Manipulability of voting by sincere truncation of preferences

A weak form of strategic voting, called ‘sincere truncation,’ occurs when a voter with a strict preference ranking does not rank all his or her choices on the ballot. A voting procedure is said to be manipulable by sincere truncation if one or more voters can obtain a preferred outcome through sincere truncation. Voting procedures that are not manipulable by sincere truncation are shown to be incompatible with the election of Condorcet (majority) candidates when they exist. A relaxation of simple majority rule, called the ‘7/12 rule,’ is also shown to conflict with nonmanipulability when additional conditions are imposed. These results are formally independent of the strategy-proofness theorems for voting and decision schemes established by Gibbard, Satterthwaite, and others. While their analyses are more inclusive in terms of the varieties of decision procedures allowed, they are also less demanding in their requirements for manipulability since voters are permitted to reverse sincere pReferences in their voting. Thus, plurality voting is manipulable in the sense of Gibbard-Satterthwaite (by preference reversals), but it is clearly nonmanipulable by sincere truncation.     

Roadmaps to Representation: An Experimental Study of How Voter Education Tools Affect Citizen Decision Making

Efforts to educate citizens about the candidates and issues at stake in elections are widespread. These include distributing voter guides describing candidates’ policy views and interactive tools conveying similar information. Do these voter education tools help voters identify candidates who share their policy views? We address this question by conducting survey experiments that randomly assign a nonpartisan voter guide, political party endorsements, a spatial map showing voters their own and the candidates’ ideological positions, or both a spatial map and party endorsements. We find that each type of information strengthens the relationship between voters’ policy views and those of the candidates they choose. These effects are largest for uninformed voters. When spatial maps and party endorsements send conflicting signals, many voters choose candidates with more similar policy views, against their party’s recommendation. These results contribute to debates about citizen competence and demonstrate the efficacy of practical efforts to inform electorates.

     

Campaign civility under preferential and plurality voting

We present reasons to expect that campaigns are less negative under preferential voting. We then examine if preferential voting systems affect how people perceive the conduct of elections. This paper reports results from surveys designed to measure voters‘ perceptions of candidates’ campaigns, comparing places with plurality elections to those that used preferential voting rules. Our surveys of voters indicate that people in cities using preferential voting were significantly more satisfied with the conduct of local campaigns than people in similar cities with plurality elections. People in cities with preferential voting were also less likely to view campaigns as negative, and less likely to respond that candidates were frequently criticizing each other. Results are consistent across a series of robustness checks.     

Optimal voting rules under uncertainty

The theory of ‘constitutional’ choice of voting rules developed by Buchanan and Tullock is an extended to an explicit decision-theoretic form. Voters in the ‘constitutional’ position choose what they believe will be their optimal share or majority rule for making social decisions, by maximizing their individual expected utility from the anticipated social decisions, under conditions of uncertainty. The rule that maximizes expected social benefits depends upon (1) the expected distribution and intensity of preferences on future issues, and (2) the decisionmaking procedures and costs. ‘Decisionmaking’ and ‘external’ costs are shown to be interrelated. Following this analysis, failure to pass laws imposes ‘external’ costs in the same way that passing them does, so that the optimal majority may be lower when desirable laws are viewed as changing over time. Decisionmaking costs depend upon the way in which voters are persuaded to support or oppose bills, upon the distribution of preferences on bills, and on vote-trading possibilities. If vote-trading is almost costless, a wide range of decision rules has nearly equal social benefits. Finally, the model is used to discuss optimal voting rules for several decisionmaking bodies.     

