Mathematical structure of voting paradoxes

Summary. A theory is developed to identify, characterize, and explain all possible positional and pairwise voting outcomes that can occur for any number of alternatives and any profile. This paper describes pairwise voting where new results include explanations for all paradoxes, cycles, conflict between Borda and Condorcet rankings, differences among procedures using pairwise votes (such as the Borda Count, Kemeny's method, and the Arrow-Raynaud rule), and discrepancies among the societal rankings as candidates are dropped or added. Other new results include new relationships among the Borda and Condorcet "winners" and "losers." The theory also shows how to construct all supporting profiles. The following companion paper does the same for positional methods.     

The effect of randomized school admissions on voter participation

There is little causal evidence on the effect of economic and policy outcomes on voting behavior. This paper uses randomized outcomes from a school choice lottery to examine if lottery outcomes affect voting behavior in a school board election. We show that losing the lottery has no significant impact on overall voting behavior; however, among white families, those with above median income and prior voting history, lottery losers were significantly more likely to vote than lottery winners. Using propensity score methods, we compare the voting of lottery participants to similar families who did not participate in the lottery. We find that losing the school choice lottery caused an increase in voter turnout among whites, while winning the lottery had no effect relative to non-participants. Overall, our empirical results lend support to models of expressive and retrospective voting, where likely voters are motivated to vote by past negative policy outcomes.     

How many voters are needed for paradoxes?

Summary. This paper presents a general procedure for finding profiles with the minimum number of voters required for many important paradoxes. Borda's and Condorcet's classic examples are revisited as well as generalizations. Using Saari's procedure line, we obtain an upper bound for the minimum number of voters needed for a profile for which the Condorcet winner is not strictly top ranked for all weighted positional procedures. Also we give a simple upper bound on the minimum number of voters needed for a set of prescribed voting outcomes. In contrast to situations wherein small numbers of voters are needed, we consider paradoxes requiring arbitrarily large numbers of voters as well as large numbers of alternatives. Finally we indicate connections with statistical rank based tests. Received: April 18, 2001; revised version: May 25, 2001     

The Disunity of Unanimity

Unanimity is the optimal voting rule in a world of zero transactions costs, when side payments are impossible. When side payments are available and transactions costs are zero, the voting rule is irrelevant to the ultimate outcome. In the more realistic situation where side payments are allowed but transactions costs are positive, a unanimity voting rule creates situations where the collective choice may fail a proposed measure even if all members favor the measure in principle. This evidences a disunity between unanimity rules and unanimous outcomes. Constitutional design should focus on rules leading to unanimous outcomes, as opposed to unanimity rules.     

The likelihood of dubious election outcomes

Summary. A disturbing phenomenon in voting, which causes most of the problems as well as the interest in the field, is that election outcomes (for fixed preferences) can change with the way the ballots are tallied. This causes difficulties because with each possible choice, some set of voters can be dubious about whether it is the “correct” one. But, how likely are these settings allowing multiple election outcomes? By combining properties of the geometry of voting developed by Saari with a analytic-geometric technique created by Schlafli, we determine the likelihood that a three candidate election can cause these potentially dubious outcomes. Received: April 11, 1997; revised version: November 12, 1997     

Deliberative voting

We analyze a model of jury decision making in which jurors deliberate before casting their votes. We consider a wide range of voting institutions and show that deliberations render these equivalent with respect to the sequential equilibrium outcomes they generate. In particular, in the context of a jury setup, all voting rules excluding the two types of unanimity rules (one requiring a unanimous consensus to acquit, one requiring a unanimous consensus to convict) induce the same set of equilibria outcomes. We show the robustness of our results with respect to several restrictions on communication protocols and jurors’ strategies. Furthermore, we demonstrate that our observations extend to practically all of the voting structures commonly studied in the voting literature. The paper suggests the importance of accounting for communication in models of collective choice.     

Approval voting with endogenous candidates

We present a formal model of political competition under approval voting which allows for endogenous candidate entry. Our analysis yields a number of novel insights. First, we develop a notion of sincere voting behavior under approval voting, called relative sincerity. We then show that the relatively sincere voting behavior is consistent with the strategic calculus of voting. Second, we show that in a one-dimensional model with distance preferences, equilibria in relatively sincere strategies and without spoiler candidates always generate outcomes close to the median voter. Moreover, approval voting satisfies Duverger's Law in the sense that there are at most two winning positions! Finally, we extend our analysis to arbitrary policy spaces. In the general setting, approval voting is shown to be susceptible to the same kinds of problems as the plurality rule, such as the possibility of non-majoritarian outcomes, failure to elect the Condorcet winner and existence of spoiler candidates.     

