a leader’s position to the median voter. E la prima coniettura che si fa del cervello d’uno signore, é vedere li uomini che lui ha d’intorno. Niccolo’ Machiavelli, Il Principe, Ch. 22. INTRODUCTION Who should rule? Which individual characteristics are required for good and successful leadership? These questions are central to political writing and thought. They are addressed in Plato’s Republic and, perhaps most famously, in Machiavelli’s masterpiece Il Principe.A central contention of Machiavelli is that good governance stems from the characteristics of a ruler and that these determine political success. This view is shared by contemporary political scientists. Since Stokes (1963), studies have recognized the importance to electoral success of a candidates’ valence—a term used to describe competence, talent, and good judgment, which are generally desirable qualities of a leader.1 The personal attributes that contribute toward good leadership might be innate, as in the “great man” theory espoused by the social historian Thomas Carlyle (1841). Alternatively, they might be the product of education and training. Plato, for example, believed the education of future leaders to be a core function of the state. There is, however, a different view. Leadership characteristics may stem from the Torun Dewan is a Professor of Government London School of Economics and Political Science, Houghton Street, London, UK, WC2A 2AE (t.dewan@lse.ac.uk) Francesco Squintani is a Professor of Economics Warwick University, Coventry, UK, CV4 7AL (F.Squintani@Warwick. ac.uk) We thank for their comments audiences at several seminars, including Harvard University, Stanford University, University of Chicago, Berkeley University, Princeton University, University of Rochester, and Washington University in St. Louis, and at several conferences, and Melissa Schwartzberg. Received: May 23, 2017; revised: December 3, 2017; accepted: April 4, 2018. First published online: June 21, 2018. 1 See McCurley and Mondak (1995); Ansolabehere, Snyder, and Stewart (2001); Burden (2004); Stone and Simas (2010); amongst others. relations a leader enjoys with others in the governance process and the advice that she obtains from them. We find this perspective in Aristotle who, in Politics III.16, 1287 27–35, argues that advice from friends is central to a leader’s judgment: “It would perhaps be accounted strange if someone, when judging with one pair of eyes and one pair of ears, and acting with one pair of feet and hands, could see better than many people with many pairs, since, as things stand,monarchs provide themselves with many eyes, ears, hands and feet. For they appoint as co-rulers those who are friends to themselves and to their rule. If they are not his friends, they will not do as the monarch chooses. But suppose they are friends to him and to his rule – well, a friend is someone similar and equal, so if he thinks they should rule, he must think that those who are equal and similar to her should rule like him.” A related theme emerges in Machiavelli’s Il Principe. Our opening quote comes from chapter 22, where he writes on knowledge acquisition and making use of trusted advisers, and is translated as “The first opinion that one forms of a prince, and of his understanding, is by observing the men he has around him.” One interpretation, according to the idiom “a person is known for the company she seeks,” suggests that we infer a leader’s quality from the type of person she associates with. Another, perhaps more intriguing interpretation, is that a leader’s qualities arise because of those she associates with.2 Machiavelli entertains this second interpretation, attributing the greatness of Pandolfo Petrucci, Prince of Siena, to the relationship he enjoyed with his valent minister Antonio da Venafro. Indeed,Machiavelli highlights that Pandolfo’s ability as a ruler depended upon the information and good judgment provided by Antonio.3 2 A different interpretation is that an intrinsically good leader is not threatened even when surrounded by highly capable, if potentially hostile, associates. For example, Kearns Goodwin (2005) relates the political genius of Abraham Lincoln to his ability in forming a cabinet consisting of erstwhile rivals to his presidency. 3 These two prominent examples develop the theme that reliable advice from friends, allies, and associates leads to better judgment and 844 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000229
Leadership with Trustworthy Associates In this article.we develop a novel theory of leader- judgment,by contrast,depends upon the concentration ship that relates a leader's judgment to the relations of viewpoints similar to her own.Put otherwise,moder- she forms with other group members whose advice she ation refers to "global"properties of the ideology dis- may benefit from.Such advice can help her form bet- tribution.while judgment is related to"local"ones. ter judgment and so take more informed decisions.But What then are the characteristics of the chosen for this to be so,a leader must be able to trust the ad leader?Since the majority choice is determined by the vice obtained.That is,the advice must be truthful.To median player,one might expect a moderate leader to explore this notion of leadership,we analyze a group be chosen.On the other hand,a leader's network is also that collectively chooses a leader who is granted au- an important consideration.Indeed we find.in line with thority to take a decision on their behalf.Players'pay- common intuition and the practical wisdom of Aristo- offs depend on an uncertain state of the world about tle,that a leader may be chosen because she has many which each is independently,privately,and imperfectly friends.Here,a large network of friends translates into informed.Each,however,has different preferred out- better judgment.A direct prediction stems from this. comes that reflect their idiosyncratic ideological pref- The group leader may,in fact,be relatively extreme. erences.After the leader is chosen,but before the de. Indeed,this is so when ideological opinions are con- cision is taken,group members may advise the chosen centrated at the extremes. leader,whoever she may be.Such advice takes the form Next,we compare the group's choice of leader under 4 of cheap-talk communication. majority rule with the optimal choice and so address an First,we study the endogenous formation of a issue raised by Levi and Ahlquist(2011)who note that leader's network of trustworthy associates:those the "leadership does not always improve aggregate wel- leader can rely upon for truthful advice.The results are fare and we need to know more about the conditions intuitive.We show that a leader can rely on truthful ad- under which it does and it does not."We show that vice only from those whose ideological preferences are the chosen leader maximizes aggregate welfare when similar to her own.Taking the next step,we show that a the ideology of group members is evenly distributed or 4号元 leader's judgment depends upon the number of trust- clustered around the median.However,when ideolo- worthy associates that she has.A larger group of such gies are clustered away from the median,then she fails associates translates into more informed decisions.This to achieve maximal aggregate welfare.Deeper insights & intuitive result establishes our take on the Machiavel- emerge once we recognize our model as one of implicit lian lesson:A leader's wisdom and judgment are deter- (strategic)delegation,as first analyzed by Schelling mined by those she has around her.And it resonates (1960).The incentive of the median politician to dele- with Aristotle's claim:a good leader has many friends, gate arises when another politician has more trustwor- who are ideologically similar to her,and whose advice thy associates and so will take a more informed deci- she benefits from sion.When choosing whether to delegate,however,the In light of these results,we then ask:What are the median considers only her own preferences.A surpris- characteristics of a good leader?She is defined as the ing consequence is that she may delegate to a relatively one that the group should choose when maximizing extreme leader when a more moderate one (such as their joint welfare.In line with the classic texts,we find herself)would better serve the group interest.The up- that moderation (or temperance)is desirable.Never- shot of this result is a reversal of the famous"ally prin- theless,a good leader relies on her judgment,which is ciple,"which states that delegation should take place determined by the number of allies in her circle.De to an ally who is as close as possible to the principal.4 pending on the distribution of ideological views in the A surprising implication,from a welfare perspective,is 8 group,a moderate leader may be isolated in that she that the group choice places too much emphasis on a cannot rely on anyone's advice.Thus,a tradeoff arises leader's judgment,and too little on her moderation. between moderation,on the one hand,and judgment A useful exercise is to consider how the group's on the other. choice of leader changes when the preferences of its Our model delivers a simple mathematical equation members change.This might occur due to transition in that describes this potential tradeoff and the optimal the group's membership or from exogenous shocks to choice of leader.This equation reveals that the trade- members'preferences.In models of collective choice off is related to different properties of the distribution that build on Black's celebrated theorem (1948).only of views in the group.A leader's moderation is under- the identity (and hence opinion)of the median(player stood with respect to the entire spectrum of views.Her or committee member)matters for decisions made. 四 Consequently,any change to the distribution of views within a group that leaves the identity of the me- successful leadership.This view was in fact quite general in the Mid. dian unchanged has no effect on policy outcomes.Our dle Ages.Recent analysis of a collection of the"mirror for princes" texts (a class of texts offering advice on governance,developed in comparative static analysis produces sharply differ- both Christian Europe and the Islamic world in the Middle Ages,of ent predictions.Changes in the ideological views of which Machiavelli's work is the most famous)uses state-of-the-art group members can affect leadership and hence pol- text-as-data measurement techniques developed by political scien- icy choice even though they do not alter the identity tists (Blaydes,Grimmer,and McQueen 2013).This textual analysis of the "global"median player.This result stems from reveals a prominent theme referring to the characteristics of exem- /:sony plary rulers,such as their moderation(or temperance)and judgment Within this theme,a main subtopic highlights the importance of a See Bendor,Glazer,and Hammond (2001)for a review of this lit- leader's relations with others. erature. 845
