SEQUENTIAL VOTING WHEN LONG ELECTIONS ARE COSTLY

This paper analyzes sequential voting in binary elections when voters are motivated by a desire both to elect their preferred candidate and to avoid a long and costly election. I find a unique equilibrium in which a voter's action depends both on the intensity of the voter's preferences as well as how well the candidates have done in earlier voting rounds. This equilibrium results in momentum in which voters are more likely to vote for the candidate currently in the lead. Furthermore, the probability a voter votes for a candidate is increasing in the size of the candidate's lead. As a consequence, a candidate is more likely to win the election if the candidate's stronger supporters vote earlier in the election.     

SEQUENTIAL OR SIMULTANEOUS ELECTIONS? A WELFARE ANALYSIS

Should all voters vote on the same day or should elections be staggered? Using a model of voting and social learning, we illustrate that sequential elections place too much weight on early states but also provide late voters with valuable information. Simultaneous elections equally weigh states but place too much weight on voter priors, providing an inappropriate advantage to front‐runners. Simultaneous elections are thus preferred if the front‐runner advantage is small, but sequential elections are preferred if the advantage is large. Our quantitative welfare analysis of presidential primaries suggests that simultaneous systems slightly outperform sequential systems.     

Condorcet Jury Theorem or Rational Ignorance

We analyze a symmetric model of an election in which voters are uncertain about which of two alternatives is desirable for them. Each voter must incur some cost to acquire information about the alternatives. We show that by focusing on unbiased voting strategies, general symmetric signal structures can be degenerated to a two‐signal model. In addition, we show that for any sequence of unbiased voting equilibria, if the second‐order derivative of the information cost function at no information is zero, then the probability of electing the desirable alternative converges to one, that is, the Condorcet Jury Theorem is valid. Otherwise, this probability converges to some value less than one; that is, the “rational ignorance” hypothesis is valid.     

Bandwagons and Momentum in Sequential Voting

In this paper I show that an equilibrium exists to the sequential voting game in which a bandwagon begins with probability 1. These bandwagons are driven by a combination of beliefs and the desire of voters to vote for the winning candidate. Significantly, in this equilibrium the pivot probability for each voter is non-zero, even in an infinite population. Consequently, the bandwagons do not always start after one (or at most two) favourable decisions (as do economic cascades) and varying levels of informative voting are observed, consistent with observations from sequential voting in U.S. presidential primaries. Further, voters are exposed to counterintuitive incentives, referred to as "buyers' remorse", that have been attributed to real primary voters.
I also derive equilibrium behaviour in this environment when voting is simultaneous and compare the quality of information aggregation within each mechanism. I relate the conclusions to U.S. presidential primaries and find they are consistent with a common conclusion about the front-loading of the primary process: that in tight elections (with no front-runner) simultaneous voting is preferred, whereas in lopsided elections sequential voting is preferred. The superior performance of sequential voting in lopsided races is precisely because bandwagons occur.     

Electoral fraud and voter turnout: An experimental study

In this paper we experimentally investigate the consequences of electoral fraud on voter turnout. The experiment is based on a strategic binary voting model where voters decide whether to cast a costly vote in favour of their preferred candidate or to abstain. The electoral process is illicitly influenced by applying ballot-box stuffing. In the experiment we implement two different framings: we compare voter turnout in a neutral environment and with framed instructions to explicitly replicate elections. This approach enables us to both test the model's predictions and to estimate the framing effects of voting and fraud. Comparison of experimental results with theoretical predictions reveals over-voting, which is exacerbated when fraud occurs. Turnout increases as predicted with a moderate level of fraud while, with higher levels of electoral fraud, voters fail to recognize that the existence of a relatively larger number of “agents” voting with certainty considerably decreases the benefits of voting. Importantly, framing matters, as revealed by the higher turnout of those in the majority group, against which the fraud is applied.     

