Policy convergence under approval and plurality voting: the role of policy commitment

Proponents of Approval Voting argue that this electoral rule leads to more centrist outcomes compared to Plurality Voting. This claim has been substantiated by scholarly work using spatial models of political competition. We revisit this issue in the context of a model of political competition in which (1) candidates are policy-motivated; (2) candidacy decisions are endogenous; and (3) candidates can credibly commit to implementing any policy. Under these assumptions we find the opposite to be true – Plurality Voting yields convergence to the median voter’s ideal policy but Approval Voting may not. We argue that this result is driven by the differential incentives for candidate entry under the two voting rules. Our results suggest that whether Approval Voting yields more centrist outcomes vis-á-vis Plurality Voting depends on the possibility of policy commitment on the part of the candidates. In an election held under PV each citizen is given one vote he can cast for one (and only one) candidate, and the candidate who gets the most votes wins the election.     

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.     

Two field experiments on Approval Voting in Germany

We report on two field experiments on Approval Voting conducted during actual state and federal elections in Germany. Voters provided approval ballots both for named district candidates and for state parties. The data reveal significant discrepancies in the outcomes under the official method and Approval Voting. Further, our analysis suggests that currently used voting methods do a poor job of representing the electorate??s preferences. As a consequence, some recurring features of the political landscape in a given country might be, in part, an artifice of the employed voting method.     

Approval Voting on Dichotomous Preferences

The aim of this paper is to find normative foundations of Approval Voting when individuals have dichotomous preferences. We show that a social choice function is anonymous, neutral, strategy-proof and strictly monotone if and only if it is Approval Voting and interpret this result as an extension of May’s theorem (Econometrica 20:680–684, 1952). Then, we show that Approval Voting is the only strictly symmetric, neutral and efficient social choice function. This result is related to a characterization of Baigent and Xu (Math Soc Sci 21:21–29, 1991).     

Political support for minimum wage legislation: 1989

A model explaining senators’ votes on minimum wage increases in 1966 and 1974 was applied to the 1977 and 1989 votes with similar results. The extent of unionization in each state was positively associated with votes in favor of minimum wage increases. State wage levels were not significantly associated with senators’ votes. These results held for Republican senators as well as for all senators. However, neither wage levels nor unionization rates was a significant factor explaning Democrats’ votes on minimum wage increases.     

Voces populi and the art of listening

The strategy most damaging to many preferential election methods is to give insincerely low rank to the main opponent of one’s favourite candidate. Theorem 1 determines the 3-candidate Condorcet method that minimizes the number of noncyclic profiles allowing the strategic use of a given cyclic profile. Theorems 2, 3 and 4 establish conditions for an anonymous and neutral 3-candidate single-seat election to be monotonic and still avoid this strategy completely. Plurality elections combine these properties; among the others ‘conditional IRV’ gives the strongest challenge to the plurality winner. Conditional IRV is extended to any number of candidates. Theorem 5 is an impossibility of Gibbard–Satterthwaite type, describing three specific strategies that cannot all be avoided in meaningful anonymous and neutral election methods.     

Optimal voting rules for two-member tenure committees

A tenure committee first votes on whether to hire a candidate; if it does, it receives an informative performance signal, and then votes on whether to tenure the candidate; rejection at either stage returns the committee to a candidate pool, endogenising the value of the outside option. A candidate’s fate depends only on the behaviour of two ‘weather-vane’ committee members. Committee members may vote against favoured candidates if the weather-vane is opposed; enthusiastic assessments by one of these weather-vanes may harm a candidate’s chances by increasing others’ thresholds for hiring him; sunk time costs may lead voters who voted against hiring to vote for tenuring him, even after a poor probationary performance. For two member committees that are patient and perceptive, the optimal voting rule is a (weak) majority at the hiring stage and unanimity at the tenure stage; when such committees are impatient or imperceptive, the double (weak) majority rule is optimal. Perversely, the performance of a patient, imperceptive committee improves as its perceptiveness further declines. Consistent with practice, falling threshold rules are not optimal. Results on optimal voting rules are also presented in limit cases as committee members’ beliefs become more correlated. Finally, we compare the model to a discrete-time European options model.     

How frequently do different voting rules encounter voting paradoxes in three-candidate elections?

