Jonathan Woon feedback subiects received.Part 1 consisted of ten elec- Second,while the general election candidate closer tions without any feedback.21 Part 2 consisted of 30 to the median voter's position generally wins,it is rare elections with feedback provided to subjects after each for the winning candidate to be located exactly at election.The information subjects received included the predicted equilibrium position.Even in session 4 the positions of the subjects who were selected as can- (1S),in which the electoral outcome appears most fre- didates,the number of votes for each candidate,the quently near the median voter's position,the winning winning position,and the payoff from the final out- candidate is located at the median's position in only come.Within each part,I varied the distance between three elections (in another eight elections,the winning the groups'ideal points by dividing each set of elec- candidate is +1 from the median voter's position).In tions into two halves.In the first half,the left and right session ten,the winning candidate usually appears to groups'ideal points were 100 units apart(d=50),while be just barely closer to the median voter than the losing in the second half,they were 150 units apart(d =75). candidate. Note that both of these within-subjects manipulations Third,primary voters are inconsistent in selecting ei- varied ancillary assumptions (feedback and distance ther extreme or moderate candidates.Notably,there between ideal points)and therefore serve as robust- are several candidates in two-stage elections who lo- ness checks.The experimental manipulation of theo- cate at exactly the median voter's position yet lose the retical interest is the between-subjects manipulation of primary.In session one,there were 12 out of 14 such the electoral institution. candidates,and in session six,there were six out of ten.While this could suggest that primary voters prefer Electoral Dynamics extremists,there are also many elections in which the more moderate candidate wins.For example,in elec- To get a sense of the kinds of promises candidates make tion 11 of session six,the left party candidate at-30 and whether moderates or extremists win elections defeated the candidate at-45,and the right party can- Figure 3 presents the sequence of candidate positions didate at 20 defeated the candidate located at 50.with and outcomes for selected sessions (two 1S sessions the right party candidate (who is closer to the median and two 2S sessions).The horizontal axis indicates the voter)winning the general election.Indeed,Figure 3 election,and the vertical axis indicates the promises of depicts losing candidates in primary elections on either the subjects selected as the candidates.These positions side of the parties'winning candidates (indicated by are adjusted(centered)so that the general election me- the fact that the hollow candidate markers appear both dian voter's position is zero.The vertical lines indicate above and below the solid ones) when the electoral conditions change in terms of feed- These sample dynamics suggest that standard game back and the distance between the parties'ideal points. theoretic analysis poorly predicts candidate positions General election candidates are depicted using solid and voting behavior in the experiment.Whereas equi- shapes(candidates in 1S elections and the primary win- librium predicts complete candidate convergence in ners in 2S elections)while primary candidates who lost both 1S and 2S elections,I find that candidates'po- the first stage election are depicted with hollow shapes. sitions instead diverge.The considerable heterogene- The winning position of the general election is shown ity in candidate positions and the selection of extreme by the solid line.Although the dynamics of each session candidates by primary voters indicate that behavioral differ,these plots reveal several noteworthy patterns. game theory and nonequilibrium analysis may be use- First,the positions of candidates from the two par- ful tools for understanding the consequences of elec- ties clearly diverge from the median voter's position toral institutions.Of course,Figure 3 only provides a This is true for both 1S and 2S elections,and it ap- snapshot of experimental behavior.The remainder of pears to persist over the course of the experiment even the analysis demonstrates that many of the patterns de- after subjects gain considerable experience.In session scribed above generalize across subjects and sessions. ten (1S),for example,the candidates from each party choose positions close to their own ideal points,and po- Candidate Positions larization between the candidates'positions increases when the underlying preference polarization increases. Figure 4 shows the average positions over time and by Along with divergence,there also appears to be sub- election format for all candidates (top panel)and for stantial heterogeneity and fluctuation in candidate winning candidates (bottom panel).In the remainder positions.22 of the analysis.I measure the extremity of a candi- date's position (vertical axis)by normalizing positions 21 The fact that the game is sequential means that it would be impos- so that a subject's own ideal point is one and the me- sible to prevent learning across elections if subjects completed each dian voter's ideal point is zero(so the opposing party's election game before proceeding to the next.I solved this problem by implementing a procedure similar in spirit to the strategy method ideal point is-1 on this transformed scale).The top whereby the game was divided into stages and subjects made their panel of Figure 4 shows that candidate positions clearly decisions for all elections in one stage before moving to the next diverge from the median voter's position throughout stage.That is,subjects first chose their positions for all ten elections the experiment regardless of the election format.This in Part 1,subjects in the 2S treatment then voted for their party's can- didates in all ten primary elections,and then subjects in both treat. The figures also reveal that candidates and voters sometimes make dates are located to the left of the median voter,with the party R mistakes.For example,in election 1 in session 4,both parties'candi- candidate located at leftmost position in the policy space. 