《社会保障概论》课程教学资源（课后阅读资料）APSR_Volume112. Issue 4.Nov 2018_Distributive_Politics_with_Vote_and_Turnout_Buying

American Political Science Review (2018)112,4,1111-1119 doi:10.1017/S0003055418000291 American Political Science Association 2018 Letter Distributive Politics with Vote and Turnout Buying AGUSTIN CASAS Colegio Universitario de Estudios Financieros The objective of this paper is to model the incumbent's allocation of efforts that maximize his elec- toral chances in the presence of both vote buying(persuasion)and turnout buying(mobilization). The existing literature on distributive politics concludes that political candidates should concen- trate their campaigning efforts either on safe districts or on swing districts.This paper shows that when candidates can use both persuasion and mobilization strategies,and the ideology of voters is unknown to the incumbent party,a third option should be taken into account.In fact,the optimal allocation of resources-rather than focusing on safe or swing districts-should target opposition strongholds,that is, the incumbent should try to sway voters in those districts in which the challenger is favored.The intuition for this result is simple.Since the incumbent does not know individual preferences (he only observes the distribution of preferences in the districts),all voters in a given district look identical to him.Hence,when approaching voters in a district to buy their vote,the incumbent always faces the risk of buying the vote of his supporters (who would have voted for him anyway). INTRODUCTION The differences between these two approaches are not innocuous.While the clientelist model focuses on he pervasiveness and persistence of vote buying vote buying at the individual level (Whose vote is in elections around the world seems uncontested cheaper to buy?),distributive politics models rest on in the literature (Diaz-Cayeros,Estevez,and targeting groups of individuals,typically defined by ge- Magaloni 2012:Finan and Schechter 2012:Golden and ographic or ethnic boundaries.Moreover,the literature Min 2013).However.the mechanisms underlying the on distributive politics predominantly neglects the is- effectiveness of vote buying are less clear.Two nonex sue of turnout. cludable approaches shed some light on this issue:the In this paper,I argue that there is another way in clientelist model and the distributive politics model. In the models of clientelism,the political parties which parties engage in vote buying using the govern- ment's budget.Although,with less information than have access to private information on individual vot- the local broker,incumbent politicians can employ the ers'preferences,which is used to target citizens and state's resources to generate transactions with indi- promise (or advance)rewards in exchange for votes vidual voters,for instance through discretionary so- 是 (Stokes 2005;Nichter 2008;Zarazaga 2016).Although cial programs and grants.Hence,I propose a model in there is abundant anecdotal evidence about these which the incumbent offers individual transfers,either transactions,the source of the money to pay the re- to persuade and/or mobilize voters,despite having in- wards and the brokers'incentives to distribute it are complete information on voters'preferences.2 575.1018 less apparent.On the other hand,the distributive poli- I use microfoundations that incorporate vote and tics literature focuses on the most electorally reward- turnout buying in a model of distributive politics,in a ing allocation of (local)public goods or fiscal bene- context in which only the incumbent engages in clien- fits (Dixit and Londregan 1995:Lindbeck and Weibull telist strategies.3 Voters are forward looking,but in the 1987).The latter rely on the assumption that campaign promises are fulfilled,which is unlikely to hold,es- model there are no potential ramifications of their in- dividual actions.Thus,like in the distributive politics pecially in developing countries (Keefer and Vlaicu models,the budget allocation is the most strategic deci- 2007). sion in this game.Also,although the exchange of votes for rewards takes place at the individual level,the bud- Agustin Casas is an Assistant Professor at Colegio Universitario de Estudios Financieros (CUNEF),Calle Leonardo Prieto Castro,2, get is managed in a centralized manner by the incum- Madrid,28040.Spain (acasas@u.northwestern.edu). bent,with incomplete information on the voters'pref- I am grateful to David Austen-Smith and Steve Callander.who erences.I find that,contrary to the findings in the dis were very patient at the early stages of this project.I also thank Bard tributive politics literature,the incumbent concentrates Harstad,Antoine Loeper and Andrea Mattozzi and seminar and his spending in opposition strongholds to minimize conference participants at several institutions for useful comments and suggestions.I also benefited greatly from the comments of three wasting resources on individuals who would have voted anonymous referees and the editor.All possible remaining errors are for him anyway.Furthermore,I show that,within those my own. opposition strongholds,the largest share of expenses is Received:January 26,2017:revised:September 11,2017;accepted: May 16,2018.First published online:July 13,2018. e Notice that most of the conditional cash transfer social programs Typically,the literature on clientelism assumes that this informa- would fit these characteristics.In terms of Stokes et al.(2013),these tion is provided by a local party leader who acts as an intermediary programs would not be defined as clientelist,but rather as program- between the patron (the party)and the client (the citizen).These matic or nonconditional (on voting)transfers intermediaries-or brokers-whose existence seems beyond doubt As in Gans-Morse.Mazzuca,and Nichter (2014);Stokes (2005); in the clientelism literature,are not formally modeled in those papers. and others,I do not model“dueling machines.” 1111

American Political Science Review (2018) 112, 4, 1111–1119 doi:10.1017/S0003055418000291 © American Political Science Association 2018 Letter Distributive Politics with Vote and Turnout Buying AGUSTIN CASAS Colegio Universitario de Estudios Financieros The objective of this paper is to model the incumbent’s allocation of efforts that maximize his elec￾toral chances in the presence of both vote buying (persuasion) and turnout buying (mobilization). The existing literature on distributive politics concludes that political candidates should concen￾trate their campaigning efforts either on safe districts or on swing districts. This paper shows that when candidates can use both persuasion and mobilization strategies, and the ideology of voters is unknown to the incumbent party, a third option should be taken into account. In fact, the optimal allocation of resources—rather than focusing on safe or swing districts—should target opposition strongholds, that is, the incumbent should try to sway voters in those districts in which the challenger is favored. The intuition for this result is simple. Since the incumbent does not know individual preferences (he only observes the distribution of preferences in the districts), all voters in a given district look identical to him. Hence, when approaching voters in a district to buy their vote, the incumbent always faces the risk of buying the vote of his supporters (who would have voted for him anyway). INTRODUCTION The pervasiveness and persistence of vote buying in elections around the world seems uncontested in the literature (Diaz-Cayeros, Estevez, and Magaloni 2012; Finan and Schechter 2012; Golden and Min 2013). However, the mechanisms underlying the effectiveness of vote buying are less clear. Two nonex￾cludable approaches shed some light on this issue: the clientelist model and the distributive politics model. In the models of clientelism, the political parties have access to private information on individual vot￾ers’ preferences, which is used to target citizens and promise (or advance) rewards in exchange for votes (Stokes 2005; Nichter 2008; Zarazaga 2016).1 Although there is abundant anecdotal evidence about these transactions, the source of the money to pay the re￾wards and the brokers’ incentives to distribute it are less apparent. On the other hand, the distributive poli￾tics literature focuses on the most electorally reward￾ing allocation of (local) public goods or fiscal bene￾fits (Dixit and Londregan 1995; Lindbeck and Weibull 1987). The latter rely on the assumption that campaign promises are fulfilled, which is unlikely to hold, es￾pecially in developing countries (Keefer and Vlaicu 2007). Agustin Casas is an Assistant Professor at Colegio Universitario de Estudios Financieros (CUNEF), Calle Leonardo Prieto Castro, 2, Madrid, 28040, Spain (acasas@u.northwestern.edu). I am grateful to David Austen-Smith and Steve Callander, who were very patient at the early stages of this project. I also thank Bard Harstad, Antoine Loeper and Andrea Mattozzi and seminar and conference participants at several institutions for useful comments and suggestions. I also benefited greatly from the comments of three anonymous referees and the editor.All possible remaining errors are my own. Received: January 26, 2017; revised: September 11, 2017; accepted: May 16, 2018. First published online: July 13, 2018. 1 Typically, the literature on clientelism assumes that this informa￾tion is provided by a local party leader who acts as an intermediary between the patron (the party) and the client (the citizen). These intermediaries—or brokers—whose existence seems beyond doubt in the clientelism literature, are not formally modeled in those papers. The differences between these two approaches are not innocuous. While the clientelist model focuses on vote buying at the individual level (Whose vote is cheaper to buy?), distributive politics models rest on targeting groups of individuals, typically defined by ge￾ographic or ethnic boundaries.Moreover, the literature on distributive politics predominantly neglects the is￾sue of turnout. In this paper, I argue that there is another way in which parties engage in vote buying using the govern￾ment’s budget. Although, with less information than the local broker, incumbent politicians can employ the state’s resources to generate transactions with indi￾vidual voters, for instance through discretionary so￾cial programs and grants. Hence, I propose a model in which the incumbent offers individual transfers, either to persuade and/or mobilize voters, despite having in￾complete information on voters’ preferences.2 I use microfoundations that incorporate vote and turnout buying in a model of distributive politics, in a context in which only the incumbent engages in clien￾telist strategies.3 Voters are forward looking, but in the model there are no potential ramifications of their in￾dividual actions. Thus, like in the distributive politics models, the budget allocation is the most strategic deci￾sion in this game. Also, although the exchange of votes for rewards takes place at the individual level, the bud￾get is managed in a centralized manner by the incum￾bent, with incomplete information on the voters’ pref￾erences. I find that, contrary to the findings in the dis￾tributive politics literature, the incumbent concentrates his spending in opposition strongholds to minimize wasting resources on individuals who would have voted for him anyway. Furthermore, I show that, within those opposition strongholds, the largest share of expenses is 2 Notice that most of the conditional cash transfer social programs would fit these characteristics. In terms of Stokes et al. (2013), these programs would not be defined as clientelist, but rather as program￾matic or nonconditional (on voting) transfers. 3 As in Gans-Morse, Mazzuca, and Nichter (2014); Stokes (2005); and others, I do not model “dueling machines.” 1111 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:56:49, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000291

