Pre-election polling and third party candidates

I analyze voters’ incentives in responding to pre-election polls with a third party candidate. Third party supporters normally have an incentive to vote strategically in the election by voting for one of the major candidates. But these voters would vote third party if the third party candidate is doing surprisingly well in the polls. Because voters are more likely to vote third party if the third party candidate is doing well in polls, voters who like the third party candidate best have an incentive to claim they will vote third party in the polls so that more voters will ultimately vote third party in the election. The differing incentives faced during polls and elections accounts for why third party candidates do better in polls than in elections.     

Simple plurality versus plurality runoff with privately informed voters

This paper compares two voting methods commonly used in presidential elections: simple plurality voting and plurality runoff. In a situation in which a group of voters have common interests but do not agree on which candidate to support due to private information, information aggregation requires them to split their support between their favorite candidates. However, if a group of voters split their support, they increase the probability that the winner of the election is not one of their favorite candidates. In a model with three candidates, due to this tension between information aggregation and the need for coordination, plurality runoff leads to higher expected utility for the majority than simple plurality voting if the information held by voters about the candidates is not very accurate. Received: 12 September 2000/Accepted: 8 November 2001     

The Relative Irrelevance of Candidate Sex

Abstract

This study tests the relevance of candidate sex to electoral contests. We predict that voters, in general, will use issue or party cues to select between candidates and not the sex of the candidate. This will not hold under two conditions: party or issue cues are unavailable or candidate sex is likely to be particularly salient to the voter. Data were collected from a random sample of registered voters who were presented with hypothetical elections featuring candidates who were systematically varied by party, position on abortion, and sex. The results are consistent with the line of research that suggests that the majority of voters do not use candidate sex as a cue for choice, but candidate sex does affect choice among those for whom gender equality issues are particularly salient. Although generally irrelevant, candidate sex can have significant implications for the outcome of particular contests.     

Estimating the effects of activists in two-party and multi-party systems: comparing the United States and Israel

This article presents an electoral model where activist groups contribute resources to their favored parties. These resources are then used by the party candidates to enhance the electoral perception of their quality or valence. We construct an empirical model of the United States presidential election of 2008 and employ the electoral perception of the character traits of the two candidates. We use a simulation technique to determine the local Nash equilibrium, under vote share maximization, of this model. The result shows that the unique vote-maximizing equilibrium is one where the two candidates adopt convergent positions, close to the electoral center. This result conflicts with the estimated positions of the candidates in opposed quadrants of the policy space. The difference between estimated positions and equilibrium positions allows us to estimate the influence of activist groups on the candidates. We compare this estimation with that of Israel for the election of 1996, and show that vote maximization leads low valence parties to position themselves far from the electoral origin. We argue that these low valence parties in Israel will be dependent on support of radical activist groups, resulting in a degree of political fragmentation.     

The Chairman’s Paradox Revisited

This paper re-examines the so-called ‘chairman’s paradox‘ that was first noticed by Farquharson in his path breaking tract on sophisticated voting, Theory of Voting (1969). The Chairman’s paradox is concerned with the case of a three member committee in which a particular player who has a regular and a tie-breaking vote – the ‘chairman’ – not only will do worse in specific instances under the plurality procedure for three alternatives than if he did not have such a vote, but will also do worse overall. That is, the chairman’s a priori probability of success (‘getting what one wants’) for all possible games with linear (strict) preference orders is lower than that of the two regular members. It is demonstrated that this result, which comes about if voters act strategically rather than sincerely, is not as robust as it has been thought to be. By merely replacing the standard assumption of linear preference orders with weak preference orders, which allow for indifference, we can escape from the paradox for the canonical case of three players and three alternatives. With weak preference orders, the a priori success of the chairman is now greater than that of the other two players. We also point to a new paradox of sophisticated voting.     