834Jonathan Woon feedback subjects received. Part 1 consisted of ten elec￾tions without any feedback.21 Part 2 consisted of 30 elections with feedback provided to subjects after each election. The information subjects received included the positions of the subjects who were selected as can￾didates, the number of votes for each candidate, the winning position, and the payoff from the final out￾come. Within each part, I varied the distance between the groups’ ideal points by dividing each set of elec￾tions into two halves. In the first half, the left and right groups’ ideal points were 100 units apart (d = 50), while in the second half, they were 150 units apart (d = 75). Note that both of these within-subjects manipulations varied ancillary assumptions (feedback and distance between ideal points) and therefore serve as robust￾ness checks. The experimental manipulation of theo￾retical interest is the between-subjects manipulation of the electoral institution. Electoral Dynamics To get a sense of the kinds of promises candidates make and whether moderates or extremists win elections, Figure 3 presents the sequence of candidate positions and outcomes for selected sessions (two 1S sessions and two 2S sessions). The horizontal axis indicates the election, and the vertical axis indicates the promises of the subjects selected as the candidates. These positions are adjusted (centered) so that the general election me￾dian voter’s position is zero. The vertical lines indicate when the electoral conditions change in terms of feed￾back and the distance between the parties’ ideal points. General election candidates are depicted using solid shapes (candidates in 1S elections and the primary win￾ners in 2S elections) while primary candidates who lost the first stage election are depicted with hollow shapes. The winning position of the general election is shown by the solid line.Although the dynamics of each session differ, these plots reveal several noteworthy patterns. First, the positions of candidates from the two par￾ties clearly diverge from the median voter’s position. This is true for both 1S and 2S elections, and it ap￾pears to persist over the course of the experiment even after subjects gain considerable experience. In session ten (1S), for example, the candidates from each party choose positions close to their own ideal points, and po￾larization between the candidates’ positions increases when the underlying preference polarization increases. Along with divergence, there also appears to be sub￾stantial heterogeneity and fluctuation in candidate positions.22 21 The fact that the game is sequential means that it would be impos￾sible to prevent learning across elections if subjects completed each election game before proceeding to the next. I solved this problem by implementing a procedure similar in spirit to the strategy method whereby the game was divided into stages and subjects made their decisions for all elections in one stage before moving to the next stage. That is, subjects first chose their positions for all ten elections in Part 1, subjects in the 2S treatment then voted for their party’s can￾didates in all ten primary elections, and then subjects in both treat￾ments voted in all ten general elections. 22 The figures also reveal that candidates and voters sometimes make mistakes. For example, in election 1 in session 4, both parties’ candi￾Second, while the general election candidate closer to the median voter’s position generally wins, it is rare for the winning candidate to be located exactly at the predicted equilibrium position. Even in session 4 (1S), in which the electoral outcome appears most fre￾quently near the median voter’s position, the winning candidate is located at the median’s position in only three elections (in another eight elections, the winning candidate is ±1 from the median voter’s position). In session ten, the winning candidate usually appears to be just barely closer to the median voter than the losing candidate. Third, primary voters are inconsistent in selecting ei￾ther extreme or moderate candidates. Notably, there are several candidates in two-stage elections who lo￾cate at exactly the median voter’s position yet lose the primary. In session one, there were 12 out of 14 such candidates, and in session six, there were six out of ten.While this could suggest that primary voters prefer extremists, there are also many elections in which the more moderate candidate wins. For example, in elec￾tion 11 of session six, the left party candidate at −30 defeated the candidate at −45, and the right party can￾didate at 20 defeated the candidate located at 50, with the right party candidate (who is closer to the median voter) winning the general election. Indeed, Figure 3 depicts losing candidates in primary elections on either side of the parties’ winning candidates (indicated by the fact that the hollow candidate markers appear both above and below the solid ones). These sample dynamics suggest that standard game theoretic analysis poorly predicts candidate positions and voting behavior in the experiment. Whereas equi￾librium predicts complete candidate convergence in both 1S and 2S elections, I find that candidates’ po￾sitions instead diverge. The considerable heterogene￾ity in candidate positions and the selection of extreme candidates by primary voters indicate that behavioral game theory and nonequilibrium analysis may be use￾ful tools for understanding the consequences of elec￾toral institutions. Of course, Figure 3 only provides a snapshot of experimental behavior. The remainder of the analysis demonstrates that many of the patterns de￾scribed above generalize across subjects and sessions. Candidate Positions Figure 4 shows the average positions over time and by election format for all candidates (top panel) and for winning candidates (bottom panel). In the remainder of the analysis, I measure the extremity of a candi￾date’s position (vertical axis) by normalizing positions so that a subject’s own ideal point is one and the me￾dian voter’s ideal point is zero (so the opposing party’s ideal point is −1 on this transformed scale). The top panel of Figure 4 shows that candidate positions clearly diverge from the median voter’s position throughout the experiment regardless of the election format. This dates are located to the left of the median voter, with the party R candidate located at leftmost position in the policy space. 834 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:04, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000515