Agustin Casas devoted to mobilizing"weak"supporters and persuad- core strategies were associated with at most a 2.4% ing "weak"opposition voters.Loyalists(or strong sup- change in coverage-but in the opposite direction to porters)and "strong"opposition voters do not benefit that predicted by existing theories"(p.1048).In other from vote and turnout buying as much.4 words,although he finds evidence that the incumbent targeted more heavily the opposition strongholds,he Related Literature and Supporting Evidence concludes that Bolsa Familia was not used politically- maybe because of the lack of a theoretical framework Among the models of clientelism,Gans-Morse,Maz- of vote buying that fits his findings. zuca,and Nichter(2014)and Morgan and Vardy (2010) The case of Plan Jefes y Jefas de Hogar is similar.In are the only ones,to my knowledge,to propose a model 2002,the Peronist President,Eduardo Duhalde,set up op//s in which a party can simultaneously consider vote and this plan a few months before the presidential election turnout buying as I do.The former,closer to my paper, Figure 1 shows the number of beneficiaries by district, considers a model with an incumbent or party machine ordered from the average Peronist municipality to the that knows the individual voters'preferences.This as- most Peronist one.The red line shows the negative cor- sumption allows the authors to characterize the opti- relation between the incumbent's spending and Pero- mal transfer to each individual.They conclude that,in nist support in a municipality,from a linear estimation. equilibrium,there is some degree of double persuasion, Even though it cannot be interpreted as causal evi- that is,mobilization and persuasion,among the nonvot- dence and the context in Argentina after the crises was ers who favor the opposition party.Hence,their conclu- "critical economically and politically,Figure 1 shows sion resonates with mine.However,in my model,indi- a pattern in which the opposition municipalities were vidual voters'preferences are not observed and-as a targeted. result-the incumbent can only target groups of voters Although in a different setting,Curto-Grau, (core,swing or opposition strongholds). Herranz-Loncan,and Sole-Olle (2012)are also in Among the models of distributive politics,the find- line with my predictions:they study the construction ings are structured in terms of two competing hy- of roads in Spain and they find that the "incumbent" potheses:whether more resources should be devoted builds more roads in opposition districts-that is, to "swing"groups that-if convinced by political third-party districts-for political gain. promises or spending-would alter the outcome of the election(Dixit and Londregan 1995;Lindbeck and THE MODEL Weibull 1987)or,on the contrary,whether the re- sources should be primarily allocated to "core"groups In this economy,there are Nd eligible voters per district of voters who are most responsive to the promises (or d.Every citizen i in district d has a privately known transfers)and are thus cheaper to convince (Dixit and ideology xi,drawn from the CDF Fu(x)with bounded Londregan 1995:Cox and McCubbins 1986).Instead. support [xa,]in XC9,unimodal,and absolutely con in my model,parties cannot make binding promises tinuous.There are two national political parties,the in hence,they will offer take-it-or-leave-it transfers up- cumbent and the opposition O,with exogenous plat- front;that is,before citizens vote. forms XI and Xo,in the policy space [x,=XC. Interestingly,even though targeting opposition Fu(x)is common knowledge.Parties compete for office 5795.801g strongholds is a new theoretical finding,there is evi- in a single-member election,in which the party with dence that supports it.Two of the largest poverty relief more votes across all districts is the winner.The incum- programs in Latin America fit my model closely:Bolsa bent party has a discretionary budget B from the fed- Familia in Brazil (Fried 2012)and the Plan Jefes y Jefas eral funds that can be used to engage in "clientelist" de Hogar (Head of Households Plan)in Argentina. competition by offering.before the election,a private Implemented at the turn of the century,both programs take-it-or-leave-it transfer to individuals.ta had the individuals as direct beneficiaries and implied Citizens derive utility from their policy payoff,from a monthly paycheck from the national government their voting behavior,and from the transfers.We con- (indeed,the former is a traditional conditional cash sider each of these in detail below.Consider first the transfer program).Even if these programmes could utility derived from policy (the outcome contingent be considered“programmatic'” (the beneficiaries utility).Since we focus on large elections with a con- are defined strictly according to a policy goal),when tinuum of voters,the probability that a single vote is governments operate with constraints on their budgets pivotal is zero for all voters and,hence,independently they can prioritize some groups according to their of the citizen's action,he always gets an expected policy political convenience.Fried (2012)makes a neat use of the Brazilian data and concludes that Bolsa Familia was not biased by political interests.He writes During their period of study,known as turno pacifico in Spanish (pacific alternation of parties),two parties colluded to monopolize that "a standard deviation shift in support for the the executive branch by buying off the districts dominated by smaller incumbent presidential candidate (Lula)leads to 1% parties.They write "..the two-party system may be seen as a duopoly L decrease in coverage.Shifts in the other indicators of regime,in which opposition districts were actually those which did not respect the alternation system."In particular,"Starting in the last decade of the nineteenth century,provinces that elected candidates These results are also new with respect to the findings in the canon from third parties began to receive an increasing share of resources." ical book of Stokes et al.(2013),which suggests targeting core sup- The results consistent with my hypothesis are in Table 3 in their porters in relatively swing districts. paper. 1112