We estimate the frequencies with which ten voting anomalies (ties and nine voting paradoxes) occur under 14 voting rules, using a statistical model that simulates voting situations that follow the same distribution as voting situations in actual elections. Thus the frequencies that we estimate from our simulated data are likely to be very close to the frequencies that would be observed in actual three-candidate elections. We find that two Condorcet-consistent voting rules do, the Black rule and the Nanson rule, encounter most paradoxes and ties less frequently than the other rules do, especially in elections with few voters. The Bucklin rule, the Plurality rule, and the Anti-plurality rule tend to perform worse than the other eleven rules, especially when the number of voters becomes large.     

Polarization, Information Collection and Electoral Control

We identify the conditions under which voters can induce political parties to collect information and to select policies which are optimal from the representative voter’s point of view. We show that when parties are office motivated the voting rule should encourage parties to collect information. Voting rules that focus on the opposition party sometimes dominate voting rules that focus on the incumbent party. When parties are policy motivated, they also have to be motivated to select good policies. Generally, it is easier to stimulate policy motivated parties than office motivated parties to collect information. However, in contrast to office motivated parties, policy motivated parties will sometimes select policies that conflict with the representative voter’s interest.     

Going from theory to practice: the mixed success of approval voting

Approval voting (AV) is a voting system in which voters can vote for, or approve of, as many candidates as they like in multicandidate elections. In 1987 and 1988, four scientific and engineering societies, collectively comprising several hundred thousand members, used AV for the first time. Since then, about half a dozen other societies have adopted AV. Usually its adoption was seriously debated, but other times pragmatic or political considerations proved decisive in its selection. While AV has an ancient pedigree, its recent history is the focus of this paper. Ballot data from some of the societies that adopted AV are used to compare theoretical results with experience, including the nature of voting under AV and the kinds of candidates that are elected. Although the use of AV is generally considered to have been successful in the societies—living up to the rhetoric of its proponents—AV has been a controversial reform. AV is not currently used in any public elections, despite efforts to institute it, so its success should be judged as mixed. The chief reason for its nonadoption in public elections, and by some societies, seems to be a lack of key “insider” support.     

Strategic voting and nomination

Using computer simulations based on three separate data generating processes, I estimate the fraction of elections in which sincere voting is a core equilibrium given each of eight single-winner voting rules. Additionally, I determine how often each rule is vulnerable to simple voting strategies such as ‘burying’ and ‘compromising’, and how often each rule gives an incentive for non-winning candidates to enter or leave races. I find that Hare is least vulnerable to strategic voting in general, whereas Borda, Coombs, approval, and range are most vulnerable. I find that plurality is most vulnerable to compromising and strategic exit (causing an unusually strong tendency toward two-party systems), and that Borda is most vulnerable to strategic entry. I use analytical proofs to provide further intuition for some of my key results.     

Gender Differences in Voting for Female Candidates: Evidence from the 1982 Election

This paper analyzes voting in five 1982 elections in which womenran as major party candidates for high-level offices: Governorin Vermont and Iowa; and U.S. Senator in Missouri, New York,and New Jersey. Results indicate that the sex of the candidategenerally has little impact on voting and that solid women candidatescan attract cross-over votes, while weaker ones can lose them.The implications of these results are discussed in the concludingsection.     

The paradox of multiple elections

Assume that voters must choose between voting yes (Y) and voting no (N) on three propositions on a referendum. If the winning combination is NYY on the first, second, and third propositions, respectively, the paradox of multiple elections is that NYY can receive the fewest votes of the 2³ = 8 combinations. Several variants of this paradox are illustrated, and necessary and sufficient conditions for its occurrence, related to the “incoherence” of support, are given. The paradox is shown, via an isomorphism, to be a generalization of the well-known paradox of voting. One real-life example of the paradox involving voting on propositions in California, in which not a single voter voted on the winning side of all the propositions, is given. Several empirical examples of variants of the paradox that manifested themselves in federal elections – one of which led to divided government – and legislative votes in the US House of Representatives, are also analyzed. Possible normative implications of the paradox, such as allowing voters to vote directly for combinations using approval voting or the Borda count, are discussed. Received: 31 July 1996 / Accepted: 1 October 1996     

Predicting the decisions to vote and support unions in certification elections: An integrated perspective

This article develops and empirically tests a model of the dual decision-making process employees undergo to guide their behavior during organizing campaigns and elections. The model combines principles of risk-aversion theory with more traditional views that election decisions stem from cost-benefit analyses of union representation. Previous research lacks this integrated approach to the study of election behavior. Regression analyses on a sample of approximately 16,000 certification elections strongly supported the use of risk-aversion theory to predict employees’ willingness to formally participate in elections. Furthermore, we found that time exhibited a statistically significant, negative relationship with voting participation rates, the percentage of union votes, and union victories. The results also indicated that a saturation effect may exist for delays in the election process. Financial support for this research was provided by the Syracuse University Research Fund. The authors wish to thank two anonymous reviewers for helpful suggestions that significantly improved the paper.     