Approval voting in subset elections

Summary. Approval voting is designed to be “insensitive to numbers” of voters, and likely to elect a Condorcet candidate. However, the result of an election among one group of candidates gives no information about the results of elections among any other groups, even if every voter follows the recommended utility-maximizing strategy, which places strong restrictions on the individual voter's subset ballots. Thus the addition of a single candidate could completely reverse the outcome of an election, or a Condorcet candidate could finish last. Received: November 5, 1998; revised version: November 30, 1998     

Learning in Elections and Voter Turnout

Voter turnout in game theoretic models of voting has typically been difficult to predict because of the problem of multiple Nash equilibria ( Palfrey and Rosenthal 1983, 1985 ). Many of these equilibria require an extreme precision of beliefs among voters that is unlikely to be reached in real elections. At the same time, mechanisms like pre‐election polls exist to shape the beliefs of voters about expected turnout. We combine these two features in a model of voter learning in elections and characterize the asymptotically stable equilibria of both complete and incomplete information games in a simple symmetric setting with two candidates. We also show how the model can be used to qualitatively explain several phenomena observed in reality: increases in costs of voting affect turnout adversely but there may be persistence of turnout levels between elections even though costs and other parameters change. Increase in uncertainty increases turnout while increases in the size of the electorate decrease it, in line with intuition.     

Mapping the theory of political representation to the empirics: An investigation for proportional and majoritarian rules

We combine roll call votes and referendum decisions on identically worded legislative proposals to identify the effect of electoral rules on the way Swiss Members of Parliament (MPs) represent their constituents’ preferences. We exploit the fact that MPs in both Houses of Parliament are elected in the same electoral districts (the cantons). Yet, in the Lower House, MPs are elected using a proportional rule, while in the Upper House they are elected employing a majoritarian rule. We find that electoral rules matter strongly for political representation. The voting patterns of MPs are fully in line with three theoretical predictions regarding the influence of electoral rules on representation of constituents’ preferences: 1) The probability that a proportional-elected MP accepts a legislative proposal closely follows the share of voters that accept the proposal in the referendum. 2) In contrast, for majority-elected MPs the probability of acceptance is strongly increasing in the share of voter acceptance if the latter is close to the 50% threshold. 3) The estimated probability that an Upper House MP votes “yes” as a function of the share of voters voting “yes” in the referendum has an S-shape form with an inflection point close to 50%.     

Dissertation abstract: Voting in the laboratory

Almost every week national elections are held somewhere in the world. Many more elections take place at federal and local levels of government. Surely, these are important events to many of us. This thesis aims at providing a better understanding of why and how people vote in elections. Three original modifications of Palfrey and Rosenthal’s (1983) participation game are used to study voter turnout theoretically and experimentally.¹ In the basic game, each voter supports (i.e., prefers) one of two exogenous candidates and privately decides between voting at a cost and abstaining (without costs). The candidate who receives more votes wins the election (ties are broken randomly) and each supporter of this candidate receives an equal reward, independent of whether or not she voted. The first study (published in the American Political Science Review 100, pp. 235–248) analyzes the effects of social embeddedness on turnout, assuming that voters may be influenced by observing the decisions of other voters around them (e.g., a family or working place). Our experimental results show that the social context matters: this information increases turnout by more than 50%. The increase is greater when neighbors support the same candidate rather than when they support opponents. The second study investigates the effects of public opinion polls on voter turnout and welfare. Poll releases resolve uncertainty about the level of support for each candidate caused by `floating’ voters, whose preferences change across elections. This information increases turnout in the laboratory by 28–34%, depending on the fraction of floating voters in the electorate. If polls indicate equal levels of support for both candidates—in which case aggregate benefits for society are not affected by the outcome—welfare decreases substantially due to costs from excessive turnout. In the final study, elections are preceded by the competition between two candidates: they simultaneously announce binding policy offers in which some voters can be favored at the expense of others through inclusion and exclusion in budget expenditure (Myerson 1993).² We observe that policy offers include 33% more voters—yielding a smaller budget share for each—when voting is compulsory rather than voluntary. Moreover, we find evidence of political bonds between voters and long-lived parties. Overall, in all three experiments many subjects strongly react to economic incentives (i.e., benefits, costs, and informational clues), often in line with what is observed outside of the laboratory. JEL Classification C72, C92, D72 Dissertation Committee: Arthur Schram, University of Amsterdam (advisor) Axel Ockenfels, University of Cologne Thomas Palfrey, California Institute of Technology Cees van der Eijk, University of Nottingham Frans van Winden, University of Amsterdam ¹Palfrey, T.R., & Rosenthal, H. (1983). A strategic calculus of voting. Public Choice, 41, 7–53. ²Myerson, R.B. (1993). Incentives to cultivate favored minorities under alternative electoral systems. American Political Science Review, 87, 856–869.     