Agustin Casas devoted to mobilizing “weak” supporters and persuad￾ing “weak” opposition voters. Loyalists (or strong sup￾porters) and “strong” opposition voters do not benefit from vote and turnout buying as much.4 Related Literature and Supporting Evidence Among the models of clientelism, Gans-Morse, Maz￾zuca, and Nichter (2014) and Morgan and Várdy (2010) are the only ones, to my knowledge, to propose a model in which a party can simultaneously consider vote and turnout buying as I do. The former, closer to my paper, considers a model with an incumbent or party machine that knows the individual voters’ preferences. This as￾sumption allows the authors to characterize the opti￾mal transfer to each individual. They conclude that, in equilibrium, there is some degree of double persuasion, that is,mobilization and persuasion, among the nonvot￾ers who favor the opposition party.Hence, their conclu￾sion resonates with mine. However, in my model, indi￾vidual voters’ preferences are not observed and—as a result—the incumbent can only target groups of voters (core, swing or opposition strongholds). Among the models of distributive politics, the find￾ings are structured in terms of two competing hy￾potheses: whether more resources should be devoted to “swing” groups that—if convinced by political promises or spending—would alter the outcome of the election (Dixit and Londregan 1995; Lindbeck and Weibull 1987) or, on the contrary, whether the re￾sources should be primarily allocated to “core” groups of voters who are most responsive to the promises (or transfers) and are thus cheaper to convince (Dixit and Londregan 1995; Cox and McCubbins 1986). Instead, in my model, parties cannot make binding promises, hence, they will offer take-it-or-leave-it transfers up￾front; that is, before citizens vote. Interestingly, even though targeting opposition strongholds is a new theoretical finding, there is evi￾dence that supports it. Two of the largest poverty relief programs in Latin America fit my model closely: Bolsa Familia in Brazil (Fried 2012) and the Plan Jefes y Jefas de Hogar (Head of Households Plan) in Argentina. Implemented at the turn of the century, both programs had the individuals as direct beneficiaries and implied a monthly paycheck from the national government (indeed, the former is a traditional conditional cash transfer program). Even if these programmes could be considered “programmatic” (the beneficiaries are defined strictly according to a policy goal), when governments operate with constraints on their budgets, they can prioritize some groups according to their political convenience. Fried (2012) makes a neat use of the Brazilian data and concludes that Bolsa Familia was not biased by political interests. He writes that “... a standard deviation shift in support for the incumbent presidential candidate (Lula) leads to 1% decrease in coverage. Shifts in the other indicators of 4 These results are also new with respect to the findings in the canon￾ical book of Stokes et al. (2013), which suggests targeting core sup￾porters in relatively swing districts. core strategies were associated with at most a 2.4% change in coverage—but in the opposite direction to that predicted by existing theories” (p. 1048). In other words, although he finds evidence that the incumbent targeted more heavily the opposition strongholds, he concludes that Bolsa Familia was not used politically— maybe because of the lack of a theoretical framework of vote buying that fits his findings. The case of Plan Jefes y Jefas de Hogar is similar. In 2002, the Peronist President, Eduardo Duhalde, set up this plan a few months before the presidential election. Figure 1 shows the number of beneficiaries by district, ordered from the average Peronist municipality to the most Peronist one. The red line shows the negative cor￾relation between the incumbent’s spending and Pero￾nist support in a municipality, from a linear estimation. Even though it cannot be interpreted as causal evi￾dence and the context in Argentina after the crises was “critical” economically and politically, Figure 1 shows a pattern in which the opposition municipalities were targeted. Although in a different setting, Curto-Grau, Herranz-Loncan, and Sole-Olle (2012) are also in line with my predictions: they study the construction of roads in Spain and they find that the “incumbent” builds more roads in opposition districts—that is, third-party districts—for political gain.5 THE MODEL In this economy, there are Nd eligible voters per district d. Every citizen i in district d has a privately known ideology xi, drawn from the CDF Fd(x) with bounded support [xd, x¯ d] in X⊂, unimodal, and absolutely con￾tinuous. There are two national political parties, the in￾cumbent I and the opposition O, with exogenous plat￾forms XI and XO, in the policy space [x, x¯] = X ⊂ . Fd(x) is common knowledge. Parties compete for office in a single-member election, in which the party with more votes across all districts is the winner. The incum￾bent party has a discretionary budget B from the fed￾eral funds that can be used to engage in “clientelist” competition by offering, before the election, a private take-it-or-leave-it transfer to individuals, t d i . Citizens derive utility from their policy payoff, from their voting behavior, and from the transfers. We con￾sider each of these in detail below. Consider first the utility derived from policy (the outcome contingent utility). Since we focus on large elections with a con￾tinuum of voters, the probability that a single vote is pivotal is zero for all voters and, hence, independently of the citizen’s action, he always gets an expected policy 5 During their period of study, known as turno pacifico in Spanish (pacific alternation of parties), two parties colluded to monopolize the executive branch by buying off the districts dominated by smaller parties. They write “...the two-party system may be seen as a duopoly regime, in which opposition districts were actually those which did not respect the alternation system.” In particular, “Starting in the last decade of the nineteenth century, provinces that elected candidates from third parties began to receive an increasing share of resources.” The results consistent with my hypothesis are in Table 3 in their paper. 1112 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:56:49, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000291

Distributive Politics with Vote and Turnout Buying FIGURE 1.Districts with Relatively More Peronist-Leaning Preferences Receive Less Money 00000 20 40 60 peronist ●Spending Fitted values 4号 The horizontal axis depicts the Peronist share of votes per municipality in 2001,measured as absolute deviations(in percentages)from the mean Peronist district(with a support of around 20%in 2001).The vertical axis measures the absolute number of recipients of the unemployment benefit"Plan Jefes y Jefas de Hogar by municipality in April 2003 (the month before the presidential elections).The straight red line indicates the partial correlation of the allocation of plans and the Peronist share.The more Peronist a district is,the fewer recipients payoff,as it is commonly assumed in the literature (see from the clientelistic exchange and he only gets the "ex- for instance.Dekel.Jackson.and Wolinsky 2008).For pressive voting payoff." simplicity,I do not write this expected policy payoff. Let us now consider in detail the payoff of a voter I now consider the utility derived from expressive who accepts ta and therefore is subject to the vote- voting (i.e.,the act-contingent utility).5 All citizens get buying contract.If i accepts the transfer and votes for a direct benefit b and bear a direct cost related to turn- the incumbent,he gets an extra payoff of ing out to vote.The cost depends on the ideological distance to the party's platform,quadratically.Hence, org. i's expressive voting payoff is There is evidence that indicates that voters do not be- b-(Xp-xi)2 if i votes for party P(1,O) lieve that their vote is always secret (Gerber et al. 0 if i does not vote 2013b illustrate it for the US)and they behave as if they could be punished if they deviate from a vote- buying "contract"(Gerber et al.2013a;Vicente 2014; Let us consider now the payoff from the transfers. Finan and Schechter 2012).Hence.in line with the em- The incumbent makes a take-it-or-leave-it offer of t dollars to each citizen i in district d,for whom the pirical evidence,let qd capture the perceived expected marginal valuation of a dollar is 6.If citizen i in district punishment(perceived monitoring probability of vot- ing times the "punishment").Then,if the voter accepts d accepts the transfer,the payoff of his electoral deci- sions would be constrained by the implicit vote-buying the transfer but votes for the opposition,he gets contract between the incumbent and the voter:if the 6t-q. citizen accepts t,he should show up to vote for the in- cumbent,otherwise he would suffer an expected pun- Because the citizens have the option to reject a trans- ishment.If the citizen rejects ta,then he is excluded fer and stay out of this clientelistic exchange-as it is well documented in Bratton (2008)and references 6 In this setup.expressive voting has a big role in explaining the therein-the incumbent's total expenditure in a dis- turnout decision because,as Cox(1999)puts it,"..act-contingent util- trict depends on the amount of citizens who accept the ities rather than outcome-contingent utilities,drive turnout probabil- transfer,as will be clear in the constraint of the maxi- ities at the microlevel." This implicit vote-buying contract is exactly the same as the patron mization problem in Equation(2). client contract-present in the clientelism literature-which defines Let g capture the perceived monitoring probability clientelistic networks and relationships. of turnout times the punishment,with ga<g for all d. 1113