Ballot Design and Unrecorded Votes on Paper-Based Ballots

The 2000 presidential election focused attention on the problemof unrecorded votes, in which a person casts a ballot but failsto record a valid vote for a particular contest. Although muchrecent research has evaluated voting technologies and theireffects on unrecorded votes, there has been little researchon the effects of ballot design. We argue that the same theoriesused to design and evaluate self-administered surveys can beused to analyze ballot features. We collect and code paper-basedballots used in the 2002 general election from 250 countiesin 5 states. We code the ballots in terms of several graphicdesign elements, including the content and location of ballotinstructions and the layout of candidate names and office titles.Our analysis suggests that several ballot features are associatedwith unrecorded votes (both overvotes and undervotes) in thegubernatorial contests. We also find that ballot design featuresexacerbate the racial disparity in unrecorded votes. Ballotdesign can be an important factor in determining whether votersare able to cast a ballot accurately, which can influence thelegitimacy of elections.     

Elections in Post-Communist Ukraine, 1994–2004: An Overview

The paper attempts a comprehensive and theoretically grounded analysis of all parliamentary and presidential elections carried out in Ukraine in the decade 1994 to 2004. It is organized into four sections. The first deals with the electoral system, how it came into being and has been amended, how it translates votes into seats, the "effective number" of political parties in the electorate and the legislature, and the battle over the electoral system itself during the presidency of Leonid Kuchma. In the second section, voting behaviour of the Ukrainian electorate is examined. Using voting data, along with the results of public opinion surveys and reports on the conduct of the various election campaigns, the paper sorts through the relevant determinants of voting choice to identify the most pertinent ones as they operate in the Ukrainian context. Generally speaking, such determinants are: (1) background social characteristics of the voters, including the regional and ethnic factors; (2) the public's assessments of the current political and economic conditions in the country; (3) individual voters' partisan identification and opinions on prominent issues; (4) their retrospective evaluations of the incumbents; (5) leadership qualities of the contenders; and (6) prospective evaluations of parties and candidates as to their expected performance in office. To determine which of these are consistently more important is an essential aim of the paper. The third section assesses the degree to which accountability has been achieved in any of these elections—those to the Verkhovna Rada of 1994, 1998, and 2002, and the presidential elections of 1994, 1999, and 2004. A penultimate section is devoted to evaluating the policy consequences of these elections: what difference have Ukraine's elections made to policies over the past decade? In the concluding portion, a characterization of the emerging party system is given along with a summing-up on the voting behaviour of Ukrainians in the post-communist era.     

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.     

Annick Laruelle and Federico Valenciano: Voting and collective decision-making

The book ‘Voting and Collective Decision Making’ by A. Laruelle and F. Valenciano provides a critical revision of the theoretical foundations of collective yes-or-no decisions. It is a study of the theory of bargaining and voting power, revolving around a fundamental question: given a committee, what voting rule should be used?     

Exploiting polyhedral symmetries in social choice

A large amount of literature in social choice theory deals with quantifying the probability of certain election outcomes. One way of computing the probability of a specific voting situation under the Impartial Anonymous Culture assumption is via counting integral points in polyhedra. Here, Ehrhart theory can help, but unfortunately the dimension and complexity of the involved polyhedra grows rapidly with the number of candidates. However, if we exploit available polyhedral symmetries, some computations become possible that previously were infeasible. We show this in three well known examples: Condorcet’s paradox, Condorcet efficiency of plurality voting and in Plurality voting vs Plurality Runoff.     

The spatial model with non-policy factors: a theory of policy-motivated candidates

The theoretical literature on two candidate elections is dominated by symmetric contests and vote-maximizing candidates. These models fail to capture two important features of real elections. First, most elections pit a stronger candidate against a weaker one. Second, candidates care not only about holding office, but also about policy outcomes. Ignoring any one of these features means we will fail to capture an important dynamic—strong candidates must balance their desire to change policy with their need to win the election. We provide conditions for the existence of an equilibrium in the spatial model with non-policy factors, when candidates are policy motivated. We provide a characterization of ‘regular’ equilibria and show that there exists at most one regular equilibrium. We provide conditions that guarantee that all equilibria are regular. We derive comparative statics for the model and show that increasing a candidate’s non-policy advantage causes that candidate to move towards his ideal point.