Vote splitting,reelection and electoral control: Towards a unified model

This article presents a dynamic game theoretic model of voting in the presence of asymmetric information about a relevant parameter of the economy, the state of the world. Voters may use both vote splitting and reelection as mechanisms of electoral control. In a perfect Bayesian equilibrium, voters will reelect an Executive incumbent if a minimum level of social outcome, n ^*, is attained. The main findings are that voters tend to be more demanding, requiring a higher value for n ^*, if they expect the true state of the world to be favorable, and less demanding if they believe the state of the world is unfavorable. Moreover, vote splitting will be chosen if a favorable state is expected, whereas if an unfavorable state is more likely, voters reduce pressure over the incumbent by choosing a unified government. Received: 9 October 2000/Accepted: 11 February 2002 The author is grateful to Mirta Bugarin, Brian Gaines, Wilfredo Maldonado, Otto Reich, Brian Sala, Marilda Sotomayor, Steven Williams, the participants of the Third Lacea Meeting, the Summer Seminars of the Political Science Department, University of Illinois, the Seminar Program of the Department of Economics of the University of Brasilia and the First World Congress of the Game Theory Society for valuable discussions on previous versions of this article. None of the above is responsible for errors or opinions expressed. The financial support from CNPq/Brazil is gratefully acknowledged.     

Condorcet efficiency: A preference for indifference

The Condorcet winner in an election is the candidate who would be able to defeat all other candidates in a series of pairwise elections. The Condorcet efficiency of a voting procedure is the conditional probability that it will elect the Condorcet winner, given that a Condorcet winner exists. The study considers the Condorcet efficiency of weighted scoring rules (WSR's) on three candidates for large electorates when voter indifference between candidates is allowed. It is shown that increasing the proportion of voters who have partial indifference will increase the probability that a Condorcet winner exists, and will also increase the Condorcet efficiency of all WSR's. The same observation is observed when the proportion of voters with complete preferences on candidates is reduced. Borda Rule is shown to be the WSR with maximum Condorcet efficiency over a broad range of assumptions related to voter preferences. The result of forcing voters to completely rank all candidates, by randomly breaking ties on candidates that are viewed as indifferent, leads to a reduction in the probability that a Condorcet winner exists and to a reduction in the Condorcet efficiency of all WSR's. Received: 31 July 1999/Accepted: 11 February 2000     

DECEPTION AND POLITICAL PARTICIPATION: THEORY AND LABORATORY EVIDENCE

We model two‐candidate elections in which (1) voters are uncertain about candidates' attributes; and (2) candidates can inform voters of their attributes by sending advertisements. We compare between political campaigns with truthful advertising and campaigns in which there is a small chance of deceptive advertising. Our model predicts that voters should vote in‐line with an advertisement's information. We test our model's predictions using laboratory elections. We find, in the presence of even a small probability that an advertisement is deceptive, voters become substantially more likely to elect a “low‐quality” candidate. We discuss implications of this for existing models of voting decisions. (JEL C92, D72, D82)     

Generic difference of expected vote share and probability of victory maximization in simple plurality elections with probabilistic voters

In this paper I examine single member, simple plurality elections with n ≥ 3 probabilistic voters and show that the maximization of expected vote share and maximization of probability of victory are “generically different” in a specific sense. More specifically, I first describe finite shyness (Anderson and Zame in Adv Theor Econ 1:1–62, 2000), a notion of genericity for infinite dimensional spaces. Using this notion, I show that, for any policy in the interior of the policy space and any candidate j, the set of n-dimensional profiles of twice continuously differentiable probabilistic voting functions for which simultaneously satisfies the first and second order conditions for maximization of j’s probability of victory and j’s expected vote share at is finitely shy with respect to the set of n-dimensional profiles of twice continuously differentiable probabilistic voting functions for which satisfies the first and second order conditions for maximization of j’s expected vote share.     

Inefficient committees: small elections with three alternatives

We consider small committees which have to elect one of three alternatives using the simple plurality rule. Committee members have common, state-dependent preferences and receive imprecise private signals about the state of nature prior to the election. We are interested in whether the committee decision is efficient, that is whether the probability with which the committee elects the correct alternative is higher than the probability with which one single individual alone—on behalf of the others—would. It has been shown that there exists a unique efficient equilibrium in elections with two alternatives. We show that this result does not extend to elections with more alternatives. Multiple equilibria may exist for the same committee, and there may be both efficient and inefficient ones. Informative voting may or may not be an equilibrium. Also contrary to two-alternative elections, there exist responsive equilibria in which voters vote ‘against’ their signal. As a consequence, only two alternatives receive positive expected vote shares and the outcome is inefficient.     