Distributive Politics with Vote and Turnout Buying FIGURE 1. Districts with Relatively More Peronist-Leaning Preferences Receive Less Money 0 10000 20000 30000 40000 0 20 40 60 peronist Spending Fitted values The horizontal axis depicts the Peronist share of votes per municipality in 2001, measured as absolute deviations (in percentages) from the mean Peronist district (with a support of around 20% in 2001). The vertical axis measures the absolute number of recipients of the “unemployment benefit” Plan Jefes y Jefas de Hogar by municipality in April 2003 (the month before the presidential elections). The straight red line indicates the partial correlation of the allocation of plans and the Peronist share. The more Peronist a district is, the fewer recipients. payoff, as it is commonly assumed in the literature (see for instance, Dekel, Jackson, and Wolinsky 2008). For simplicity, I do not write this expected policy payoff. I now consider the utility derived from expressive voting (i.e., the act-contingent utility).6 All citizens get a direct benefit b and bear a direct cost related to turn￾ing out to vote. The cost depends on the ideological distance to the party’s platform, quadratically. Hence, i’s expressive voting payoff is b − (XP − xi)2 if i votes for party P ∈ {I, O} 0 if i does not vote . Let us consider now the payoff from the transfers. The incumbent makes a take-it-or-leave-it offer of t d i dollars to each citizen i in district d, for whom the marginal valuation of a dollar is θ. If citizen i in district d accepts the transfer, the payoff of his electoral deci￾sions would be constrained by the implicit vote-buying contract between the incumbent and the voter: if the citizen accepts t d i , he should show up to vote for the in￾cumbent, otherwise he would suffer an expected pun￾ishment.7 If the citizen rejects t d i , then he is excluded 6 In this setup, expressive voting has a big role in explaining the turnout decision because, as Cox (1999) puts it, “...act-contingent util￾ities rather than outcome-contingent utilities, drive turnout probabil￾ities at the microlevel.” 7 This implicit vote-buying contract is exactly the same as the patron￾client contract—present in the clientelism literature—which defines clientelistic networks and relationships. from the clientelistic exchange and he only gets the “ex￾pressive voting payoff.” Let us now consider in detail the payoff of a voter who accepts t d i and therefore is subject to the vote￾buying contract. If i accepts the transfer and votes for the incumbent, he gets an extra payoff of θt d i . There is evidence that indicates that voters do not be￾lieve that their vote is always secret (Gerber et al. 2013b illustrate it for the US) and they behave as if they could be punished if they deviate from a vote￾buying “contract” (Gerber et al. 2013a; Vicente 2014; Finan and Schechter 2012). Hence, in line with the em￾pirical evidence, let qd capture the perceived expected punishment (perceived monitoring probability of vot￾ing times the “punishment”). Then, if the voter accepts the transfer but votes for the opposition, he gets θt d i − qd. Because the citizens have the option to reject a trans￾fer and stay out of this clientelistic exchange—as it is well documented in Bratton (2008) and references therein—the incumbent’s total expenditure in a dis￾trict depends on the amount of citizens who accept the transfer, as will be clear in the constraint of the maxi￾mization problem in Equation (2). Let q¯ capture the perceived monitoring probability of turnout times the punishment, with qd < q¯ for all d. 1113 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:56:49, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000291

Agustin Casas Thus,the sum of all components leaves the citizen with the following utility: 0 if i does not vote b-(XP-)2 if i votes for party P(1,O) b-(X-x)2+0t4 if i accepts the transfer and votes for I b-(Xo-xi)2 -a if i accepts the transfer and votes for O -4 if i accepts the transfer and does not vote Districts are the artifact that allows the incumbent would vote for the incumbent,with or without trans- to target his resources.Districts differ in the technol- fers,that is,with xi[X-vb,X+vb].Similarly, ogy available to monitor and punish voting behavior 'opposing voters"would do the same with the opposi- (q),and in the underlying ideological bias drawn from tion party,that is,withxi∈[Xo-√b,Xo+√b].Inbe- F(x).The incumbent allocates its budget B before the tween,there are the "supporting"and "opposing"non- elections to buy votes and turnout through transfers, voters.Hence,vote buying (persuasion)takes place if exploiting the observable differences across districts: an"opposing voter"votes for the incumbent due to the the party directly observes gd,Nd,and Fu(x)and for transfer(P(t)in Figure 2).Turnout buying (mobiliza- each district.s tion)takes place if a "supporting nonvoter"turns out Notice that all citizens in a given district look ex ante to vote for the incumbent due to the transfer (M(t)in identical to the incumbent.Hence,I focus on the case Figure 2).And,finally,vote and turnout buying(double in which he must offer the same transfer to all citizens persuasion)take place simultaneously if an "opposing in d,=td,which depends on the budget B,the distri- nonvoter"turns out to vote for the incumbent (DP(t) bution of preferences(and the monitoring tech- in Figure 2). 4号 nology (i) The incumbent decides how to allocate the bud- A Representative District get B across districts that differ in the cost of buying & Let b,X1,and the policy space [x,]=X be such that votes and/or turnout to affect the electoral outcome. Let S(td)and S4 (td)be the share of citizens that vote x≥Xi-√；therefore,according to Equation(1),in for the incumbent and the share of citizens that accept equilibrium there are no extremist voters who do not the transfer,in district d.?Then,in each district d,the turn out,and mobilization can only occur among those incumbent distributes resources so that he maximizes voters located "between"the parties.This assumption the share of votes (VI): simplifies the analysis without loss of generality.10 Below,I define a vote-buying threshold nvb(r)and a turnout-buying threshold nb().These thresholds maxV=∑Nasy) s.to identify the ideology of a voter who is indifferent be- tween voting for the incumbent or not,and turning out B=∑B4≥∑ or not,respectively. (2) Definition 1 For otd <qd,let n(td)and nvb(t)be a turnout-buying threshold and a vote-buying threshold, The timing of the game is the following:At t=0. respectively,such that all citizens observe the platforms Xi and Xo.At t=1, the incumbent decides the level of individual transfers 01a per district.At.voters decide whether to nvb(td)=+ and nb(td)=XI+b+0rd 2△X accept the transfer or not.At t =3,the election takes place,that is,citizens decide whether to vote,and for Hence,Definition 1 implies a partition of the space whom. (xi,)represented in Figure 2(b),for rd<gd.The voters whose ideology is to the left of the minimum of RESULTS nb()and nvb(rd)would accept the transfer and vote for the incumbent.But more importantly,the figure Following Gans-Morse,Mazzuca,and Nichter (2014), shows that all citizens whose ideology is to the right Figure 2(a)shows the ex ante classification of citi- of the minimum threshold(in the shaded area)reject zens:"supporting voters"or loyalists are those who the transfer.These citizens are sufficiently far from X to prefer rejecting the transfer than accepting it and voting for the incumbent,or the transfer is not large 8 The incumbent does not need to group voters depending only on their geographical location,but on any other observable characteris- tic:unions,ethnic groups,religions,and so on. 9In any district d.the total amount of the allocated local budget. 10 The same results and intuition hold with less restrictive assump- tions:if the intrinsic motivation of voting is large,there are enough Bd.must meet the constraint B ds().Thus,adding up all voting supporters (loyalists)such that the incumbent would still districts,I obtain∑aBm≥∑atdNds(td),which leads to the con- want to avoid core districts so to avoid "wasting"resources on loyal straint in Equation(2)because B■∑dB supporters. 1114