Leadership with Trustworthy Associates In this article, we develop a novel theory of leadership that relates a leader’s judgment to the relations she forms with other group members whose advice she may benefit from. Such advice can help her form better judgment and so take more informed decisions. But, for this to be so, a leader must be able to trust the advice obtained. That is, the advice must be truthful. To explore this notion of leadership, we analyze a group that collectively chooses a leader who is granted authority to take a decision on their behalf. Players’ payoffs depend on an uncertain state of the world about which each is independently, privately, and imperfectly informed. Each, however, has different preferred outcomes that reflect their idiosyncratic ideological preferences. After the leader is chosen, but before the decision is taken, group members may advise the chosen leader, whoever she may be. Such advice takes the form of cheap-talk communication. First, we study the endogenous formation of a leader’s network of trustworthy associates: those the leader can rely upon for truthful advice. The results are intuitive.We show that a leader can rely on truthful advice only from those whose ideological preferences are similar to her own. Taking the next step, we show that a leader’s judgment depends upon the number of trustworthy associates that she has. A larger group of such associates translates into more informed decisions.This intuitive result establishes our take on the Machiavellian lesson: A leader’s wisdom and judgment are determined by those she has around her. And it resonates with Aristotle’s claim: a good leader has many friends, who are ideologically similar to her, and whose advice she benefits from. In light of these results, we then ask: What are the characteristics of a good leader? She is defined as the one that the group should choose when maximizing their joint welfare. In line with the classic texts, we find that moderation (or temperance) is desirable. Nevertheless, a good leader relies on her judgment, which is determined by the number of allies in her circle. Depending on the distribution of ideological views in the group, a moderate leader may be isolated in that she cannot rely on anyone’s advice. Thus, a tradeoff arises between moderation, on the one hand, and judgment on the other. Our model delivers a simple mathematical equation that describes this potential tradeoff and the optimal choice of leader. This equation reveals that the tradeoff is related to different properties of the distribution of views in the group. A leader’s moderation is understood with respect to the entire spectrum of views. Her successful leadership. This view was in fact quite general in the Middle Ages. Recent analysis of a collection of the “mirror for princes” texts (a class of texts offering advice on governance, developed in both Christian Europe and the Islamic world in the Middle Ages, of which Machiavelli’s work is the most famous) uses state-of-the-art text-as-data measurement techniques developed by political scientists (Blaydes, Grimmer, and McQueen 2013). This textual analysis reveals a prominent theme referring to the characteristics of exemplary rulers, such as their moderation (or temperance) and judgment. Within this theme, a main subtopic highlights the importance of a leader’s relations with others. judgment, by contrast, depends upon the concentration of viewpoints similar to her own. Put otherwise,moderation refers to “global” properties of the ideology distribution, while judgment is related to “local” ones. What then are the characteristics of the chosen leader? Since the majority choice is determined by the median player, one might expect a moderate leader to be chosen.On the other hand, a leader’s network is also an important consideration. Indeed we find,in line with common intuition and the practical wisdom of Aristotle, that a leader may be chosen because she has many friends. Here, a large network of friends translates into better judgment. A direct prediction stems from this. The group leader may, in fact, be relatively extreme. Indeed, this is so when ideological opinions are concentrated at the extremes. Next, we compare the group’s choice of leader under majority rule with the optimal choice and so address an issue raised by Levi and Ahlquist (2011) who note that “leadership does not always improve aggregate welfare and we need to know more about the conditions under which it does and it does not.” We show that the chosen leader maximizes aggregate welfare when the ideology of group members is evenly distributed or clustered around the median. However, when ideologies are clustered away from the median, then she fails to achieve maximal aggregate welfare. Deeper insights emerge once we recognize our model as one of implicit (strategic) delegation, as first analyzed by Schelling (1960). The incentive of the median politician to delegate arises when another politician has more trustworthy associates and so will take a more informed decision.When choosing whether to delegate, however, the median considers only her own preferences. A surprising consequence is that she may delegate to a relatively extreme leader when a more moderate one (such as herself) would better serve the group interest. The upshot of this result is a reversal of the famous “ally principle,” which states that delegation should take place to an ally who is as close as possible to the principal.4 A surprising implication, from a welfare perspective, is that the group choice places too much emphasis on a leader’s judgment, and too little on her moderation. A useful exercise is to consider how the group’s choice of leader changes when the preferences of its members change. This might occur due to transition in the group’s membership or from exogenous shocks to members’ preferences. In models of collective choice that build on Black’s celebrated theorem (1948), only the identity (and hence opinion) of the median (player or committee member) matters for decisions made. Consequently, any change to the distribution of views within a group that leaves the identity of the median unchanged has no effect on policy outcomes. Our comparative static analysis produces sharply different predictions. Changes in the ideological views of group members can affect leadership and hence policy choice even though they do not alter the identity of the “global” median player. This result stems from 4 See Bendor, Glazer, and Hammond (2001) for a review of this literature. 845 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000229
Torun Dewan and Francesco Squintani the fact that such ideological changes affect a leader's unexpected implications when considering party com- network of trustworthy associates.If some players be- petition.We find that a party can turn a winning(los- come more extreme (moderate)in their views,then a ing)situation into a losing (winning)one when mod- moderate (extreme)leader may lose important trust- erates (extremists)become more moderate (extreme). worthy allies.This affects her ability to exercise good Moreover,we illustrate how a political leader can turn judgment and hence her prospects of being chosen. a potential winning situation into a losing one by These new theoretical results shed light on empirical moderating her policy position.In so doing,she re- questions arising from applications of the spatial model duces her leadership potential,becomes isolated and in political science,such as,for example,work analyzing less well-placed to benefit from advice of others,and is appointments made by the President to the Supreme unable to deliver informed policies. Court that are approved by the Senate(Krehbiel 2007; Bringing these insights together reveals the impor- Rohde and Shepsle 2007).In these models of complete tance of a party's cohesion on its electoral success.Our information,based on Blacks'theorem,a Senate mem- results suggest that the electoral success of relatively ber's vote is based only on whether a proposed ap- moderate leaders is not due to their moderation per pointee changes the identity of the median court mem- se,but to the fact that their parties are cohesive.Corre ber.This reasoning does not sit well with common in- spondingly,we argue that the success of moderate lead- tuition that the viewpoints of all players are relevant to ers(e.g.,Tony Blair and Bill Clinton)can be related to decision-making.Moreover,empirical evidence shows the fact that key figures in their party had moderated that extreme justices are less likely to have their nom- their own opinions.Indeed,excerpts from Blair's au- ination confirmed.Clark(2012)reviews this literature tobiography suggest that his judgment during his first and notes that the facts are difficult to reconcile with term in office depended upon the advice that was pro- existing theoretical models.He argues that an expla- vided by trustworthy allies (such as David Blunkett) nation requires relaxing the complete information as- who themselves had moved from the hard to the center sumption that underpins those models.Our analysis of left of the party decision-making in small groups with incomplete infor- mation supports the common intuition that the view- points of all group members are relevant,and suggests OUR CONTRIBUTION TO THE RELATED that Clark's conjecture is correct. LITERATURE The main body of our article explores the idea that a While we shall comment on and discuss our contri- leader's judgment depends on her close associates and butions throughout,here we precede our analysis by so,in turn,on the local distribution of preferences in briefly pointing out some of the main related litera- the group.Next we check whether the empirical con- ture and themes.We contribute to a small but grow- sequences of that assertion are robust when consider- ing formal literature that develops different notions ing electoral competition between groups.To explore of leadership.For example,Hermalin (1998)develops this,we study internal leadership contests (involving the notion of leading by example whereby a leader politicians,members,and/or registered voters)in two provides a costly signal that aligns followers'incen- parties whose leaders then contest a general election tives with her own.Canes-Wrone.Herron,and Shotts after which the winner implements her preferred poli- (2001)draw a distinction between "leadership'-the S5.501g cies.A conjecture is that our surprising findings will act of implementing a policy that a leader believes to disappear with competition that(as illustrated in the be correct-and "pandering"to a majority.Relatedly, classic spatial model of Downs)provides incentives for Canes-Wrone (2006)develops a notion of "transfor- parties to moderate their position.While that conjec- mative leadership":in the context of an agenda-setting ture is correct in the absence of (strategic)communi- model,a leader (the President)strategically chooses cation within parties,it no longer holds true when a whether to bring an issue to the public's attention, leader's judgment depends upon advice obtained from anticipating that (the pivotal)member of Congress others.Parties may choose relatively extreme leaders will move toward the public's position.Dewan and even when more moderate candidates are available Myatt (2007)develop the notion of focal leadership and,moreover,doing so can enhance their chances of that draws on earlier work by Schelling (1960)and electoral victory.In fact,and surprisingly,our results Calvert (1995).Here a leader is connected via a net- are stronger as a consequence of competition.That is, work to trustworthy associates who influence her judg- there exist circumstances in which the most moderate ment through truthful communication of privately held available political candidate would be elected as leader information.5 Leadership emerges via majority deci- in the absence of electoral competition (that is,if all sion taken by group members who anticipate the for- politicians belong to a single group),whereas two-party mation of a leader's network.While the phenomena we competition would cause the election of relatively describe-leadership,judgment,and trustworthiness- extreme leader. are macro-level processes(and subject to different in- A surprising comparative static prediction of our terpretations),here they emerge endogenously from a L model involves the ideological direction of leadership model built on sparse assumptions. change.A rightward shift in the ideology of a party politician can have an opposite effect on leadership choice,making it more likely that a leftist leader is cho We thus develop the notion of"relational leadership"found in the sen,and vice versa.This nonmonotonicity has further social psychology literature,see Uhl-Bien(2006). 846