Do non-citizens affect U.S. Congressional elections?

U.S. citizens against immigration argue that immigrants commit voter fraud and skew election outcomes towards progressive candidates. These arguments have increased in number and severity since the Supreme Court ruled in 2013 that states cannot require photo identification from voters. We examine whether the size of the non-citizen population is related to election outcomes. Previous research indicates that non-citizens sway elections in favour of progressive candidates but only in elections where the victory margin is small. We find no evidence of a relationship between non-citizens and vote outcomes. We find evidence that the percent of the population that is non-white is positively related to percent of votes cast for democratic candidates.     

Anonymous yes–no voting with abstention and multiple levels of approval

Symmetric (3,2) simple games serve as models for anonymous voting systems in which each voter may vote “yes,” abstain, or vote “no,” the outcome is “yes” or “no,” and all voters play interchangeable roles. The extension to symmetric (j,2) simple games, in which each voter chooses from among j ordered levels of approval, also models some natural decision rules, such as pass–fail grading systems. Each such game is determined by the set of (anonymous) minimal winning profiles. This makes it possible to count the possible systems, and the counts suggest some interesting patterns. In the (3,2) case, the approach yields a version of May's Theorem, classifying all possible anonymous voting rules with abstention in terms of quota functions. In contrast to the situation for ordinary simple games these results reveal that the class of simple games with 3 or more levels of approval remains large and varied, even after the imposition of symmetry.     

Let the experts decide? Asymmetric information,abstention, and coordination in standing committees

We examine abstention when voters in standing committees are asymmetrically informed and there are multiple pure-strategy equilibria – swing voterʼs curse (SVC) equilibria where voters with low-quality information abstain and equilibria when all participants vote their information. When the asymmetry in information quality is large, we find that voting groups largely coordinate on the SVC equilibrium which is also Pareto optimal. However, we find that when the asymmetry in information quality is not large and the Pareto optimal equilibrium is for all to participate, significant numbers of voters with low-quality information abstain. Furthermore, we find that information asymmetry induces voters with low-quality information to coordinate on a non-equilibrium outcome. This suggests that coordination on “letting the experts” decide is a likely voting norm that sometimes validates SVC equilibrium predictions but other times does not.     

Exit polls,turnout, and bandwagon voting: Evidence from a natural experiment

We exploit a voting reform in France to estimate the causal effect of exit poll information on turnout and bandwagon voting. Before the change in legislation, individuals in some French overseas territories voted after the election result had already been made public via exit poll information from mainland France. We estimate that knowing the exit poll information decreases voter turnout by about 11 percentage points. Our study is the first clean empirical design outside of the laboratory to demonstrate the effect of such knowledge on voter turnout. Furthermore, we find that exit poll information significantly increases bandwagon voting; that is, voters who choose to turn out are more likely to vote for the expected winner.     

Election frequency,choice fatigue,and voter turnout

Influential scholars have argued that frequent elections lead to voter fatigue and can therefore be directly responsible for low turnout in countries characterized by frequent contests. However, other theories predict that frequent elections can even increase turnout. The existing empirical evidence is problematic as it simply correlates election frequency with turnout. By contrast, I exploit a natural experiment in the German state of Hesse, where voters from different municipalities faced the same electoral contest but experienced different election frequency, due to the staggered timing of some local elections. I find that when two elections are scheduled within a relatively short period of time, voter turnout at the later election is significantly reduced. This effect is stronger when the election is deemed less important in the eyes of the voters. Election frequency thus might also partly explain the wide turnout gap between first- and second-order elections, as suggested by Lijphart (1997).     