Agustin Casas Thus, the sum of all components leaves the citizen with the following utility: ud i = ⎧ ⎪⎪⎪⎨ ⎪⎪⎪⎩ 0 if i does not vote b − (XP − xi)2 if i votes for party P ∈ {I, O} b − (XI − xi)2 + θt d i if i accepts the transfer and votes for I b − (XO − xi)2 + θt d i − qd if i accepts the transfer and votes for O θt d i − q¯ if i accepts the transfer and does not vote . (1) Districts are the artifact that allows the incumbent to target his resources. Districts differ in the technol￾ogy available to monitor and punish voting behavior (qd), and in the underlying ideological bias drawn from Fd(x). The incumbent allocates its budget B before the elections to buy votes and turnout through transfers, exploiting the observable differences across districts: the party directly observes qd, Nd, and Fd(x) and θ for each district.8 Notice that all citizens in a given district look ex ante identical to the incumbent. Hence, I focus on the case in which he must offer the same transfer to all citizens in d, t d i = t d, which depends on the budget B, the distri￾bution of preferences{F j }D j=1, and the monitoring tech￾nology {qj }D j=1. The incumbent decides how to allocate the bud￾get B across districts that differ in the cost of buying votes and/or turnout to affect the electoral outcome. Let Sd I (t d ) and Sd A(t d ) be the share of citizens that vote for the incumbent and the share of citizens that accept the transfer, in district d. 9 Then, in each district d, the incumbent distributes resources so that he maximizes the share of votes (VI): max td VI =  d Nd Sd I (t d ) s.to B ≡  d Bd ≥  d t dNdSd A(t d ). (2) The timing of the game is the following: At t = 0, all citizens observe the platforms XI and XO. At t = 1, the incumbent decides the level of individual transfers per district {t d}d=D d=1 . At t = 2, voters decide whether to accept the transfer or not. At t = 3, the election takes place, that is, citizens decide whether to vote, and for whom. RESULTS Following Gans-Morse, Mazzuca, and Nichter (2014), Figure 2(a) shows the ex ante classification of citi￾zens: “supporting voters” or loyalists are those who 8 The incumbent does not need to group voters depending only on their geographical location, but on any other observable characteris￾tic: unions, ethnic groups, religions, and so on. 9 In any district d, the total amount of the allocated local budget, Bd, must meet the constraint Bd ≥ t dNdSd A(t d ). Thus, adding up all districts, I obtain  d Bd ≥  d t dNdSd A(t d ), which leads to the con￾straint in Equation (2) because B ≡ dBd. would vote for the incumbent, with or without trans￾fers, that is, with xi ∈ [XI − √ b, XI + √ b]. Similarly, “opposing voters” would do the same with the opposi￾tion party, that is, with xi ∈ [XO − √ b, XO + √ b]. In be￾tween, there are the “supporting” and “opposing” non￾voters. Hence, vote buying (persuasion) takes place if an “opposing voter” votes for the incumbent due to the transfer (P(t) in Figure 2). Turnout buying (mobiliza￾tion) takes place if a “supporting nonvoter” turns out to vote for the incumbent due to the transfer (M(t) in Figure 2).And, finally, vote and turnout buying (double persuasion) take place simultaneously if an “opposing nonvoter” turns out to vote for the incumbent (DP(t) in Figure 2). A Representative District Let b, XI, and the policy space [x, x¯] = X be such that x ≥ XI − √ b; therefore, according to Equation (1), in equilibrium there are no extremist voters who do not turn out, and mobilization can only occur among those voters located “between” the parties. This assumption simplifies the analysis without loss of generality.10 Below, I define a vote-buying threshold nvb(t d) and a turnout-buying threshold ntb(t d). These thresholds identify the ideology of a voter who is indifferent be￾tween voting for the incumbent or not, and turning out or not, respectively. Definition 1 For θt d < qd, let ntb(t d) and nvb(t d) be a turnout-buying threshold and a vote-buying threshold, respectively, such that nvb(t d ) = X¯ + θt d 2X , and ntb(t d ) = XI +  b + θtd. Hence, Definition 1 implies a partition of the space (xi, t d), represented in Figure 2(b), for θt d < qd. The voters whose ideology is to the left of the minimum of ntb(t d) and nvb(t d) would accept the transfer and vote for the incumbent. But more importantly, the figure shows that all citizens whose ideology is to the right of the minimum threshold (in the shaded area) reject the transfer. These citizens are sufficiently far from XI to prefer rejecting the transfer than accepting it and voting for the incumbent, or the transfer is not large 10 The same results and intuition hold with less restrictive assump￾tions: if the intrinsic motivation of voting is large, there are enough voting supporters (loyalists) such that the incumbent would still want to avoid core districts so to avoid “wasting” resources on loyal supporters. 1114 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:56:49, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000291

Distributive Politics with Vote and Turnout Buying FIGURE 2.Example of the Effect of a Transfer in a District Panel(a:t≤号 n(t) M(ti) DP(ti) P(t1) ntb(t) Supporting Voters M(to) X,+ Xo-b Xo e 'asn ni(to) nb(t1） Panel (b):t=0 Supporting Non-Voters Opposing Non-Voters Opposing Voters Xo-b Xo For any level of transfers t,only the citizens with ideology in the shaded areas do not accept the transfer.P()above a segment indicates the level of persuasion implied by a transfer t:DP(t)indicates the level of double persuasion and M(t)indicates the level of mobilization.Hence,for a transfer t as above,those voters whose ideologies coincide with the segment P()are persuaded(i.e. an "opposing voter"with ideology between Xo-b and n()votes for the incumbent due to the transfer).Those voters whose ideologies coincided with the segment M()are mobilized(i.e.,a"supporting nonvoter"with ideology between X+vb and X turns out to vote for the incumbent due to the transfer).Those voters whose ideologies coincide with DP()are doubly persuaded(i.e.,"opposing nonvoters"with ideologies between X and Xo-b who turn out to vote for the incumbent.For a transfer to,only Mto)voters are mobilized,that is,those with ideologies between X+b and n(to). enough to"subsidize"them to show up to vote (even From the definition above,it can be checked that the for the opposition). turnout-buying threshold increases more rapidly with The last point depends on the assumptiondqd the transfers than the vote-buying one.Moreover,as we which ensures that any citizen who accepts the transfer see in Figure 2(b),they are equal when they reach the shows up to vote for the incumbent,and so Sy(td)= "persuadable"voters,that is,when n(d)=nb()= S(d),which simplifies the maximization problem in Xo-vb.Hence,taking this information into account Equation (2).Mechanically,this assumption rules out in the following proposition highlights the voters'opti- inefficiently large transfers that an optimizing incum- mal response to transfers. bent would not do anyway.For rdzqd,some voters may accept the transfer but vote for the opposition. For instance,imagine the infinitesimal increase from a Proposition 1 For Otd qd,there exists a turnout- transfer d=-e with s0 to a transfer with s= buying threshold nb(t),and a vote-buying threshold 0.This change implies a discontinuous increase in the nb(t),such that incumbents'expenses without any significant gain in votes,that is,all opposition voters accept the transfer but vote for the opposition anyway.1 l.Ifnb(td)≤nvb(t)then all citizens with x;∈ 1 In other words for any share of votes obtained by a transfer [Xi+√b,nb(t)】are mobilized and those larger than若，there is another transfer'<号<that results in with xi [0,n(t))are also persuaded (ie., the same amount of voters or more. double persuasion). 1115

Distributive Politics with Vote and Turnout Buying FIGURE 2. Example of the Effect of a Transfer in a District t Panel (a): t ≤ q θ XI XI + XO √ b XO − √ b nvb(t) ntb(t) t1 t0 M(t1) DP(t1) P(t1) M(t0) X¯ ntb(t0) nvb(t1) Supporting Voters Panel (b): t = 0 Supporting Non-Voters Opposing Non-Voters Opposing Voters XI XI + XO √ b XO − √ b X¯ 1 For any level of transfers t, only the citizens with ideology in the shaded areas do not accept the transfer. P(t) above a segment indicates the level of persuasion implied by a transfer t; DP(t) indicates the level of double persuasion and M(t) indicates the level of mobilization. Hence, for a transfer t1 as above, those voters whose ideologies coincide with the segment P(t1) are persuaded (i.e., an “opposing voter” with ideology between XO − √ b and nvb(t1) votes for the incumbent due to the transfer). Those voters whose ideologies coincided with the segment M(t1) are mobilized (i.e., a “supporting nonvoter” with ideology between XI + √ b and X¯ turns out to vote for the incumbent due to the transfer). Those voters whose ideologies coincide with DP(t1) are doubly persuaded (i.e., “opposing nonvoters” with ideologies between X¯ and XO − √ b who turn out to vote for the incumbent. For a transfer t0, only M(t0) voters are mobilized, that is, those with ideologies between XI + √ b and ntb(t0). enough to “subsidize” them to show up to vote (even for the opposition). The last point depends on the assumption θt d < qd, which ensures that any citizen who accepts the transfer shows up to vote for the incumbent, and so Sd I (t d ) = Sd A(t d ), which simplifies the maximization problem in Equation (2). Mechanically, this assumption rules out inefficiently large transfers that an optimizing incum￾bent would not do anyway. For θt d ≥ qd, some voters may accept the transfer but vote for the opposition. For instance, imagine the infinitesimal increase from a transfer t d = qd θ −  with ε → 0 to a transfer with ε = 0. This change implies a discontinuous increase in the incumbents’ expenses without any significant gain in votes, that is, all opposition voters accept the transfer but vote for the opposition anyway.11 11 In other words, for any share of votes obtained by a transfer t d, larger than qd θ , there is another transfer t ∗ < qd θ < t d that results in the same amount of voters or more. From the definition above, it can be checked that the turnout-buying threshold increases more rapidly with the transfers than the vote-buying one.Moreover, as we see in Figure 2(b), they are equal when they reach the “persuadable” voters, that is, when ntb(t d ) = nvb(t d ) = XO − √ b. Hence, taking this information into account in the following proposition highlights the voters’ opti￾mal response to transfers. Proposition 1 For θt d < qd, there exists a turnout￾buying threshold ntb(t d), and a vote-buying threshold nvb(t d), such that 1. If ntb(td) ≤ nvb(td) then all citizens with xi ∈ [XI + √ b, ntb(t d )] are mobilized and those with xi ∈ [0, ntb(td)) are also persuaded (i.e., double persuasion). 1115 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:56:49, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000291