Simple manipulation-resistant voting systems designed to elect Condorcet candidates and suitable for large-scale public elections

This article focuses on voting systems that (i) aim to select the Condorcet candidate in the common case where one exists and (ii) impede manipulation by exploiting voter knowledge of electorate preferences. The systems are relatively simple, both mathematically and for voter understanding, and are fully workable for large-scale elections. Their designated equilibrium strategies, under which voters vote sincerely, involve discerning the top one or two candidates in the preference ordering of the electorate. One set of systems uses its ballot to obtain voters’ preference rankings plus approval votes, and tallies the latter if no Condorcet winner exists. It offers solid advantages vis-à-vis instant-runoff voting, which uses a kindred ballot and has attracted recent reformers. Another set of systems uses only approval voting, which is examined from a new angle.     

A law of large numbers for weighted plurality

Consider an election between $k$ candidates in which each voter votes randomly (but not necessarily independently) for a single candidate, and suppose that there is a single candidate that every voter prefers (in the sense that each voter is more likely to vote for this special candidate than any other candidate). Suppose we have a voting rule that takes all of the votes and produces a single outcome and suppose that each individual voter has little effect on the outcome of the voting rule. If the voting rule is a weighted plurality, then we show that with high probability, the preferred candidate will win the election. Conversely, we show that this statement fails for all other reasonable voting rules. This result is an extension of one by Häggström, Kalai and Mossel, who proved the above in the case $k=2$ .     

Ballot Paper Cues and the Vote in Australia and Britain: Alphabetic Voting, Sex, and Title

When a voter comes to cast a ballot, some information aboutthe candidates is evident on the ballot paper itself. Usingmultiple regression techniques, this study provides quantitativeestimates of the impact of such information in recent Britishand Australian elections. The results suggest that whether thecandidate's name comes first, middle, or last on the ballotpaper has no effect on the vote in Britain. But it does matterin Australia, partly because voters are more likely to choosecandidates whose names come first, but mostly because the majorparties believe voters will do so and select candidates accordingly.In addition, women candidates are at an electoral disadvantagein Britain and at an even greater disadvantage in Australia.Most, but not all, of this disadvantage comes about becausemajor parties are reluctant to nominate women candidates. Finally,in Britain candidates with an honorary title garner an appreciabledeferential vote although candidates with an academic titledo not. These effects range in size from a modest 2.5 percentof the vote to a substantial 12.5 percent.     

The two-party system under alternative voting procedures

Countries that elect their policy-makers by means of Plurality Voting tend to have a two-party system. This observation can be explained by the strategic behavior of voters. This article derives two broad classes of voting procedures under which strategic voting behavior induces a two-party system under standard assumptions on voter preferences. One class consists of the voting procedures with unique top-score, i.e., under which a voter can cast a top-score vote for only one candidate (e.g., Plurality Voting, Borda Count). The other class consists of the voting procedures that permit truncated ballots, i.e., under which voters do not have to cast all their votes (e.g., Approval Voting). This analysis suggests that the key for strategic voting behavior to induce a two-party system is that voters can always cast a different score for the two candidates they rank first and second on their ballots.     