Torun Dewan and Francesco Squintani the fact that such ideological changes affect a leader’s network of trustworthy associates. If some players become more extreme (moderate) in their views, then a moderate (extreme) leader may lose important trustworthy allies. This affects her ability to exercise good judgment and hence her prospects of being chosen. These new theoretical results shed light on empirical questions arising from applications of the spatial model in political science, such as, for example,work analyzing appointments made by the President to the Supreme Court that are approved by the Senate (Krehbiel 2007; Rohde and Shepsle 2007). In these models of complete information, based on Blacks’ theorem, a Senate member’s vote is based only on whether a proposed appointee changes the identity of the median court member. This reasoning does not sit well with common intuition that the viewpoints of all players are relevant to decision-making. Moreover, empirical evidence shows that extreme justices are less likely to have their nomination confirmed. Clark (2012) reviews this literature and notes that the facts are difficult to reconcile with existing theoretical models. He argues that an explanation requires relaxing the complete information assumption that underpins those models. Our analysis of decision-making in small groups with incomplete information supports the common intuition that the viewpoints of all group members are relevant, and suggests that Clark’s conjecture is correct. The main body of our article explores the idea that a leader’s judgment depends on her close associates and so, in turn, on the local distribution of preferences in the group. Next we check whether the empirical consequences of that assertion are robust when considering electoral competition between groups. To explore this, we study internal leadership contests (involving politicians, members, and/or registered voters) in two parties whose leaders then contest a general election after which the winner implements her preferred policies. A conjecture is that our surprising findings will disappear with competition that (as illustrated in the classic spatial model of Downs) provides incentives for parties to moderate their position. While that conjecture is correct in the absence of (strategic) communication within parties, it no longer holds true when a leader’s judgment depends upon advice obtained from others. Parties may choose relatively extreme leaders even when more moderate candidates are available and, moreover, doing so can enhance their chances of electoral victory. In fact, and surprisingly, our results are stronger as a consequence of competition. That is, there exist circumstances in which the most moderate available political candidate would be elected as leader in the absence of electoral competition (that is, if all politicians belong to a single group), whereas two-party competition would cause the election of relatively extreme leader. A surprising comparative static prediction of our model involves the ideological direction of leadership change. A rightward shift in the ideology of a party politician can have an opposite effect on leadership choice, making it more likely that a leftist leader is chosen, and vice versa. This nonmonotonicity has further unexpected implications when considering party competition. We find that a party can turn a winning (losing) situation into a losing (winning) one when moderates (extremists) become more moderate (extreme). Moreover, we illustrate how a political leader can turn a potential winning situation into a losing one by moderating her policy position. In so doing, she reduces her leadership potential, becomes isolated and less well-placed to benefit from advice of others, and is unable to deliver informed policies. Bringing these insights together reveals the importance of a party’s cohesion on its electoral success. Our results suggest that the electoral success of relatively moderate leaders is not due to their moderation per se, but to the fact that their parties are cohesive. Correspondingly, we argue that the success of moderate leaders (e.g., Tony Blair and Bill Clinton) can be related to the fact that key figures in their party had moderated their own opinions. Indeed, excerpts from Blair’s autobiography suggest that his judgment during his first term in office depended upon the advice that was provided by trustworthy allies (such as David Blunkett) who themselves had moved from the hard to the center left of the party. OUR CONTRIBUTION TO THE RELATED LITERATURE While we shall comment on and discuss our contributions throughout, here we precede our analysis by briefly pointing out some of the main related literature and themes. We contribute to a small but growing formal literature that develops different notions of leadership. For example, Hermalin (1998) develops the notion of leading by example whereby a leader provides a costly signal that aligns followers’ incentives with her own. Canes-Wrone, Herron, and Shotts (2001) draw a distinction between “leadership’—the act of implementing a policy that a leader believes to be correct—and “pandering” to a majority. Relatedly, Canes-Wrone (2006) develops a notion of “transformative leadership”: in the context of an agenda-setting model, a leader (the President) strategically chooses whether to bring an issue to the public’s attention, anticipating that (the pivotal) member of Congress will move toward the public’s position. Dewan and Myatt (2007) develop the notion of focal leadership that draws on earlier work by Schelling (1960) and Calvert (1995). Here a leader is connected via a network to trustworthy associates who influence her judgment through truthful communication of privately held information.5 Leadership emerges via majority decision taken by group members who anticipate the formation of a leader’s network.While the phenomena we describe—leadership,judgment, and trustworthiness— are macro-level processes (and subject to different interpretations), here they emerge endogenously from a model built on sparse assumptions. 5 We thus develop the notion of “relational leadership” found in the social psychology literature, see Uhl-Bien (2006). 846 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000229
Leadership with Trustworthy Associates We study verbal (cheap talk)communication be- noting that,while politicians may delegate to bureau- tween privately informed participants who provide ad- crats with a mandate limited to policy implementation vice to a leader anticipating that such advice may af- they may also delegate the act of decision-making to fect her decisions.Our insights are developed within other politicians due to the fact that they are better the context of multi-player communication between informed. imperfectly informed players as studied by Galeotti, Finally,our model relates to a large literature on Ghiglino,and Squintani (2013).There are numerous candidate valence defined as candidate's characteris- applications of multi-player communication in the po- tics that benefit all voters regardless of their ideology. litical science literature:Patty and Penn (2014)study Many formal theoretical models have analyzed the im- information transmission in small networks of decision plication of valence on candidate policies and electoral makers;Patty(2013)determines the optimal exclusion outcomes (Ansolabehere and Snyder 2000:Groseclose and inclusion policies to maximize information sharing 2001:Aragones and Palfrey 2002:Callander and Wilkie in meetings;Dewan et al.(2015)investigate the opti- 2007;Bernhardt,Camara,and Squintani 2011).We pro- mal assignment of decision-making power in the execu- vide a derivation from first principles of electoral can- tive of a parliamentary democracy;Penn(2016)studies didate's valence,in the form of good judgment.In the the formation of stable aggregation of different units standard definition of valence,it is independent of ide- within an association;Dewan and Squintani(2016)an- ology.Here,in our microfoundation,a leadership can- alyze the formation of party factions.Our contribu- didate's valence is related to,and partly determined tion is in developing the multi-player communication by,the ideological distribution of politicians in her model to deliver a large set of distinctive findings on group leadership and extending these in the context of party competition in which voters anticipate (multi-player) communication within parties. MODEL Other models of leadership relate to individual char- This section sets out our basic model of leadership in a 4r元 acteristics such as honesty,courage,and/or generosity group of politicians who value informed decisions and as in the "great man theory"mentioned in our intro hold ideological preferences.The distinctive feature of ductory remarks and so share our focus on character our model is that a leader gathers advice from politi- istics that make a leader desirable.Dewan and My- cians before making her decision. att(2007,2008)contrast a leader's judgment with her Our players are a group of politicians N=(1,.... ability to communicate clearly.Bolton,Brunnermeier, n who are faced with a decision ye R.One amongst and Velkamp(2010)highlight the role of a leader's them-a leader-makes the decision on the group's "overconfidence."Egorov and Sonin (2011)focus on behalf.The utility of each politician i depends on how the tradeoff between competence and loyalty to the well y matches an unknown state of the world 0.Politi- leader.Besley and Revnal-Ouerol (2011)show that cians are ideologically differentiated and so the util- democratically elected leaders are more likely to have ity of i depends also on her ideological bias bi.Bring- higher academic credentials than unelected ones.Re ing these elements together in a familiar quadratic loss latedly,Galasso and Nannicini (2011)view talented form,we suppose that,were she to know 6,politician leaders as a scarce resource and analyze party alloca- i's payoff ui(,would be a function of according tion of competent politicians,proxied by their educa- tion level,across electoral districts.We draw a distinc- tion between a leader's judgment and her moderation. A key contribution here is in studying leader charac w0,8)=-⊙-6-b)2 teristics that are derived from first principles. As mentioned in our introductory notes,our model With this specification,each politician i's ideal policy can be seen as one of implicit strategic delegation ini is +bi:she would like the policy implemented to be tiated by Schelling (1960)to which more recent contri- related to the state while accounting for her idiosyn- butions include Harstad(2010)and Chari.Jones.and cratic bias.We assume without loss of generality.that Marimon(1997).The question we ask is when and why b1≤b2≤…≤bn,and use the notation B:=bi+i a political leader would confer decision making au- bi,for all i =1,...n-1.The vector of ideologies thority to specialized or better informed bureaucrats b=(b1,...,b)is common knowledge.The unknown (see Huber and Shipan 2002,for a review).According state is uniformly distributed on [0,1]. 四 to perceived wisdom,a political principal would pre- Each politician i has some private information on 0. fer delegating to a bureaucrat with views that are the Specifically,conditional on 0,i holds a signal si,which most similar to her own.The logic behind this so-called takes the value one with probability 0 and zero with ally principle has recently been challenged.Bendor and probability 1-6.Politicians can communicate these Meirowitz(2004)identify a tradeoff between a bureau- signals to the leader before the decision is taken.A crat's information and ideological proximity as a rea- player's willingness to provide truthful advice may de- son for its failure.Our work advances this insight in pend on who among them is selected as the leader.For example,a player i may be unwilling to truthfully reveal Within the context of a Keynsian beauty contest model,leaders are a signal si=1 if her ideology bi is to the left of the group exogenous information sources that help party activists to advocate leader's ideology.Supposing that player j is selected as the best policies and coordinate their actions. the leader,we say that each politician i may send a 847