Agustin Casas 2.If ntb(td)>nvb(td)then, trict.Then,I obtain an implicit solution for.12 (a)all voters withxi∈[Xi+√b,Xo-√⑥ d= ∑amd+B 2Ax Fd(n(d)) are mobilized and (b)all voters with xi [0,nyb(t)]are per- ∑amd 0fa(n(td)） suaded. aFd(n(d)) (c)Thus,all voters with xi∈[0，Xo-√b) with fd(n())= an(td) are doubly persuaded. and md =tdNd fd. (4) ///.sdu That is.the behavior of all the voters between the In equilibrium,Eramd and Emd are constants.Hence, thresholds depends on the size of the transfer.If the from Equation (4),we see that the only thing that transfer is large enough so n(rd)s nb(rd),then drives the differences between districts is the ideolog- all the voters in between would have voted for the incumbent if they were voting,but they are not ical distribution,which we call the inverse of the (because they are to the right of n()).Hence,those "success voting ratio"(also known as the inverse of the voters are neither persuaded nor mobilized.When "reversed hazard rate"). Xo-vbNdFd(n(d)). More precisely,.t(n(t)）stochastically dominatest中ao)）ac. cording to the likelihood ratio order-MIRP-then( M/:sonu a8and(同啡e)0,and let B be large enough dominance (ii).Hence,all opposition strongholds also have the larger such that there is some level of persuasion in each dis- "success voting ratio"and should be targeted by the incumbent. 1116

Agustin Casas 2. If ntb(td) > nvb(td) then, (a) all voters with xi ∈ [XI + √ b, XO − √ b] are mobilized and (b) all voters with xi ∈ [0, nvb(td)] are per￾suaded. (c) Thus, all voters with xi ∈ [0, XO − √ b) are doubly persuaded. That is, the behavior of all the voters between the thresholds depends on the size of the transfer. If the transfer is large enough so ntb(t d) ≤ nvb(t d), then all the voters in between would have voted for the incumbent if they were voting, but they are not (because they are to the right of ntb(t d)). Hence, those voters are neither persuaded nor mobilized. When XO − √ b 0, and let B be large enough such that there is some level of persuasion in each dis￾trict. Then, I obtain an implicit solution for t d: 12 t d =  d t dmd + B  d md − 2x θ Fd(n(t d )) f d(n(td )) with f d(n(t d )) ≡ ∂Fd(n(t d )) ∂n(td ) and md ≡ t dNd f d. (4) In equilibrium, t dmd and md are constants. Hence, from Equation (4), we see that the only thing that drives the differences between districts is the ideolog￾ical distribution, Fd f d , which we call the inverse of the “success voting ratio” (also known as the inverse of the “reversed hazard rate”). The following proposition establishes the conditions for focusing on opposition strongholds, highlighting the importance of enlarging the, so far dichotomous, de￾bate between core and swing districts. Proposition 2 Let d ∈ {j, h} be such that h is the op￾position stronghold relative to j, that is, with E(xi|i ∈ j) Fh(n(t h )) f h(n(th )) . If so, a greater transfer is allocated in the opposition stronghold (tj Fh(n(t)) f h(n(t)) and (ii) E(xi|i ∈ j) < E(xi|i ∈ h) hold simultaneously. MLRP implies reversed hazard rate dominance (i) and first order stochastic dominance (ii).Hence, all opposition strongholds also have the larger “success voting ratio” and should be targeted by the incumbent. 1116 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:56:49, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000291

Distributive Politics with Vote and Turnout Buying delivers the following: sity f(t)at the threshold),4 in my model the transfer also depends(negatively)on the amount of individu- als who accept it (i.e.,the cumulative distribution func- F(n() =n(td)-xd=k() tion F(t)at the threshold).Therefore,the incumbent fa(n(d)) focuses his spending on opposition strongholds instead of core and swing districts when there is a large number of lovalists who would accept the transfer even though Intuitively,to mobilize more supporting nonvoters they would have voted for the incumbent without any and/or double persuade(mobilize and persuade)oppo- transfer. sition nonvoters,larger transfers have to be disbursed. Nonetheless.since all citizens are offered the same APPENDIX transfer,the marginal cost of increasing the transfer by a penny to mobilize an indifferent citizen is that penny Proofs times all the voters who accept the transfer (which in- cludes all supporting voters and some nonvoters,that Proposition 1 is,the loyalists and some weak supporters).In terms The intuition is as follows.Only consider party I for now of Proposition 2.with the uniform distribution,At)is and use the thresholds in Definition 1:any citizen iin district d constant but F(t)increases with t.Hence,the incum- whose ideology lies to the left ofn(r)votes.And if his ideol- bent prefers to focus on those districts with the smallest ogy is to the left of n(),he votes for the incumbent.Hence, amount of people accepting the transfer;that is,those suppose that nb(r)nb(r),then all the voters whose ide- with the smaller F(t),and so the larger success voting ology is between these thresholds,if any would vote for the ratio,f(t)/F(t). opposition because the incumbent paid them enough to turn By the same reasoning,increasing the transfer to per- out but not enough to vote for I.On the other hand,if n() suade an opposition nonvoter(weak opposer)implies nv(r),then zens in the form of take-it-or-leave-it transfers.As a consequence,when deciding the allocation of these re- sources,the incumbent takes into account the amount x≤元+ →x≤X+Vb+Btd→ of citizens accepting the transfers.In other words,the 2△X incumbent does not want to transfer resources where ui(It)>ui(O no transfer). the citizens would support him anyway.While,in Dixit and Londregan (1996),the optimal transfer only de- pends(positively)on the number of individuals who 14 See Equation(5)on page 278 and the following two paragraphs in Lindbeck and Weibull (1987).and the equations on page 1152 in can be swayed by the proposed transfer (i.e.,the den- Dixit and Londregan(1996). 1117