Setting the record straight: A note on sophisticated voting under Borda's method

The purpose of this note is to correct some inaccuracies in the literature regarding sophisticated voting under Borda's method. It is shown that if a single candidate must be elected and voters vote sophisticatedly under Borda's method, then: (1) Contrary to both Black's (1976) and Ludwin's (1978) claims, a voter's undominated voting strategy may require him not to give top ranking to his most preferred candidate; (2) Contrary to Black's (1976) claim, an undominated strategy may be such that all candidates except the most preferred one are ranked last; (3) Whereas a candidate who constitutes the true bottom preference of an absolute majority of the voters will never be elected if voters vote sincerely, this candidate may be elected if voters vote strategically; (4) The election of a candidate who constitutes the true top preference of an absolute majority of the voters is not systematic: ceteris paribus this candidate may be definitely elected when voters vote sincerely but not when they vote strategically, as well as vice versa.     

Institutional Arrangements and Logrolling: Evidence from the European Union

This article illustrates how voting rules used to pass a piece of legislation and the structure of the legislation, in terms of whether or not it has single or multiple issue dimensions, influence the frequency and the purpose of position changes in legislative negotiations. Through analysis of data on a set of legislative proposals negotiated in the European Union, I show that position changes are less common under unanimity rule than under majority rule. More importantly, I argue and show that when the negotiated legislation is multidimensional (i.e., contains multiple issues) and the voting rule is unanimity, position changing is a lucrative strategy for legislators. Multidimensional legislation creates opportunities for logrolling, and legislators’ veto power under the unanimity rule enables them to exploit these opportunities. Accordingly, under this scenario, legislators often engage in what I call a within‐legislation logroll and secure favorable legislative outcomes.     

Implementing the Borda outcome via truncated scoring rules: a computational study

This study is an attempt to empirically understand the likelihood of choosing the Borda outcome through a truncated scoring rule when n voters are asked to report only part of their linear preferences over m alternatives. We run Monte Carlo simulations through a grid search algorithm as we employ an impartial culture model to sample voters’ preferences. Given the range of parameter values we consider, we report the truncated scoring rules that maximize the likelihood of implementing the Borda outcome and how the maximum likelihood changes with m and n. We also present our results on the relative performances of some popular truncated voting rules, such as plurality and approval voting, in implementing the Borda outcome and demonstrate that two-level approval voting performs significantly better than the plurality rule. Moreover, we propose the expected Borda rule as a good proxy for the best implementor of the Borda rule among all truncated rules.     

Do electoral rules have an effect on electoral behaviour? An impact assessment

Abstract

Electoral democracies worldwide are all organised around elections but the rules under which the elections are organised differ greatly from one country to another. These electoral rules, such as whether voting is compulsory or what electoral system is used, are thought of as strongly affecting voters’ behaviour and the choices they make. If electoral rules indeed shape citizens’ electoral behaviour, the implication is that theories of what explains voters’ choices are country-specific as well. This is in sharp contrast to the idea that theories of electoral behaviour are generalisable. This special issue tackles this question and offers an assessment of the impact of electoral rules on voters’ behaviour, on the one hand, and the generalisability of individual-level theories of voting behaviour, on the other. The collection of papers furthermore offers an important contribution in terms of the kind of electoral rules that are scrutinised, with several papers focusing on the little-investigated phenomenon of preferential voting.     

A power measure analysis of Amendment 36 in Colorado

Colorado’s Amendment 36 proposed to switch Colorado’s representation in the Electoral College from winner-takes-all to proportionality. We evaluate unilateral and uniform switches to proportionality both from Colorado’s perspective and from an impartial perspective on the basis of a priori and a posteriori voting power measures. The present system is to be preferred to a unilateral switch from any perspective on any measure. A uniform switch is to be preferred to the present system from Colorado’s perspective on an a priori measure, and from an impartial perspective on an a posteriori measure. The present system is to be preferred to a uniform switch from Colorado’s perspective on an a posteriori measure (with some qualifications), and from an impartial perspective on an a priori measure. We conclude with a discussion of the appropriateness of these measures.     

A critical reappraisal of some voting power paradoxes

Power indices are meant to assess the power that a voting rule confers a priori to each of the decision makers who use it. In order to test and compare them, some authors have proposed ‘natural’ postulates that a measure of a priori voting power ‘should’ satisfy, the violations of which are called ‘voting power paradoxes.’ In this paper two general measures of success and decisiveness based on the voting rule and voters' behavior and some of these postulates/paradoxes test each other. As a result serious doubts are cast on the discriminating power of most voting power postulates.     