Leadership with Trustworthy Associates We study verbal (cheap talk) communication between privately informed participants who provide advice to a leader anticipating that such advice may affect her decisions. Our insights are developed within the context of multi-player communication between imperfectly informed players as studied by Galeotti, Ghiglino, and Squintani (2013). There are numerous applications of multi-player communication in the political science literature: Patty and Penn (2014) study information transmission in small networks of decision makers; Patty (2013) determines the optimal exclusion and inclusion policies to maximize information sharing in meetings; Dewan et al. (2015) investigate the optimal assignment of decision-making power in the executive of a parliamentary democracy; Penn (2016) studies the formation of stable aggregation of different units within an association; Dewan and Squintani (2016) analyze the formation of party factions. Our contribution is in developing the multi-player communication model to deliver a large set of distinctive findings on leadership and extending these in the context of party competition in which voters anticipate (multi-player) communication within parties. Other models of leadership relate to individual characteristics such as honesty, courage, and/or generosity as in the “great man theory” mentioned in our introductory remarks and so share our focus on characteristics that make a leader desirable. Dewan and Myatt (2007, 2008) contrast a leader’s judgment with her ability to communicate clearly.6 Bolton, Brunnermeier, and Velkamp (2010) highlight the role of a leader’s “overconfidence.” Egorov and Sonin (2011) focus on the tradeoff between competence and loyalty to the leader. Besley and Reynal-Querol (2011) show that democratically elected leaders are more likely to have higher academic credentials than unelected ones. Relatedly, Galasso and Nannicini (2011) view talented leaders as a scarce resource and analyze party allocation of competent politicians, proxied by their education level, across electoral districts. We draw a distinction between a leader’s judgment and her moderation. A key contribution here is in studying leader characteristics that are derived from first principles. As mentioned in our introductory notes, our model can be seen as one of implicit strategic delegation initiated by Schelling (1960) to which more recent contributions include Harstad (2010) and Chari, Jones, and Marimon (1997). The question we ask is when and why a political leader would confer decision making authority to specialized or better informed bureaucrats (see Huber and Shipan 2002, for a review). According to perceived wisdom, a political principal would prefer delegating to a bureaucrat with views that are the most similar to her own. The logic behind this so-called ally principle has recently been challenged.Bendor and Meirowitz (2004) identify a tradeoff between a bureaucrat’s information and ideological proximity as a reason for its failure. Our work advances this insight in 6 Within the context of a Keynsian beauty contest model, leaders are exogenous information sources that help party activists to advocate the best policies and coordinate their actions. noting that, while politicians may delegate to bureaucrats with a mandate limited to policy implementation, they may also delegate the act of decision-making to other politicians due to the fact that they are better informed. Finally, our model relates to a large literature on candidate valence defined as candidate’s characteristics that benefit all voters regardless of their ideology. Many formal theoretical models have analyzed the implication of valence on candidate policies and electoral outcomes (Ansolabehere and Snyder 2000;Groseclose 2001;Aragones and Palfrey 2002; Callander and Wilkie 2007;Bernhardt,Câmara, and Squintani 2011).We provide a derivation from first principles of electoral candidate’s valence, in the form of good judgment. In the standard definition of valence, it is independent of ideology. Here, in our microfoundation, a leadership candidate’s valence is related to, and partly determined by, the ideological distribution of politicians in her group. MODEL This section sets out our basic model of leadership in a group of politicians who value informed decisions and hold ideological preferences. The distinctive feature of our model is that a leader gathers advice from politicians before making her decision. Our players are a group of politicians N = {1, …, n} who are faced with a decision yˆ ∈ R. One amongst them—a leader—makes the decision on the group’s behalf. The utility of each politician i depends on how well yˆ matches an unknown state of the world θ. Politicians are ideologically differentiated and so the utility of i depends also on her ideological bias bi. Bringing these elements together in a familiar quadratic loss form, we suppose that, were she to know θ, politician i’s payoff ui (yˆ, θ ) would be a function of yˆ according to ui (yˆ, θ ) = − (yˆ − θ − bi) 2 . With this specification, each politician i’s ideal policy is θ + bi: she would like the policy implemented to be related to the state while accounting for her idiosyncratic bias. We assume without loss of generality, that b1 ≤ b2 ≤ … ≤ bn, and use the notation βi = bi + 1 − bi, for all i = 1, …, n − 1. The vector of ideologies b = {b1,..., bn} is common knowledge. The unknown state θ is uniformly distributed on [0, 1]. Each politician i has some private information on θ. Specifically, conditional on θ, i holds a signal si, which takes the value one with probability θ and zero with probability 1 − θ. Politicians can communicate these signals to the leader before the decision is taken. A player’s willingness to provide truthful advice may depend on who among them is selected as the leader. For example, a playeri may be unwilling to truthfully reveal a signalsi = 1 if her ideology bi is to the left of the group leader’s ideology. Supposing that player j is selected as the leader, we say that each politician i may send a 847 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000229
Torun Dewan and Francesco Squintani message mi∈{0，l}to her..A pure communication We denote as U(j)the payoff associated with the strategy of player i to j is thus a function m that de- equilibrium that maximizes each player's payoff among pends on si.Given leader j,let m-i be the profile of the equilibria induced by j.The Condorcet winner is the 000100006/LLoL communication strategies m of plavers i i.After player j who defeats any other player k in a direct vote communication takes place,the leader chooses y so as among alternatives j and k.As this winner need not be to implement her preferred policy.We denote a deci- well defined when n is even,(then,the majority vote sion strategy by leader j as yi:(0,1)"-R. may result in a tie),we restrict attention to groups with For a given leader j,an equilibrium consists of the an odd number of politicians. strategy pair(m-i,yi)and a set of beliefs that are con- sistent with equilibrium play.Our equilibrium concept op//s is pure-strategy Perfect Bayesian Equilibrium.Up to A LEADER'S TRUSTWORTHY ASSOCIATES relabeling of messages,each equilibrium pure commu- In our model.a leader is informed via communication nication strategy mii from a player i to a leader j may from members of the group.This takes the form of cost- be either truthful,in that i reveals her signal to j,so that less,or so-called cheap talk,messages.As no one mem- m(s)=s:fors∈{0，l,or“babbling”(that is,,uninfor- ber of the group is perfectly informed,a politician be- mative ofs:),and in this case mi(si)does not depend on comes better informed the more other members truth- s:?We interpret the politicians who adopt the truthful fully reveal their signals to her in equilibrium.Such strategy with respect to j as the trustworthy associates politicians form her circle of trustworthy associates.We of that leader. first define and characterize this concept before calcu- Fixing a leader j,there may be multiple equilibria lating its size for an arbitrary leader j.We show that the (m-j,yi).For example,the strategy profile where all circle of equilibrium trustworthy associates is related players "babble"is always an equilibrium.Because of to key primitives of our model,namely the ordering of equilibrium multiplicity,the ranking of leaders and the ideological biases within the group.Therefore,we can leadership selection depend upon the choice of equi- relate a leader's judgment to the same ordering. librium:for the same leader j,different equilibria yield different player payoffs.To avoid ambiguities,we as- sume that for a given leader j,politicians coordinate A Leader's Judgment on the equilibria(m-i,y )that provide the highest ex- The equilibrium strategies(m-j,yi)given any chosen pected payoffs to all politicians.s The selection of these leader j are easily derived from the analysis leading to equilibria is standard in games of communication and Corollary 1 in Galeotti,Ghiglino,and Squintani (2013) allows us to focus attention on leadership selection. Given the received messages m;and her signal s;,by We consider two forms of leader selection. sequential rationality.the leader j chooses v to maxi- The first one addresses our normative question: mize her expected utility.Because of the quadratic loss Which leader would maximize politicians'welfare if specification of players'payoffs,she chooses chosen?Following the utilitarian principle,the welfare W(m-i,y;)associated with an equilibrium (m_i,yi)is 1) the sum of players'expected payoffs: yi(si,j)=bi+E[elsi,i]. Let di(mi)be the number of politicians willing to W(m-,y)=- >E[(yi-0-bi)2] truthfully advise j,were she to lead the group.These iEN politicians form the group of trustworthy associates of j.We prove (in the Online Appendix)that the profile We denote W*(j)as the maximal equilibrium welfare m-i is an equilibrium if and only if,whenever i is truth- when j is chosen as leader,and define the optimal lead- ful to j, ers as the players j who maximize W(j). The second determines which player will be elected b:-b1≤2[d,(m-j)+3 (2) by majority rule.When j is the leader,each player i's payoff in an equilibrium (m_i,yi)is An important consequence of the equilibrium condi- tion Equation(2)is that truthful communication from U(m-,y)=-E[yj-6-b)2]. politician i to leader jis possible only if the ideological positions of i and j are sufficiently close.We use this result to derive how informed politician j would be in the event where she becomes leader. 7 For brevity,we abstract from the analysis of mixed strategy equilib- ria,which is cumbersome.In the three-player case,Galeotti,Ghiglino First we note that the term di(m-j)is a function and Squintani(2013)demonstrates a mixed-strategy equilibrium in of the equilibrium communication strategies m-i de- which one player communicates truthfully to the decision-maker, ployed by group members.In particular,whenever i and the other one mixes between truthful communication and bab. can be truthful to jin equilibrium,then there is another bling.For some bias parameters,this equilibrium is more informative equilibrium in which i"babbles"when communicating than any pure-strategy equilibrium. with j:since she babbles j will ignore her,and given this 士 It can be easily shown that for any given leader j,each politician i's ranking among the possible equilibria (m-j.y)is the same(see response there exists no profitable deviation for i.Fix- Galeotti,Ghiglino,and Squintani(2013),Theorem 2). ing i's leadership,the equilibria(m-j,yi)that provides 848