Distributive Politics with Vote and Turnout Buying delivers the following: Fd(n(t d )) f d(n(td )) = n(t d ) − xd then t h − t j = k(xh − xj ). Intuitively, to mobilize more supporting nonvoters, and/or double persuade (mobilize and persuade) oppo￾sition nonvoters, larger transfers have to be disbursed. Nonetheless, since all citizens are offered the same transfer, the marginal cost of increasing the transfer by a penny to mobilize an indifferent citizen is that penny times all the voters who accept the transfer (which in￾cludes all supporting voters and some nonvoters, that is, the loyalists and some weak supporters). In terms of Proposition 2, with the uniform distribution, f(t) is constant but F(t) increases with t. Hence, the incum￾bent prefers to focus on those districts with the smallest amount of people accepting the transfer; that is, those with the smaller F(t), and so the larger success voting ratio, f(t)/F(t). By the same reasoning,increasing the transfer to per￾suade an opposition nonvoter (weak opposer) implies that all supporters also get a larger transfer. There￾fore, to minimize those “wasted resources,” the incum￾bent gives more money in districts with fewer support￾ers (i.e., opposition strongholds). In other words, the marginal cost of buying an additional voter is the to￾tal number of accepted transfers times the increase in the transfer. Thus, in districts with a greater numbers of loyalists, the marginal cost of buying an additional vote is large. CONCLUSION Gans-Morse, Mazzuca, and Nichter (2014) show that if we know voters’ preferences, it may be optimal to mo￾bilize and persuade voters who prefer the opposition party. Instead, I assume that voters’ preferences are not known and I extend this idea into the literature on distributive politics by showing that the dichotomous discussion between swing and core districts should ac￾knowledge the possibility of a third hypothesis: in a single-member election,opposition strongholds are the optimal target for an incumbent who aims to persuade and/or mobilize citizens. In contrast with the seminal papers of distributive politics, I do not model campaign promises but an in￾cumbent who spends the state’s resources to maxi￾mize his vote share in the upcoming elections. More￾over, these resources are offered individually to citi￾zens in the form of take-it-or-leave-it transfers. As a consequence, when deciding the allocation of these re￾sources, the incumbent takes into account the amount of citizens accepting the transfers. In other words, the incumbent does not want to transfer resources where the citizens would support him anyway. While, in Dixit and Londregan (1996), the optimal transfer only de￾pends (positively) on the number of individuals who can be swayed by the proposed transfer (i.e., the den￾sity f(t) at the threshold),14 in my model the transfer also depends (negatively) on the amount of individu￾als who accept it (i.e., the cumulative distribution func￾tion F(t) at the threshold). Therefore, the incumbent focuses his spending on opposition strongholds instead of core and swing districts when there is a large number of loyalists who would accept the transfer even though they would have voted for the incumbent without any transfer. APPENDIX Proofs Proposition 1 The intuition is as follows. Only consider party I for now and use the thresholds in Definition 1: any citizen i in district d whose ideology lies to the left of ntb(t d) votes.And if his ideol￾ogy is to the left of nvb(t d), he votes for the incumbent. Hence, suppose that ntb(t d) ≥ nvb(t d), then all the voters whose ide￾ology is between these thresholds, if any would vote for the opposition because the incumbent paid them enough to turn out but not enough to vote for I. On the other hand, if ntb(t d) ≤ nvb(t d), then those voters in between the threshold would vote for the incumbent if they were paid enough to turn out. Thus, the smaller threshold is the one that always binds. Proof.Individual i with xi ≤ X¯ prefers to accept the trans￾fer and vote for I to not voting if t d nvB(t d), then xi ≤ X¯ + θt d 2X ⇒ xi ≤ XI +  b + θtd ⇒ ui(I|t d ) ≥ ui(O|no transfer), 14 See Equation (5) on page 278 and the following two paragraphs in Lindbeck and Weibull (1987), and the equations on page 1152 in Dixit and Londregan (1996). 1117 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:56:49, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000291

Agustin Casas (Ilr)≥u(no turnout no transfer）, which can be rewritten as w(Ilr)≥(Ot). -= 2△x 「F(n(t) Fi(n(t)) f(n(r)) f(n(t)」 Then,for all i withxn(r)votes for I.On the other hand, i REFERENCES 求+ 2Ax≤≤X+VB+8n与 Bratton,Michael.2008."Vote Buying and Violence in Nigerian Elec- tion Campaigns."Electoral Studies 27(4):621-32.URL:http:/l u(nta)<u(Olno transfer). www.sciencedirect.com/science/article/pii/S0261379408000589 Cox,Gary W.1999."Electoral Rules and the Calculus of Mobiliza- u(Ilt)≥u,(no turnout no transfer）, tion."Legislative Studies Ouarterly 24 (3):387-419. Cox,Gary W.and Mathew D.McCubbins.1986."Electoral Politics as (IIt)≥(O), a Redistributive Game."The Journal of Politics 48(2):370-89. Curto-Grau,Marta,Alfonso Herranz-Loncan,and Albert Sole-Olle 2012."Pork-Barrel Politics in Semi-Democracies:The Spanish then,all i withn(t)≤，≤nh(would vote for O,without "Parliamentary Roads,'1880-1914."Journal of Economic History 72(3):771-96. accepting the transfer. Dekel,Eddie,Matthew Jackson,and Asher Wolinsky.2008."Vote Furthermore,if nvb(t）≥nb(t),then forx≤nh(),itis Buying:General Elections."Journal of Political Economy 116(2). straightforward that i would vote for I.And for n(r)sx URL:http://www.jstor.org/stable/10.1086/587624 nv(),the following holds: Diaz-Cayeros,Alberto,Federico Estevez,and Beatriz Magaloni. 2012.Strategies of Vote Buying:Democracy,Clientelism and Poverty Relief in Mexico.New York:Cambridge University Press. Ord Dixit,Avinash,and John Londregan.1995."Redistributive Politics X+Vb+≤x≤R+ and Economic Efficiency."The American Political Science Review 4号元 89(4):856-66. u(Id)z(Ono transfer). Dixit,Avinash,and John Londregan.1996."The Determinants of Success of Special Interests in Redistributive Politics."The Journal u(I)<u(no turnout no transfer). of Politics 58 (4):1132-55. Downs,Anthony.1957."An Economic Theory of Political Action ina 4(Ir4)≥u(O1t) Democracy."Journal of Political Economy 65(2):135.URL:http: //www.jstor.org/stable/10.2307/1827369 Finan,Frederico,and Laura Schechter.2012."Vote-Buying and Reci- Thus,citizen i would not vote.Notice that so far along the procity."Econometrica 80(2):863-81.URL:http://doi.wiley.com/ 10.3982/ECTA9035 proof I have dismissed the "bound"of Xo-b,because if Fried,Brian J.2012."Distributive Politics and Conditional Cash nb(r)=nvB(r),then Xo-b=nb(t4)=noB(t). ■ Transfers:The Case of Brazil's Bolsa Familia."World Development 40(5):1042-53. Proof of Proposition 2 Gans-Morse.Jordan.Sebastian Mazzuca.and Simeon Nichter.2014. "Varieties of Clientelism:Machine Politics during Elections." American Journal of Political Science 58(2):415-32.URL:http: max∑N4F4(n(t)s.toB≥∑F(un(t)Nra //doi.wiley.com/10.1111/ajps.12058 Gerber,Alan S,Gregory A.Huber,David Doherty.and Conor 5795.801g d M.Dowling.2013a."is There a Secret Ballot?Ballot Secrecy Perceptions and their Implications for Voting Behavior."Britis/ Journal of Political Science 43 (01):77-102.URL:http://journals. From manipulating the FOC as in Dixit and Londregan cambridge.org/abstract_S000712341200021X (1995).I obtain the general solution Gerber,Alan S.,Gregory A.Huber,David Doherty,Conor M.Dowl- Assume for all d:and that the budget B F ing.and Seth J.Hill.2013b."Do Perceptions of Ballot Secrecy Influ- ence Turnout?Results from a Field Experiment."American Jour- is large enough such that n=(=then, nal of Political Science 57 (3):537-51.URL:http://doi.wiley.com/ 10.1111/ajps.12019 from the FOC for r,I obtain Golden,Miriam,and Brian Min.2013."Distributive Politics Around the World."Annual Review of Political Science 14 (1):73-99. Keefer,Philip,and Razvan Vlaicu.2007."Democracy,Credibility. 县faeN=&.+FaeM and Clientelism."Journal of Law,Economics,and Organization 24 (2):371-406.URL:http://jleo.oxfordjournalsorg/cgi/doi/10.1093/ jleo/ewm054 Lindbeck,Assar,and Jorgen W.Weibull.1987."Balanced-Budget And dividing this equation by Redistribution as the Outcome of Political Competition."Public Choice52(3):273-97 Morgan,John,and Felix Vardy.2010."Negative Vote Buying and 2a.f'ac》=f'a2+F'ac'l the Secret Ballot."Journal of Law,Economics,and Organization 28 (4):818-49.URL:http://jleo.oxfordjournalsorg/cgi/doi/10.1093/ Jleo/ewq016 Nichter,Simeon.2008."Vote Buying or Turnout Buying?Machine obtained from 's FOC,I get Politics and the Secret Ballot."American Political Science Review 102 (1):19-31.URL:http://www.journals.cambridge.org/abstract_ S0003055408080106 f(n()) tf(n()》+F(nr》 Stokes,Susan C.2005."Perverse Accountability:A Formal Model of fa=f1)》品+F)' Machine Politics with Evidence from Argentina."American Polit. ical Science Review 99 (03):315-25. 1118