Collective decision-making of voters with heterogeneous levels of rationality

This paper studies the collective decision-making processes of voters who have heterogeneous levels of rationality. Specifically, we consider a voting body consisting of both rational and sincere voters. Rational voters vote strategically, correctly using both their private information and the information implicit in other voters’ actions to make decisions; sincere voters vote according to their private information alone. We first characterize the conditions under which the presence of sincere voters increases, reduces, or does not alter the probabilities of making correct collective decisions. We also discuss how the probabilities change when the incidence of sincere voters in the population varies. We then characterize the necessary and sufficient condition under which informational efficiency can be achieved when sincere voters coexist with rational voters. We find that when sincere voters are present, supermajority rules with high consensus levels are not as desirable as they are in rational voting models, as informational efficiency fails under such voting rules.

     

Which voting rule is most likely to choose the “best” candidate?

One criterion for evaluating voting rules is the frequency with which they select the best candidate. Using a spatial model of voting that is capable of simulating data with the same statistical structure as data from actual elections, we simulate elections for which we can define the best candidate. We use these simulated data to investigate the frequencies with which 14 voting rules chose this candidate as their winner. We find that the Black rule tends to perform better than the other rules, especially in elections with few voters. The Bucklin rule, the plurality rule, and the anti-plurality rule tend to perform worse than the other 11 rules, especially in elections with many voters.     

Efficacy,power and equity under approval voting

Approval voting allows each voter to vote for as many candidates as he wishes in a multicandidate election. Previous studies show that approval voting compares favorably with other practicable election systems. The present study examines the extent to which votes for different numbers of candidates can affect the outcome. It also considers generic powers of voters and the extent to which approval voting treats voters equitably. If there are three candidates, votes for one or two candidates are equally efficacious in large electorates. For four or more candidates, votes for about half the candidates are most efficacious. Although inequities among voters can arise under approval voting, the common plurality voting system is considerably less equitable than approval voting.     

Early Voting Changes and Voter Turnout: North Carolina in the 2016 General Election

North Carolina offers its residents the opportunity to cast early in-person (EIP) ballots prior to Election Day, a practice known locally as “One-Stop” voting. Following a successful legal challenge to the state’s controversial 2013 Voter Information and Verification Act, North Carolina’s 100 counties were given wide discretion over the hours and locations of EIP voting for the 2016 General Election. This discretion yielded a patchwork of election practices across the state, providing us with a set of natural experiments to study the effect of changes in early voting hours on voter turnout. Drawing on individual-level voting records from the North Carolina State Board of Elections, our research design matches voters on race, party, and geography. We find little evidence that changes to early opportunities in North Carolina had uniform effects on voter turnout. Nonetheless, we do identify areas in the presidential battleground state where voters appear to have reacted to local changes in early voting availability, albeit not always in directions consistent with the existing literature. We suspect that effects of changes to early voting rules are conditional on local conditions, and future research on the effects of election law changes on turnout should explore these conditions in detail.

     

Candidates’ policy strategies in primary elections: does strategic voting by the primary electorate matter?

Empirical research reports conflicting conclusions about whether primary election voters strategically account for candidates’ general election prospects when casting their votes. We model the strategic calculations of office-seeking candidates facing two-stage elections beginning with a primary, and we compare candidates’ policy strategies in situations where primary voters strategically support the most viable general election candidate against candidate strategies when voters expressively support their preferred primary candidate regardless of electability. Our analyses—in which the candidates’ appeal is based on their policy positions and their campaigning skills—suggest a surprising conclusion: namely, that strategic and expressive primary voting typically support identical equilibrium configurations in candidate strategies. Our conclusions are relevant to candidates facing contested primaries, and also to political parties facing the strategic decision about whether or not to use primary elections to select their candidates—a common dilemma for Latin American (and some European) parties.     