Torun Dewan and Francesco Squintani message mˆ i j ∈ {0, 1} to her. A pure communication strategy of player i to j is thus a function mij that depends on si. Given leader j, let m−j be the profile of communication strategies mij of players i = j. After communication takes place, the leader chooses yˆ so as to implement her preferred policy. We denote a decision strategy by leader j as yj : {0, 1}n → R. For a given leader j, an equilibrium consists of the strategy pair (m−j, yj) and a set of beliefs that are consistent with equilibrium play. Our equilibrium concept is pure-strategy Perfect Bayesian Equilibrium. Up to relabeling of messages, each equilibrium pure communication strategy mij from a player i to a leader j may be either truthful, in that i reveals her signal to j, so that mij(si) = si for si ∈ {0, 1}, or “babbling” (that is, uninformative ofsi), and in this case mij(si) does not depend on si. 7 We interpret the politicians who adopt the truthful strategy with respect to j as the trustworthy associates of that leader. Fixing a leader j, there may be multiple equilibria (m−j, yj). For example, the strategy profile where all players “babble” is always an equilibrium. Because of equilibrium multiplicity, the ranking of leaders and the leadership selection depend upon the choice of equilibrium: for the same leader j, different equilibria yield different player payoffs. To avoid ambiguities, we assume that for a given leader j, politicians coordinate on the equilibria (m−j, yj) that provide the highest expected payoffs to all politicians.8 The selection of these equilibria is standard in games of communication and allows us to focus attention on leadership selection. We consider two forms of leader selection. The first one addresses our normative question: Which leader would maximize politicians’ welfare if chosen? Following the utilitarian principle, the welfare W(m−j, yj) associated with an equilibrium (m−j, yj) is the sum of players’ expected payoffs: W(m−j, yj) = − i∈N E[(yj − θ − bi) 2 ]. We denote W∗(j) as the maximal equilibrium welfare when j is chosen as leader, and define the optimal leaders as the players j who maximize W∗(j). The second determines which player will be elected by majority rule. When j is the leader, each player i’s payoff in an equilibrium (m−j, yj) is Ui(m−j, yj) = −E[(yj − θ − bi) 2 ]. 7 For brevity, we abstract from the analysis of mixed strategy equilibria,which is cumbersome. In the three-player case,Galeotti,Ghiglino, and Squintani (2013) demonstrates a mixed-strategy equilibrium in which one player communicates truthfully to the decision-maker, and the other one mixes between truthful communication and babbling. For some bias parameters, this equilibrium is more informative than any pure-strategy equilibrium. 8 It can be easily shown that for any given leader j, each politician i’s ranking among the possible equilibria m−j, yj is the same (see Galeotti, Ghiglino, and Squintani (2013), Theorem 2). We denote as U∗ i (j) the payoff associated with the equilibrium that maximizes each player’s payoff among the equilibria induced by j.The Condorcet winner is the player j who defeats any other player k in a direct vote among alternatives j and k. As this winner need not be well defined when n is even, (then, the majority vote may result in a tie), we restrict attention to groups with an odd number of politicians. A LEADER’S TRUSTWORTHY ASSOCIATES In our model, a leader is informed via communication from members of the group.This takes the form of costless, or so-called cheap talk, messages. As no one member of the group is perfectly informed, a politician becomes better informed the more other members truthfully reveal their signals to her in equilibrium. Such politicians form her circle of trustworthy associates. We first define and characterize this concept before calculating its size for an arbitrary leader j.We show that the circle of equilibrium trustworthy associates is related to key primitives of our model, namely the ordering of ideological biases within the group. Therefore, we can relate a leader’s judgment to the same ordering. A Leader’s Judgment The equilibrium strategies (m−j, yj) given any chosen leader j are easily derived from the analysis leading to Corollary 1 in Galeotti,Ghiglino, and Squintani (2013). Given the received messages mˆ −j and her signal sj, by sequential rationality, the leader j chooses yˆ to maximize her expected utility. Because of the quadratic loss specification of players’ payoffs, she chooses yj(sj, mˆ −j) = bj + E[θ|sj, mˆ −j]. (1) Let dj(m−j) be the number of politicians willing to truthfully advise j, were she to lead the group. These politicians form the group of trustworthy associates of j. We prove (in the Online Appendix) that the profile m−j is an equilibrium if and only if, whenever i is truthful to j, bi − bj ≤ 1 2 dj(m−j) + 3 . (2) An important consequence of the equilibrium condition Equation (2) is that truthful communication from politician i to leader j is possible only if the ideological positions of i and j are sufficiently close. We use this result to derive how informed politician j would be in the event where she becomes leader. First we note that the term dj(m−j) is a function of the equilibrium communication strategies m−j deployed by group members. In particular, whenever i can be truthful to j in equilibrium, then there is another equilibrium in which i “babbles” when communicating with j: since she babbles j will ignore her, and given this response there exists no profitable deviation for i. Fixing j’s leadership, the equilibria (m−j, yj) that provides 848 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000229
Leadership with Trustworthy Associates the highest expected payoffs to all politicians are such with bias bi of distance within 1/10 and 1/8 to bi will that i's information di(mi)is maximal.That is,we con- be truthful to j if and only if i has no other trustworthy sider the most information that jcould obtain when any associate.10 politician who could communicate truthfully in equi- librium will in fact do so.This allows us to define d;as SELECTING THE LEADER the maximal size of the group of politician who form i's trustworthy associates.Straightforwardly,we can relate Having defined the size of a leader's network of trust- the maximal size of this group to a leader's equilibrium worthy associates,we now turn to the question of lead- judgment. ership selection.We define the optimal leader as one Next we derive this leadership characteristic from who maximizes group welfare.In the absence of a first principles.In particular,we can define it as a con- mechanism that ensures the first best choice,it is natu- sequence of fs ideological position relative to that ral to ask which leader would be chosen by the group of other politicians in her party.To do so,we define when each casts a vote with the outcome determined the function Ni:R>N as the ideological "neighbor- by majority rule.Using the result of the previous sec- hood"function of politician j.For any real number b, tion,we show that the characteristics of optimal and the quantity N(b)is the number of politicians whose majority-preferred leadership can be derived from first ideology is within distance b of her own;that is,the principles. number of politicians whose ideology is in i's ideologi- cal neighborhood of size b.To formally define the func The Optimal Leader N tion Ni,we exploit the fact that politicians are ordered according to their bias,so that We first show that optimal leader selection involves trading off a politician's ideological moderation and N;(b)=maxi∈N:lb:-bl≤b} her judgment.To formalize this insight,we denote 4号 -min{i∈N:lb:-bl≤bl, politician i's moderation as-bi -Eie Nbiln,the con- trary of the distance between b;and the average ideol- for any real number b.For example,if the group of play- ogyb=ieN bi/n.We have definedd as the maximal ers who are truthful to leader j=5 is (3,4,6,71,then size of a leader's network of trustworthy associates.It is Ni(b)=7-3=4.We use the function Ni(.)combined but a small step to relate this number to her judgment, with the equilibrium condition Equation(2)to calcu- the second critical and endogenous leadership char- late the maximal size of any politician i's network of acteristic.When combining the information obtained trustworthy associates: from others with her own view.a leader forms an inde- pendent judgment of the best course of action.Thus a leader's judgment is(strictly)increasing in the number =max :(3) of informative signals she obtains from her trustworthy associates. In fact,and armed with these definitions,we can This provides a simple rule to calculate d by count- prove that the equilibrium ex ante sum of players'pay- ing the number of politicians other than j that are ideo- offs W*(j)can be rewritten as logically close to her.For example,suppose that b;=0 and the three politicians closest to jhave bias distance 1 W*()=-∑(b:-b2-n (4 ⑧ less than 1/12 from bi;that is,they have a bias in the (d+3) interval (-1/12,1/12).These politicians would provide truthful advice to j were she to be selected as leader. For j to have one more trustworthy associate,it must Equation (4)decomposes the welfare function into two be that no member of that circle has a bias further from elements:the aggregate ideological loss EiN(bi-bi)2 bi=0 than 1/14.Interestingly,the size of the ideological associated with the decision taken by j,and the ag neighborhood of leader j(to which a politician needs to gregate residual variance of her decisionEv- belong to be trustworthy to j)decreases in the number of associates truthful to j.For example,a politician i idently,a more moderate leader,whose bias is closer This equilibrium selection can also be motivated by the concept of 10 Costly information acquisition does not change our main insights focal leadership as in Calvert (1995):a leader provides a focal mech- Although it is possible that the set of associates of leader j is differ- anism allowing followers to coordinate on truthful communication, ent and so leadership choice may differ in this scenario,nevertheless, with the consequence that information is aggregated optimally.Ex- with costly acquisition,our first main result-that a leader can rely tensions could consider equilibria in which a politician threatens to on truthful advice only from those whose ideological preferences are babble(thus not transmit information to the elected leader)as a way similar to her own-continues to hold.If a player anticipates that to try and force her own election as leader.In the extreme case,all he will be unable to convey any information to the leader,then he players could commit to babble,communication would break down will not acquire costly information in the first place.Conversely those in equilibrium,and the most moderate politician would be always who do acquire information are those able to convey this informa- elected as leader.More interestingly,early voters could have an ad- tion:they are ideologically close to the leader.As a consequence of vantage in sequential voting because of a forward induction argu this finding,we can then use the same technique to derive the size of ment:by voting for herself,an early voter would "signal"to the others a leader's network of trustworthy associates and the tradeoffs iden- that she plans to babble if not elected. tified in our key results to follow shall continue to apply. 849