Sophisticated voting and equilibrium refinements under plurality rule

In this paper we show in the context of voting games with plurality rule that the “perfect” equilibrium concept does not appear restrictive enough, since, independently of preferences, it can exclude at most the election of only one candidate. Furthermore, some examples show that there are “perfect” equilibria that are not “proper”. However, also some “proper” outcome is eliminated by sophisticated voting, while Mertens' stable set fully satisfies such criterium, for generic plurality games. Moreover, we highlight a weakness of the simple sophisticated voting principle. Finally, we find that, for some games, sophisticated voting (and strategic stability) does not elect the Condorcet winner, neither it respects Duverger's law, even with a large number of voters. Received: 16 March 1999/Accepted: 25 September 1999     

The original Borda count and partial voting

In a Borda count, bc, M. de Borda suggested the last preference cast should receive 1 point, the voter’s penultimate ranking should get 2 points, and so on. Today, however, points are often awarded to (first, second,..., last) preferences cast as per (n, n?1, ..., 1) or more frequently, (n ?1, n?2,..., 0). If partial voting is allowed, and if a first preference is to be given n or n ? 1 points regardless of how many preferences the voter casts, he/she will be incentivised to rank only one option/candidate. If everyone acts in this way, the bc metamorphoses into a plurality vote... which de Borda criticized at length. If all the voters submit full ballots, the outcome—social choice or ranking—will be the same under any of the above three counting procedures. In the event of one or more persons submitting a partial vote, however, outcomes may vary considerably. This preliminary paper suggests research should consider partial voting. The author examines the consequences of the various rules so far advocated and then purports that M. de Borda, in using his formula, was perhaps more astute than the science has hitherto recognised.     

An experiment on coordination in multi-candidate elections: The importance of polls and election histories

Do polls simply measure intended voter behavior or can they affect it and, thus, change election outcomes? Do candidate ballot positions or the results of previous elections affect voter behavior? We conduct several series of experimental, three-candidate elections and use the data to provide answers to these questions. In these elections, we pay subjects conditionally on election outcomes to create electorates with publicly known preferences. A majority (but less than two-thirds) of the voters are split in their preferences between two similar candidates, while a minority (but plurality) favor a third, dissimilar candidate. If all voters voted sincerely, the third candidate — a Condorcet loser — would win the elections. We find that pre-election polls significantly reduce the frequency with which the Condorcet loser wins. Further, the winning candidate is usually the majority candidate who is listed first on the poll and election ballots. The evidence also shows that a shared history enables majority voters to coordinate on one of their favored candidates in sequences of identical elections. With polls, majority-preferred candidates often alternate as election winners.     

Policy convergence in a two-candidate probabilistic voting model

We propose a generalization of the probabilistic voting model in two-candidate elections. We allow the candidates have general von Neumann–Morgenstern utility functions defined over the voting outcomes. We show that the candidates will choose identical policy positions only if the electoral competition game is constant-sum, such as when both candidates are probability-of-win maximizers or vote share maximizers, or for a small set of functions that for each voter define the probability of voting for each candidate, given candidate policy positions. At the same time, a pure-strategy local Nash equilibrium (in which the candidates do not necessarily choose identical positions) exists for a large set of such functions. Hence, if the candidate payoffs are unrestricted, the “mean voter theorem” for probabilistic voting models is shown to hold only for a small set of probability of vote functions.     

Pareto optimality in spatial voting models

This paper studies the Pareto optimality properties of policy proposals that are made byk(k2) strategic candidates that face uncertainty about the choices that the voters will make. Our first theorem shows that, under very general conditions, any proposal that is a best reply for a candidate is necessarily Pareto optimal. This theorem, in turn, implies that, under slightly stronger conditions, all candidate proposals that are made in a Nash equilibrium or sequentially are necessarily Pareto optimal. Our second theorem shows that, when these conditions are themselves slightly strengthened, any proposal outside of the Pareto set is strictly dominated by at least one proposal inside the Pareto set.We would like to acknowledge helpful comments and suggestions provided by Otto Davis and Richard McKelvey     

Citizen candidates under uncertainty

In this paper I add uncertainty about the total vote count to a “citizen candidate” model of representative democracy. I show that in a society with a large electorate, where the outcome of the election is uncertain and where winning candidates receive a large reward from holding office, there will be a two-candidate equilibrium and no equilibria with a single candidate. This work has benefited from valuable comments by Paul Healy, Morgan Kousser, Alejandro Saporiti, Al Slivinski, participants in a seminar in Princeton, and especially by Matt Jackson and Tom Palfrey. Their contribution is gratefully acknowledged.