Introduction to welfare economics

We show that a transfer received by a minority of the population may be sustained by majority voting, however small the minority targeted may be, when the attribution of the transfer is seen as stochastic by voters. We build a simple model wherein voters differ in income and vote over a proportional tax whose proceeds are distributed lump-sum, and each voter has a probability of receiving the transfer that depends on his income. In progressive steps, we present intuitively appealing sufficient conditions on this probability function for the social program to be supported by majority voting. We also develop intuitive conditions for the emergence of the “paradox of redistribution”, whereby more focused targeting reduces the size of the transfer program chosen by the majority. We finally apply our framework to the French social housing program and obtain that our model is consistent with a majority of French voters supporting a positive size for that program.     

Informational limits to democratic public policy: The jury theorem, yardstick competition, and ignorance

Condorcet’s jury theorem provides a possible explanation for the success of democracies relative to other forms of government. In its modern form, the jury theorem predicts that majority decisions are well informed, because they are based upon far more information than possessed by any single individual. On the other hand, it is evident that democratic politicians and policies are not always as good as the jury theorem implies they should be. This paper uses simulated elections to explore the power and limitations of majority rule as an estimator of candidate quality or policy effectiveness. The simulations demonstrate that slightly informed voters can make very accurate choices among candidates using majority rule. However, as the ratio of slightly informed voters relative to ignorant voters falls, the accuracy of majority decisions declines. The latter implies that institutions, policies, and technologies that promote the dissemination of information also tend to improve the efficiency of democratic governance.     

Designing preference voting

Electoral systems in which voters can cast preference votes for individual candidates within a party list are increasingly popular. To the best of our knowledge, there is no research on whether and how the scale used to evaluate candidates can affect electoral behavior and results. In this paper, we analyze data from an original voting experiment leveraging real-life political preferences and embedded in a nationally representative online survey in Austria. We show that the scale used by voters to evaluate candidates makes differences. For example, the possibility to give up to two points advantages male candidates because male voters are more likely to give ‘zero points’ to female candidates. Yet this pattern does not exist in the system in which voters can give positive and negative points because male voters seem reluctant to actively withdraw points from female candidates. We thus encourage constitution makers to think carefully about the design of preference voting.     

Racial or Spatial Voting? The Effects of Candidate Ethnicity and Ethnic Group Endorsements in Local Elections

With the growth of Latino and Asian American populations, candidates frequently must appeal to diverse electorates. Strategies for doing so include emphasizing candidates’ racial/ethnic identity and securing endorsements from racial/ethnic groups. While many scholars focus on candidates’ racial/ethnic attributes, ethnic group endorsements are understudied. Whether such endorsements induce voters to choose ideologically similar candidates (spatial voting), or choose based on race/ethnicity (racial voting) is unclear. We address this question by examining elections in multiethnic local settings. Using original surveys and exit polls, we create comparable measures of candidate and voter ideology, and examine how race/ethnicity and ideology affect voters’ choices. We also embed experiments that manipulate ethnic group endorsements. We find that ideology influences voters’ choices, but that ethnic group endorsements weaken spatial voting. The latter effect among whites is driven by racial/ethnic stereotypes. These reactions explain why some candidates seek such endorsements and why others might prefer to avoid them.     

The paradox of grading systems

We distinguish between (i) voting systems in which voters can rank candidates and (ii) those in which they can grade candidates, using two or more grades. In approval voting, voters can assign two grades only—approve (1) or not approve (0)—to candidates. While two grades rule out a discrepancy between the average-grade winners, who receive the highest average grade, and the superior-grade winners, who receive more superior grades in pairwise comparisons (akin to Condorcet winners), more than two grades allow it. We call this discrepancy between the two kinds of winners the paradox of grading systems, which we illustrate with several examples and whose probability we estimate for sincere and strategic voters through a Monte Carlo simulation. We discuss the tradeoff between (i) allowing more than two grades, but risking the paradox, and (ii) precluding the paradox, but restricting voters to two grades.