Leadership with Trustworthy Associates the highest expected payoffs to all politicians are such that j’s information dj(m−j) is maximal.That is,we consider the most information that j could obtain when any politician who could communicate truthfully in equilibrium will in fact do so.9 This allows us to define d∗ j as the maximal size of the group of politician who form j’s trustworthy associates. Straightforwardly, we can relate the maximal size of this group to a leader’s equilibrium judgment. Next we derive this leadership characteristic from first principles. In particular, we can define it as a consequence of j’s ideological position relative to that of other politicians in her party. To do so, we define the function Nj : R → N as the ideological “neighborhood” function of politician j. For any real number b, the quantity Nj(b) is the number of politicians whose ideology is within distance b of her own; that is, the number of politicians whose ideology is in j’s ideological neighborhood of size b. To formally define the function Nj, we exploit the fact that politicians are ordered according to their bias, so that Nj (b) = max{i ∈ N : |bi − bj| ≤ b} − min{i ∈ N : |bi − bj| ≤ b}, for any real number b.For example,if the group of players who are truthful to leader j = 5 is {3, 4, 6, 7}, then Nj(b) = 7 − 3 = 4. We use the function Nj(·) combined with the equilibrium condition Equation (2) to calculate the maximal size of any politician j’s network of trustworthy associates: d∗ j = max d ∈ N : Nj 1 2 (d + 3) ≤ d . (3) This provides a simple rule to calculate d∗ j by counting the number of politicians other than j that are ideologically close to her. For example, suppose that bj = 0 and the three politicians closest to j have bias distance less than 1/12 from bj; that is, they have a bias in the interval (− 1/12, 1/12). These politicians would provide truthful advice to j were she to be selected as leader. For j to have one more trustworthy associate, it must be that no member of that circle has a bias further from bj = 0 than 1/14. Interestingly, the size of the ideological neighborhood of leaderj(to which a politician needs to belong to be trustworthy to j) decreases in the number of associates truthful to j. For example, a politician i 9 This equilibrium selection can also be motivated by the concept of focal leadership as in Calvert (1995): a leader provides a focal mechanism allowing followers to coordinate on truthful communication, with the consequence that information is aggregated optimally. Extensions could consider equilibria in which a politician threatens to babble (thus not transmit information to the elected leader) as a way to try and force her own election as leader. In the extreme case, all players could commit to babble, communication would break down in equilibrium, and the most moderate politician would be always elected as leader. More interestingly, early voters could have an advantage in sequential voting because of a forward induction argument: by voting for herself, an early voter would “signal” to the others that she plans to babble if not elected. with bias bi of distance within 1/10 and 1/8 to bj will be truthful to j if and only if j has no other trustworthy associate.10 SELECTING THE LEADER Having defined the size of a leader’s network of trustworthy associates, we now turn to the question of leadership selection. We define the optimal leader as one who maximizes group welfare. In the absence of a mechanism that ensures the first best choice, it is natural to ask which leader would be chosen by the group when each casts a vote with the outcome determined by majority rule. Using the result of the previous section, we show that the characteristics of optimal and majority-preferred leadership can be derived from first principles. The Optimal Leader We first show that optimal leader selection involves trading off a politician’s ideological moderation and her judgment. To formalize this insight, we denote politician j’s moderation as −|bj − i ∈ Nbi/n|, the contrary of the distance between bj and the average ideology b¯ ≡ i∈N bi/n. We have defined d∗ j as the maximal size of a leader’s network of trustworthy associates. It is but a small step to relate this number to her judgment, the second critical and endogenous leadership characteristic. When combining the information obtained from others with her own view, a leader forms an independent judgment of the best course of action. Thus a leader’s judgment is (strictly) increasing in the number of informative signals she obtains from her trustworthy associates. In fact, and armed with these definitions, we can prove that the equilibrium ex ante sum of players’ payoffs W∗(j) can be rewritten as W∗ (j) = − i∈N (bi − bj) 2 − n 1 6(d∗ j + 3). (4) Equation (4) decomposes the welfare function into two elements: the aggregate ideological loss i ∈ N(bi − bj)2 associated with the decision taken by j, and the aggregate residual variance of her decision n 1 6(d∗ j +3). Evidently, a more moderate leader, whose bias is closer 10 Costly information acquisition does not change our main insights. Although it is possible that the set of associates of leader j is different and so leadership choice may differ in this scenario, nevertheless, with costly acquisition, our first main result—that a leader can rely on truthful advice only from those whose ideological preferences are similar to her own—continues to hold. If a player anticipates that he will be unable to convey any information to the leader, then he will not acquire costly information in the first place. Conversely those who do acquire information are those able to convey this information: they are ideologically close to the leader. As a consequence of this finding, we can then use the same technique to derive the size of a leader’s network of trustworthy associates and the tradeoffs identified in our key results to follow shall continue to apply. 849 Downloaded from https://www.cambridge.org/core. 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Torun Dewan and Francesco Squintani to average ideology b,makes the aggregate ideolog- straightforward.we can.nevertheless,make progress ical loss ieN(bi-bi)2 smaller.Further,the resid- by showing that utility functions are single-crossing. ual variance is inversely related to the size of Lemma 1.The utility functions U(j)are single cross- the leader's maximal informant set d;and hence to ing in iandj:ifiU ( her judgment.11 The optimal leader jmaximizes W*() implies U*()>U();and ifizi andi>i,then Thus,optimal leader selection takes into account each U李(i)>U李()implies U()>U*(i). politician's moderation and her endogenous judgment that are related to the core primitives of our model. As a consequence of this result,we appeal to The- orem 2 by Gans and Smart (1996)to show that the namely the ideologies of members of the group. op//s Leader i's moderation can be understood spatially player with median ideology will determine the out- as the relative position of i's bias bi with respect to come of the election.The unique Condorcet winner of the whole ideology distribution b=(b1,...,bn)in the the election game is the politician j who maximizes the group.In fact,every element of b,even extreme ones, expected payoff of the median player. matters for the determination of the average ideol- Proposition 2.The group elects as leader the player j ogy b.In this sense,moderation is a "global"prop- who maximizes the utility U(j)of the median politi- erty of i's ideology bi with respect to the distribution cian m =(n +1)/2.The collective choice considers the b={b1,..,bn}. ideological proximity of any player j to m,as well as j's On the other hand,judgment is a "local"property judgment d that is determined by her number of close- of i's ideology bi within b=(b1,...,bn):it depends minded associates. only on how many other politicians are ideologically close to j,in the sense defined by Equation (3).The Having established the outcome of a majority elec- leader's understanding is thus defined by those close to tion,we can compare it with the optimal leader selec- the leader,or adopting Machiavelli's text,by "the men tion by inspecting Equations(4)and(5),the latter for he has around him."This analysis of the role played by i=m.As in the earlier case,there is a tradeoff be- the local ideological distribution is,to our knowledge, tween moderation and judgment:the Condorcet win- novel in the large contemporary and formal literature ner j keeps both the ideological loss (bm-bi)2 and on collective choice:though it echoes the insights of Machiavelli made in Il Principe 500 years ago. the residual variance as low as possible.Just as We summarize our findings as follows. with optimal leadership,the majority choice involves a tradeoff between the desire for a moderate leader and Proposition 1.The optimal leader j is determined by that for a leader with good judgment,which,in turn, ideological moderation,the proximity of bi to the aver- stems from having a large group of close-minded asso- age group ideology b,and by good judgment,her num- ciates.Beyond this similarity.there is a critical differ- 是 ber d of close-minded associates. ence and it is this:whereas a majority preferred leader makes this tradeoff decision by considering only her own payoff,by contrast,an optimally selected leader Electing the Leader would consider the preferences of the entire group. We now determine which politician is elected as leader Straightforwardly,and as the weights placed on these by a simple majority decision taken within the group. two features of good leadership are different in our key Each player i's utility as a function of the leader's expressions,the majority choice of leader may not be identity jis optimal.As we shall see,the implications are surprising in that we identify instances in which the median politi- cian's utility U places less weight on moderation(and U(U)=-(b-b;)2 (5 more on judgment)than the group's welfare W.Thus, 6(d+3) majority choice may be inefficient because it places too much weight on the leader's judgment. As in Equation (4),the first term on the right-hand side illustrates the ideological loss-(bi-bi)2 suffered by WHAT MAKES A GOOD LEADER? each member of the group i when jis chosen as leader. The second term illustrates player i's preference for an Our analysis relates the characteristics that define good informed leader j,as it increases in the judgment d:.We leadership-moderation and judgment-to the com- note that player utilities are not single-peaked with re- munication structure that emerges in the equilibrium spect to a leader's identity:a politician who is ideologi- of our model.The importance of the former is well cally distant may in fact be better informed,and so have known.Indeed,it is easy to see that if there were no better judgment,than one who is ideologically similar informative signals(or just no communication)in this While Black's theorem does not apply in this setting, game,then the chosen leader would be the median L so leadership choice under majority rule is far from politician m,while the optimal one would be the one whose bias is the closest to the average bias b.On the other hand,the role played by judgment,that in turn Mathematically,the residual variancecorresponds to the is related to a leader's trustworthy associates,is novel inverse of the precision of the leader's decision. and central to the results that follow. 850