Agustin Casas ui(I|t d ) ≥ ui(no turnout|no transfer), ui(I|t d ) ≥ ui(O|t d ). Then, for all i with xi ≤ nvb(t d) votes for I. On the other hand, if X¯ + θt d 2X ≤ xi ≤ XI +  b + θtd ⇒ ui(I|t d ) < ui(O|no transfer), ui(I|t d ) ≥ ui(no turnout|no transfer), ui(I|t d ) ≥ ui(O|t d ), then, all i with nvb(t d) ≤ xi ≤ ntb(t d) would vote for O, without accepting the transfer. Furthermore, if nvb(t d) ≥ ntb(t d), then for xi ≤ ntb(t d), it is straightforward that i would vote for I. And for ntb(t d) ≤ xi ≤ nvb(t d), the following holds: XI +  b + θtd ≤ xi ≤ X¯ + θt d 2X ⇒ ui(I|t d ) ≥ ui(O|no transfer), ui(I|t d ) < ui(no turnout|no transfer), ui(I|t d ) ≥ ui(O|t d ). Thus, citizen i would not vote. Notice that so far along the proof I have dismissed the “bound” of XO − √ b, because if ntb(t d) = nvB(t d), then XO − √ b = ntb(t d ) = nvB(t d ). Proof of Proposition 2 max d NdFd (n(t d )) s.to B ≥  d Fd (n(t d ))Ndt d From manipulating the FOC as in Dixit and Londregan (1995), I obtain the general solution t d = B+t dmd md − Fd (t d ) f d (td )n (td ) . Assume θt d < qd for all d; and that the budget B is large enough such that n(t d ) = nvb(t d ) = X¯ + θt d 2x , then, from the FOC for t i , I obtain θ 2x fi (n(t i ))Ni = Ni λ[t i fi (n(t i )) θ 2x + Fi (n(t i ))]. And dividing this equation by θ 2x f j (n(t j )) = λ[t j f j (n(t j )) θ 2x + F j (n(t j ))], obtained from t j ’s FOC, I get fi (n(t i )) f j (n(t j)) = t i fi (n(t i )) θ 2x + Fi (n(t i )) t j f j (n(t j)) θ 2x + F j (n(t j)), which can be rewritten as t j − t i = 2x θ Fi (n(t i )) fi (n(ti )) − F j (n(t j )) f j (n(t j)) . REFERENCES Bratton,Michael. 2008. “Vote Buying and Violence in Nigerian Elec￾tion Campaigns.” Electoral Studies 27 (4): 621–32. URL: http:// www.sciencedirect.com/science/article/pii/S0261379408000589 Cox, Gary W. 1999. “Electoral Rules and the Calculus of Mobiliza￾tion.” Legislative Studies Quarterly 24 (3): 387–419. Cox, Gary W. and Mathew D.McCubbins. 1986. “Electoral Politics as a Redistributive Game.” The Journal of Politics 48 (2): 370–89. Curto-Grau, Marta, Alfonso Herranz-Loncan, and Albert Sole-Olle. 2012. “Pork-Barrel Politics in Semi-Democracies: The Spanish ‘Parliamentary Roads,’ 1880–1914.” Journal of Economic History 72 (3): 771–96. Dekel, Eddie, Matthew Jackson, and Asher Wolinsky. 2008. “Vote Buying: General Elections.” Journal of Political Economy 116 (2). URL: http://www.jstor.org/stable/10.1086/587624 Diaz-Cayeros, Alberto, Federico Estevez, and Beatriz Magaloni. 2012. Strategies of Vote Buying: Democracy, Clientelism and Poverty Relief in Mexico. New York: Cambridge University Press. Dixit, Avinash, and John Londregan. 1995. “Redistributive Politics and Economic Efficiency.” The American Political Science Review 89 (4): 856–66. Dixit, Avinash, and John Londregan. 1996. “The Determinants of Success of Special Interests in Redistributive Politics.”The Journal of Politics 58 (4): 1132–55. Downs,Anthony. 1957. “An Economic Theory of Political Action in a Democracy.” Journal of Political Economy 65 (2): 135. URL: http: //www.jstor.org/stable/10.2307/1827369 Finan, Frederico, and Laura Schechter. 2012. “Vote-Buying and Reci￾procity.” Econometrica 80 (2): 863–81. URL: http://doi.wiley.com/ 10.3982/ECTA9035 Fried, Brian J. 2012. “Distributive Politics and Conditional Cash Transfers:The Case of Brazil’s Bolsa Família.”World Development 40 (5): 1042–53. Gans-Morse, Jordan, Sebastián Mazzuca, and Simeon Nichter. 2014. “Varieties of Clientelism: Machine Politics during Elections.” American Journal of Political Science 58 (2): 415–32. URL: http: //doi.wiley.com/10.1111/ajps.12058 Gerber, Alan S., Gregory A. Huber, David Doherty, and Conor M. Dowling. 2013a. “Is There a Secret Ballot? Ballot Secrecy Perceptions and their Implications for Voting Behavior.” British Journal of Political Science 43 (01): 77–102. URL: http://journals. cambridge.org/abstract_S000712341200021X Gerber, Alan S., Gregory A. Huber, David Doherty, Conor M. Dowl￾ing, and Seth J.Hill. 2013b. “Do Perceptions of Ballot Secrecy Influ￾ence Turnout? Results from a Field Experiment.” American Jour￾nal of Political Science 57 (3): 537–51. URL: http://doi.wiley.com/ 10.1111/ajps.12019 Golden, Miriam, and Brian Min. 2013. “Distributive Politics Around the World.” Annual Review of Political Science 14 (1): 73–99. Keefer, Philip, and Razvan Vlaicu. 2007. “Democracy, Credibility, and Clientelism.” Journal of Law, Economics, and Organization 24 (2): 371–406. URL: http://jleo.oxfordjournals.org/cgi/doi/10.1093/ jleo/ewm054 Lindbeck, Assar, and Jörgen W. Weibull. 1987. “Balanced-Budget Redistribution as the Outcome of Political Competition.” Public Choice 52 (3): 273–97. Morgan, John, and Felix Várdy. 2010. “Negative Vote Buying and the Secret Ballot.” Journal of Law, Economics, and Organization 28 (4): 818–49.URL: http://jleo.oxfordjournals.org/cgi/doi/10.1093/ jleo/ewq016 Nichter, Simeon. 2008. “Vote Buying or Turnout Buying? Machine Politics and the Secret Ballot.” American Political Science Review 102 (1): 19–31. URL: http://www.journals.cambridge.org/abstract_ S0003055408080106 Stokes, Susan C. 2005. “Perverse Accountability: A Formal Model of Machine Politics with Evidence from Argentina.” American Polit￾ical Science Review 99 (03): 315–25. 1118 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:56:49, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000291

Distributive Politics with Vote and Turnout Buying Stokes,Susan C.Thad Dunning,Marcelo Nazareno,and Valeria Br- nal 124 (574):356-87.URL:http://citeseerx.ist.psu.edu/viewdoc/ usco.2013.Brokers,Voters,and Clientelism:The Puzzle of Distribu- summary2doi=10.1.1.366.3313 tive Politics.New York:Cambridge University Press. Zarazaga,Rodrigo.2016."Party Machines and Voter-Customized Vicente,Pedro C.2014."Is Vote Buying Effective?Evidence Rewards Strategies."Journal of Theoretical Politics28(4):678-701. from a Field Experiment in West Africa."The Economic Jour- URL:http://jtp.sagepub.com/cgi/doi/10.1177/0951629815603496 1119

Distributive Politics with Vote and Turnout Buying Stokes, Susan C., Thad Dunning, Marcelo Nazareno, and Valeria Br￾usco. 2013.Brokers,Voters, and Clientelism:The Puzzle of Distribu￾tive Politics. New York: Cambridge University Press. Vicente, Pedro C. 2014. “Is Vote Buying Effective? Evidence from a Field Experiment in West Africa.” The Economic Jour￾nal 124 (574): 356–87. URL: http://citeseerx.ist.psu.edu/viewdoc/ summary?doi=10.1.1.366.3313 Zarazaga, Rodrigo. 2016. “Party Machines and Voter-Customized Rewards Strategies.”Journal of Theoretical Politics 28 (4): 678–701. URL: http://jtp.sagepub.com/cgi/doi/10.1177/0951629815603496 1119 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:56:49, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000291