Repeated Elections with Asymmetric Information

An infinite sequence of elections with no term limits is modelled. In each period a challenger with privately known preferences is randomly drawn from the electorate to run against the incumbent, and the winner chooses a policy outcome in a one-dimensional issue space. One theorem is that there exists an equilibrium in which the median voter is decisive: an incumbent wins re-election if and only if his most recent policy choice gives the median voter a payoff at least as high as he would expect from a challenger. The equilibrium is symmetric, stationary, and the behavior of voters is consistent with both retrospective and prospective voting. A second theorem is that, in fact, it is the only equilibrium possessing the latter four conditions — decisiveness of the median voter is implied by them.     

Patronage and ideology in electoral behavior: Evidence from Egypt's first presidential elections

This paper investigates the impact of patronage and ideology on voter behavior and election outcomes. Egypt's first free presidential elections represent a good case study to answer the question whether private gain outweighs ideology in voter behavior on a broader level. First, we combine election results with household surveys and national statistics to estimate the impact of patronage (measured by public employment) on voting for the pre-revolution regime candidate. Second, using results of the first round of elections as a proxy for ideology, we test for the effect of ideological preferences on voting behavior. Additionally, we test for candidates' ability to mobilize supporters. Our results suggest that patronage has a stronger effect than secularist ideology but a weaker effect than pro-change ideology. Results show that the number of public sector and government employees in each electoral district has a positive impact on participation rates.     

The strategic sincerity of Approval voting

We show that Approval voting need not trigger sincere behavior in equilibrium of Poisson voting games and hence might lead a strategic voter to skip a candidate preferred to his worst preferred approved candidate. We identify two main rationales for these violations of sincerity. First, if a candidate has no votes, a voter might skip him. Notwithstanding, we provide sufficient conditions on the voters’ preference intensities to remove this sort of insincerity. On the contrary, if the candidate gets a positive share of the votes, a voter might skip him solely on the basis of his ordinal preferences. This second type of insincerity is a consequence of the correlation of the candidates’ scores. The incentives for sincerity of rank scoring rules are also discussed.     

Advocacy and political convergence under preference uncertainty

We study the formation of advocacy groups and how they can impact policy outcomes by revealing information about voters׳ preferences to uninformed political candidates. We conduct a laboratory experiment based on a two-candidate spatial electoral competition setting where the policy preferences of voters are (initially) unknown and change over time. In the control treatment candidates learn about the preferred policy of the median voter through the voting outcome of elections. In the advocacy treatments, voters can organize themselves into advocacy groups in order to reveal their policy preferences. We find that voters often overcome the collective action problem of forming an advocacy group. In fact, we observe the formation of both informative advocacy groups, which convey new information, and uninformative advocacy groups, which do not. Overall, advocacy groups significantly speed up the convergence to the preferred policy of the median voter. However, advocacy does not lead to higher earnings as the gains from faster convergence are offset by the costs of group formation.     

Asymmetric Equilibria in a Model with Costly Voting

Most of the voting models limit their analysis to the investigation of symmetric equilibria where “similar” voters make “similar” voting decisions. In this paper we examine the validity of this restriction in a model with costly plurality voting. We first show that in any pure strategy equilibrium every two individuals who have the same preferences and participate in elections, would vote for the same candidate. However, this result does not hold for mixed strategies equilibria.     

Scoring run-off paradoxes for variable electorates

   Summary. A no-show paradox occurs each time a single voter or a group of voters can manipulate the outcome by not participating to the election process. Among other voting procedures, the scoring run-off methods, which eliminate progressively the alternatives on the basis of scoring rules, suffer from this flaw. We here estimate how frequent this paradox is for three candidate elections under the classical Impartial Culture and Impartial Anonymous Culture assumptions, for different population sizes. The conditions under which this paradox occurs are also described, as well as the relationships with manipulations for a fixed number of voters. Received: October 21, 1999; revised version: January 12, 2000