Torun Dewan and Francesco Squintani to average ideology b¯, makes the aggregate ideological loss i ∈ N(bi − bj)2 smaller. Further, the residual variance 1 6(d∗ j +3) is inversely related to the size of the leader’s maximal informant set d∗ j and hence to her judgment.11 The optimal leader j maximizes W∗(j). Thus, optimal leader selection takes into account each politician’s moderation and her endogenous judgment that are related to the core primitives of our model, namely the ideologies of members of the group. Leader j’s moderation can be understood spatially as the relative position of j’s bias bj with respect to the whole ideology distribution b = {b1,..., bn} in the group. In fact, every element of b, even extreme ones, matters for the determination of the average ideology b¯. In this sense, moderation is a “global” property of j’s ideology bj with respect to the distribution b = {b1,..., bn}. On the other hand, judgment is a “local” property of j’s ideology bj within b = {b1,..., bn}: it depends only on how many other politicians are ideologically close to j, in the sense defined by Equation (3). The leader’s understanding is thus defined by those close to the leader, or adopting Machiavelli’s text, by “the men he has around him.” This analysis of the role played by the local ideological distribution is, to our knowledge, novel in the large contemporary and formal literature on collective choice; though it echoes the insights of Machiavelli made in Il Principe 500 years ago. We summarize our findings as follows. Proposition 1. The optimal leader j is determined by ideological moderation, the proximity of bj to the average group ideology b, and by good judgment, her num- ¯ ber d∗ j of close-minded associates. Electing the Leader We now determine which politician is elected as leader by a simple majority decision taken within the group. Each player i’s utility as a function of the leader’s identity j is U∗ i (j) = −(bi − bj) 2 − 1 6(d∗ j + 3). (5) As in Equation (4), the first term on the right-hand side illustrates the ideological loss −(bi − bj)2 suffered by each member of the group i when j is chosen as leader. The second term illustrates player i’s preference for an informed leaderj, as it increases in the judgment d∗ j .We note that player utilities are not single-peaked with respect to a leader’s identity: a politician who is ideologically distant may in fact be better informed, and so have better judgment, than one who is ideologically similar. While Black’s theorem does not apply in this setting, so leadership choice under majority rule is far from 11 Mathematically, the residual variance 1 6(d∗ j +3) corresponds to the inverse of the precision of the leader’s decision. straightforward, we can, nevertheless, make progress by showing that utility functions are single-crossing. Lemma 1. The utility functions U∗ i (j) are single crossing in i and j : if i U∗ i (j ) implies U∗ i (j) > U∗ i (j ); and if i > i and j > j , then U∗ i (j) > U∗ i (j ) implies U∗ i (j) > U∗ i (j ). As a consequence of this result, we appeal to Theorem 2 by Gans and Smart (1996) to show that the player with median ideology will determine the outcome of the election. The unique Condorcet winner of the election game is the politician j who maximizes the expected payoff of the median player. Proposition 2. The group elects as leader the player j who maximizes the utility U∗ m(j) of the median politician m ≡ (n + 1)/2. The collective choice considers the ideological proximity of any player j to m, as well as j’s judgment d∗ j that is determined by her number of closeminded associates. Having established the outcome of a majority election, we can compare it with the optimal leader selection by inspecting Equations (4) and (5), the latter for i = m. As in the earlier case, there is a tradeoff between moderation and judgment: the Condorcet winner j keeps both the ideological loss (bm − bj)2 and the residual variance 1 6(d∗ j +3) as low as possible. Just as with optimal leadership, the majority choice involves a tradeoff between the desire for a moderate leader and that for a leader with good judgment, which, in turn, stems from having a large group of close-minded associates. Beyond this similarity, there is a critical difference and it is this: whereas a majority preferred leader makes this tradeoff decision by considering only her own payoff, by contrast, an optimally selected leader would consider the preferences of the entire group. Straightforwardly, and as the weights placed on these two features of good leadership are different in our key expressions, the majority choice of leader may not be optimal.As we shall see, the implications are surprising in that we identify instances in which the median politician’s utility U∗ m places less weight on moderation (and more on judgment) than the group’s welfare W∗. Thus, majority choice may be inefficient because it places too much weight on the leader’s judgment. WHAT MAKES A GOOD LEADER? Our analysis relates the characteristics that define good leadership—moderation and judgment—to the communication structure that emerges in the equilibrium of our model. The importance of the former is well known. Indeed, it is easy to see that if there were no informative signals (or just no communication) in this game, then the chosen leader would be the median politician m, while the optimal one would be the one whose bias is the closest to the average bias b¯. On the other hand, the role played by judgment, that in turn is related to a leader’s trustworthy associates, is novel and central to the results that follow. 850 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000229
Leadership with Trustworthy Associates FIGURE 1.Leadership Choice with Equidistant Bias.This figure depicts the case where bi+1- bi=B for all politicians i=1,...4 and 1/12 0 such that bi+1-bi=B for all i =1,...,n -1) ers if and only if they have better judgment than player is a limit case covered by the definition of b as single 3.Also,interchanging B with B4 and B2 with B3 then peaked and symmetric at m. players 2 and 4 are symmetric to each other.Hence,it is with no loss of generality that we restrict attention Proposition 3.When politicians'ideologies b are single to parameter values for which W*(2)>W*(4),so that peaked and symmetric at m,the median politician m also welfare is strictly greater when 2 is the leader rather 12 This reasoning can be pushed one step further.The most extreme 13 One example of such ideological clusters has been documented politicians 1 and n can never be chosen as leaders,as they cannot have in Argentina.Politicians and policy experts come from two sepa- better judgment than their neighbors,who are also more moderate. rate "schools."One is the traditional Peronist or leftist Intelligentsia. If player 2 is truthful to 1 in the most informative equilibrium,then mainly composed of social scientists and administrators that are also 1 is truthful to 2,whereas every other player i>2 is ideologically entrenched in the Argentinian tradition.The second school is the /:sany closer to 2 than to 1,so that if i is truthful to 1,then i is also truthful Chicago/Minnesota boys,economists trained in "fresh water"US to 2 in the most informative equilibrium(and not necessarily vice PhD programs.Similar ideological clusters appear in countries such versa). as France. 851
Leadership with Trustworthy Associates FIGURE 1. Leadership Choice with Equidistant Bias. This figure depicts the case where bi + 1 − bi = β for all politicians i = 1, ..., 4 and 1/12 0 such that bi + 1 − bi = β for all i = 1, …, n − 1) is a limit case covered by the definition of b as single peaked and symmetric at m. Proposition 3. When politicians’ ideologies b are single peaked and symmetric at m,the median politician m also 12 This reasoning can be pushed one step further. The most extreme politicians 1 and n can never be chosen as leaders, as they cannot have better judgment than their neighbors, who are also more moderate. If player 2 is truthful to 1 in the most informative equilibrium, then also 1 is truthful to 2, whereas every other playeri > 2 is ideologically closer to 2 than to 1, so that if i is truthful to 1, then i is also truthful to 2 in the most informative equilibrium (and not necessarily vice versa). has the best judgment. She is the optimal leader and will always be elected as leader by majority. The result is depicted in Figure 1 for n = 5 and ordered left-right biases b1 to b5. In the figure, for each of three politicians j = 2, 3, 4, their maximal amount of equilibrium information is d∗ j = 2. Then the optimal leader, and the one who is indeed chosen by the group, is player 3. Proposition 3 relates the core characteristics of leadership to reveal that, with biases single-peaked and symmetric at m (as in the case of equidistant biases depicted in Figure 1) the most moderate politician is also (weakly) better informed and so has better judgment. The significance of our result lies in the fact that, when ideologies in the group are single-peaked and symmetric at m, there is no tradeoff between moderation and the capacity to gather reliable advice. This underlines that a necessary condition for a politician who is not the most moderate to be the optimal leader or the elected one is that ideologies are clustered away from the median.13 We explore this tradeoff next, focusing on the case of five politicians for ease of exposition. The Case with Five Politicians To explore the tradeoff between moderation and judgment, we study in-depth the case of five politicians, parametrized by the bias differences βi = bi + 1 − bi for playersi = 1,… , 4.Our case is suitably rich (allowing us to identify properties of the ideology distribution that provide novel and interesting findings) yet simple (so that we can do so in a clean and clear manner). First we note that it can never be optimal that 1 and 5 lead the group and neither will they be elected by the group as leaders. Players 2 and 4 can be chosen as leaders if and only if they have better judgment than player 3. Also, interchanging β1 with β4 and β2 with β3 then players 2 and 4 are symmetric to each other. Hence, it is with no loss of generality that we restrict attention to parameter values for which W∗(2) ≥ W∗(4), so that welfare is strictly greater when 2 is the leader rather 13 One example of such ideological clusters has been documented in Argentina. Politicians and policy experts come from two separate “schools.” One is the traditional Peronist or leftist Intelligentsia, mainly composed of social scientists and administrators that are entrenched in the Argentinian tradition. The second school is the Chicago/Minnesota boys, economists trained in “fresh water” US PhD programs. Similar ideological clusters appear in countries such as France. 851 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000229
Torun Dewan and Francesco Squintani FIGURE 2.Leadership Choice with Nonequidistant Bias.In this figure,B1U(4),so that the only If B2l/10 such that(⑧)>2N元 count on more trustworthy associates.that is when d>d.Using condition Equation (3),we calculate for all 5. (in the Online Appendix)all cases for which the condi- tion d>d holds,and determine the restrictions each The result defines a welfare threshold,r(8).The one of them imposes on the parameters Bi,i=1,..., group is better off when player 2 takes the decision if 4.Here,we illustrate our findings in the case in which and only if B2,the ideological distance between play- d'=2andd'=1.This holds when B1≤1/10，p2≤1/10 ers 2 and 3,is below (8).Intuitively,it is optimal that but B3 >1/10.In this case,players 1 and 3 are suffi- 2 leads the group when her better judgment,combined ciently close to 2 to be trustworthy,whereas the me- with the benefits to those the left of the spectrum(b2- dian politician 3 can trust only 2.but not 4.So politi- bi)are not outweighed by the ideological loss incurred cian 2 has better judgment,while 3 is more moderate 4号元 by those to the right(b4-b3 +bs-b3).We prove in This scenario is illustrated in Figure 2,where B3 =b4 the Online Appendix that t is strictly decreasing in 8, -b3 is such that (in contrast to Figure 1)player 4 can with t(1/10)>1/10andx(8)→0for8→o no longer communicate truthfully with 3.As the player & ideologies are not distributed at even distances there Lemma 2 also defines the majority threshold This takes a simpler form as it depends only on the me- may be a tradeoff between judgment and moderation and,moreover,surprising consequences of ideological dian player.She may obtain a more informed outcome shifts (such as that of player 4 in Figure 2 relative to when 2 takes the decision and this yields a constant ad- Figure 1),which we discuss below. dition to her utility.This comes at an ideological cost B2.Thus the group chooses 2 as leader if and only if B2 is below a threshold given by the constant The Tradeoff between Judgment and The final part of Lemma 2 reveals that,in equilib- Moderation rium,the welfare threshold r(8)can either be larger or Whether the choice between the more moderate politi- smaller than the majority thresholddependingon cian 3 and politician 2,who has better judgment,is re- how large 8 is.In the former case,we can distinguish solved in favor of either depends upon B2=b3-b2. three possibilities on the basis of B2:for small B2,i.e., This determines how extreme 2 is relative to 3.This the non-moderate politician 2 is both the pins down the majority choice:if 2 will make a more informed decision than 3,then 3 would be happy for Condorcet winner and the optimal leader;for large B2, specifically,B2>(8),the most moderate politician 3 her to do so,so long as the ideological distance between is both the Condorcet winner and the optimal leader; them is not too large.This allows us to define a majority threshold with respect to B2.In fact,we can relate the in the intermediate case(),the optimal optimal choice and the majority choice between politi- leader is the most informed politician 2.whereas the cian 2 and 3 according to the size of B2 relative to the majority elects politician 3.This identifies an instance other primitives of the model,as demonstrated by the in which majority voting leads to a moderate but inef- lemma below that allows us to define a welfare thresh- ficient choice of leader. old.Let 8=bs-b3 +b4-b3-(b2-b1)be the sum A perhaps more interesting and unexpected case of the ideological distance from 3 of the players to the arises when(⑥)1/10(and hence8>1/I0). leader is the most moderate politician 3,the majority elects instead a relatively extreme leader in politician 2. The logic behind this result is simple.The median f2<2元 1 0.0913.then the Condorcet winner politician may trade off moderation and judgment in is politician 2,else,the most moderate politician 3 a way that differs from the optimal choices made by a wins the majority choice. social planner.Starting from her ideal point,she may 852
Torun Dewan and Francesco Squintani FIGURE 2. Leadership Choice with Nonequidistant Bias. In this figure, β1 ≤ 1/10, β2 ≤ 1/10 and β4 ≤ 1/10 d∗ 3 . Using condition Equation (3), we calculate (in the Online Appendix) all cases for which the condition d∗ 2 > d∗ 3 holds, and determine the restrictions each one of them imposes on the parameters βi, i = 1, …, 4. Here, we illustrate our findings in the case in which d∗ 2 = 2 and d∗ 3 = 1. This holds when β1 ≤ 1/10,β2 ≤ 1/10 but β3 > 1/10. In this case, players 1 and 3 are sufficiently close to 2 to be trustworthy, whereas the median politician 3 can trust only 2, but not 4. So politician 2 has better judgment, while 3 is more moderate. This scenario is illustrated in Figure 2, where β3 = b4 − b3 is such that (in contrast to Figure 1) player 4 can no longer communicate truthfully with 3. As the player ideologies are not distributed at even distances there may be a tradeoff between judgment and moderation and, moreover, surprising consequences of ideological shifts (such as that of player 4 in Figure 2 relative to Figure 1), which we discuss below. The Tradeoff between Judgment and Moderation Whether the choice between the more moderate politician 3 and politician 2, who has better judgment, is resolved in favor of either depends upon β2 = b3 − b2. This determines how extreme 2 is relative to 3. This pins down the majority choice: if 2 will make a more informed decision than 3, then 3 would be happy for her to do so, so long as the ideological distance between them is not too large.This allows us to define a majority threshold with respect to β2. In fact, we can relate the optimal choice and the majority choice between politician 2 and 3 according to the size of β2 relative to the other primitives of the model, as demonstrated by the lemma below that allows us to define a welfare threshold. Let δ = b5 − b3 + b4 − b3 − (b2 − b1) be the sum of the ideological distance from 3 of the players to the right of 3 (that is, 4 and 5) net of the distance from 2 of player 1, the only player to the left of 2. Lemma 2. Consider the case of five politicians, with the above restrictions: W∗(2) ≥ W∗(4), U∗ 3 (2) ≥ U∗ 3 (4), β1 ≤ 1/10, β2 ≤ 1/10, β3 > 1/10 (and hence δ > 1/10). If β2 ¯ 1/10 such that τ (δ) > 1 2 √30 for all δ δ¯. The result defines a welfare threshold, τ (δ). The group is better off when player 2 takes the decision if and only if β2, the ideological distance between players 2 and 3, is below τ (δ). Intuitively, it is optimal that 2 leads the group when her better judgment, combined with the benefits to those the left of the spectrum (b2 − b1) are not outweighed by the ideological loss incurred by those to the right (b4 − b3 + b5 − b3). We prove in the Online Appendix that τ is strictly decreasing in δ, with τ (1/10) > 1/10 and τ (δ) → 0 for δ → ∞. Lemma 2 also defines the majority threshold 1 2 √30 . This takes a simpler form as it depends only on the median player. She may obtain a more informed outcome when 2 takes the decision and this yields a constant addition to her utility. This comes at an ideological cost β2. Thus the group chooses 2 as leader if and only if β2 is below a threshold given by the constant 1 2 √30 . The final part of Lemma 2 reveals that, in equilibrium, the welfare threshold τ (δ) can either be larger or smaller than the majority threshold 1 2 √30 , depending on how large δ is. In the former case, we can distinguish three possibilities on the basis of β2: for small β2, i.e., β2 τ (δ), the most moderate politician 3 is both the Condorcet winner and the optimal leader; in the intermediate case 1 2 √30 < β2 < τ (δ), the optimal leader is the most informed politician 2, whereas the majority elects politician 3. This identifies an instance in which majority voting leads to a moderate but inefficient choice of leader. A perhaps more interesting and unexpected case arises when τ (δ) < 1 2 √30 . Again, for small β2, the non-moderate politician 2 is both the Condorcet winner and the optimal leader, and for large β2 it is politician 3. Now inefficiency arises in the intermediate case in which τ (δ) < β2 < 1 2 √30 . Although the optimal leader is the most moderate politician 3, the majority elects instead a relatively extreme leader in politician 2. The logic behind this result is simple. The median politician may trade off moderation and judgment in a way that differs from the optimal choices made by a social planner. Starting from her ideal point, she may 852 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000229
Leadership with Trustworthy Associates sacrifice a policy more in line with her bias for a more Conversely,suppose that the five politicians are such informed outcome.In our five-player example,she will that,in the benchmark case with evenly distributed indeed do so when B2 is sufficiently small and d>d. ideologies,there is no truthful communication across Choosing a leftist leader then benefits the median and players;that is,B;is constant across i0 for all playersi=1,....n,and =1,identifying we show the benefits of (possibly)extreme factions that aggregate the support of a as the set of leaders in the group.We show in the information and that induce a tradeoff with moderation.A direct ex- Online Appendix that,while the possibility of collective leadership tension of our model is to government formation between different weakly improves utilitarian welfare over individual leaders,it does uooud outi the omal not eliminate the inefficiencies identified here.The analysis for five players of Lemma 2 is extended to show that,also when allowing selection of the leader in the absence of communication:and,follow- for shared leadership,there exist bias profiles b such that the optimal /:sony ing on from comments above,neither can they occur in the absence shared leadership vector o gives all authority to the median politician of communication when the leader is elected under the Condorcet 3,but majority voting selects the vector a'that gives all authority to procedure. player 2. 853
Leadership with Trustworthy Associates sacrifice a policy more in line with her bias for a more informed outcome. In our five-player example, she will indeed do so when β2 is sufficiently small and d∗ 2 > d∗ 3 . Choosing a leftist leader then benefits the median and of course leftist members of the group. But it harms the right-wing members 4 and 5, who bear costs (b4 − b2)2 and (b5 − b2)2 respectively. Because the ideological loss function (bi − bj)2 is convex in the ideological distance |bi − bj|, the leadership move from 3 to 2 is more harmful to rightwing politicians than it is beneficial to the leftist ones. Then it may be the case that a social planner would force the median politician to take the decision, if only she could.14 Comparative Statics Further analysis of the five-player case uncovers some interesting comparative statics results. Our comparative static exercise is as follows. We first consider leadership choice with a given set of primitives (players ideological biases) and then consider what happens to leadership choice when a player changes her ideology from right (left) to left (right). We show that this can in fact induce a shift in leadership in the opposite direction.15 To illustrate, consider a benchmark case with players ideologies evenly distributed apart and where politicians 2, 3, and 4 can all count on the truthful advice of their ideological neighbors, so that βi is constant in i = 1,…, 4, and 1/12 1/8. Suppose now that the leftist politicians 1 and 2 become more moderate, so that now politician 2 can count on the truthful advice of players 1 and 3 (formally, suppose that β1 and β2 decrease, so that they both become smaller than 1/10). Because player 4 is still not truthful to 3, leadership switches from the median player 3 to the center-right player 2, again, when β2 < 1 2 √30 . Here, the rightward ideological movement of leftist players moves leadership choice (and hence policy outcomes) in the opposite direction. Thus moderation allows them to capture control of leadership of the group. In both cases, and unexpectedly, a change in the ideological distribution by which politicians (weakly) move right leads to a shift in the group decision to the left. We summarize our findings for this section in the following result. Proposition 4 When the distribution of ideologies is not single peaked and symmetric, a politician other than the most moderate one can be the optimal leader and the majority choice. Relative to the group of politicians, the median player weighs judgment more than moderation: she may lead when it is in the group’s interest that another with better judgment is chosen, and she may not be chosen when it is optimal that she leads.16 If politicians become more moderate (extremist), they capture (lose) control of the group, and turn the group policy closer to (away from) their views. Discussion The findings of our positive study of leadership highlight the predictive importance of judgment. The fact that the majority choice may place too much weight on this characteristic is perhaps surprising, the more so when interpreting the decisive median vote in the election as a decision to delegate authority to leaders with specific characteristics. This notion goes back to Schelling (1960) who, in his seminal book The Strategy of Conflict, discussed the use of delegates with particular characteristics as a way to credibly commit a negotiating party to a position. He suggested that agents 16 One interesting question is whether these kinds of inefficiencies could be eliminated, allowing for collective leadership instead of considering only individual leaders.Within this article’s model, collective leadership can be represented as vectors α of “shares of leadership” such that αi ≥ 0 for all playersi = 1,…,n, and n i=1 αi = 1, identifying the support of α as the set of leaders in the group. We show in the Online Appendix that, while the possibility of collective leadership weakly improves utilitarian welfare over individual leaders, it does not eliminate the inefficiencies identified here. The analysis for five players of Lemma 2 is extended to show that, also when allowing for shared leadership, there exist bias profiles b such that the optimal shared leadership vector α gives all authority to the median politician 3, but majority voting selects the vector α that gives all authority to player 2. 853 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000229