Inequality aversion and voting on redistribution

Some people have a concern for a fair distribution of incomes while others do not. Does such a concern matter for majority voting on redistribution? Fairness preferences are relevant for redistribution outcomes only if fair-minded voters are pivotal. Pivotality, in turn, depends on the structure of income classes. We experimentally study voting on redistribution between two income classes and show that the effect of inequality aversion is asymmetric. Inequality aversion is more likely to matter if the “rich” are in majority. With a “poor” majority, we find that redistribution outcomes look as if all voters were exclusively motivated by self-interest.     

CANDIDATE VALENCE: EVIDENCE FROM CONSECUTIVE PRESIDENTIAL ELECTIONS*

This article develops and estimates a dynamic spatial model of voting. The distribution of voters' policy positions and candidates' valence are recovered using individual‐level data on voting decisions in two consecutive presidential elections. The estimated model is used to provide an equilibrium interpretation of observed individual voting profiles and aggregate electoral outcomes as well as to conduct counterfactual experiments that assess the impact of candidates' policy positions, valence, and voters' information on electoral outcomes.     

Elections and unemployment benefits for families: Did the Family Benefit Dispute affect election outcomes in Germany?

Underlying reasons for certain voting outcomes are subject to a vivid debate – especially in times of landslide changes in voting outcomes of long-established parties in many European countries including Germany. The linkages between these voting outcomes and economic indicators are rather elusive since many confounding and unobservable aspects determine voting decisions. Exploiting a quasi-natural experiment resulting from a legislation change in the German state of Bavaria that effectively increased family benefits for unemployment benefit recipients in certain districts, we try to identify the effect of this legislation on voting outcomes in the Bavarian state election of 2018. While we do not find a significant effect on general election outcomes in the affected districts, our results imply that the general debate seems to have affected the voting behavior of families with unemployment benefits and children under the age of three.     

Voting over selfishly optimal tax schedules: Can Pigouvian tax redistribute income?

This paper studies pairwise majority voting over selfishly optimal nonlinear income tax schedules proposed by a continuum of individuals who differ in privately observable skills and make consumption comparisons, which creates a negative positional externality. It shows that the tax schedule preferred by the median skill type will win the voting contest. Given a reference consumption defined as the average consumption in the population, all skills face the same Pigouvian tax rate in the utilitarian optimum, whereas in selfish optima high skills face a Pigouvian tax rate larger than that facing low skills, generating a novel income redistributive effect. Under a constant elasticity of labor supply, two more results are obtained. First, for Pareto, Champernowne, Weibull, and lognormal skill distributions, the selfishly optimal tax schedule facing high (low) skills tends to be more progressive when the bottom‐skill's (top‐skill's) status concern intensifies. Second, it identifies the conditions under which, in the voting equilibrium, high skills face higher marginal tax rates while low skills face lower ones than what they face in the utilitarian optimum.     

A new approach to measure tactical voting: evidence from the British elections

Although tactical voting attracts a great deal of attention, it is very hard to measure as it requires knowledge of both individuals’ voting choices as well as their unobserved preferences. In this article, we present a simple empirical strategy to nonparametrically identify tactical voting patterns directly from balloting results. This approach allows us to study the magnitude and direction of strategic voting as well as to verify which information voters and parties take into account to determine marginal constituencies. We show that tactical voting played a significant role in the 2010 election, mainly for Liberal–Democratic voters supporting Labour. Moreover, our results suggest that voters seem to form their expectations based on a national swing in vote shares rather than newspaper guides published in the main media outlets or previous election outcomes. We also present some evidence that suggests that campaign spending is not driving tactical voting.     

The structure of bias in peer voting systems: lessons from the Eurovision Song Contest

This paper assesses whether and how common characteristics of jury members or peer voters affect the outcomes of voting systems. In particular, we analyze to what extent these common features result in voting bias. We take as a case study the Eurovision Song Contest for which an extensive amount of historical data is available. In contrast to earlier studies we analyze the impact of common factors on the bias individually for each country, which is necessary to substantiate the publicly debated accusations of regional block voting by certain groups of countries. We establish strong evidence for voting bias in the song contest on the basis of geography, even after correction for culture, language, religion and ethnicity. However, these effects do generally not correspond to the usual accusations. We believe that our findings extend to all instances where groups of jury members or peer voters share certain common factors, which may cause voting bias. It is important to identify such structures explicitly, as it can help avoiding bias in the first place. The authors are grateful to Marieke van Dijk for excellent research assistance and to Laurens Swinkels, Ieva Pudane, Gijsbert van Lomwel, Jelena Stefanovic, and Bas van den Heuvel for useful comments. The usual disclaimer applies.     

Get Out The Vote: How Encouraging Voting Changes Political Outcomes

How do measures to increase turnout affect election outcomes? I use a novel approach to analyze how these measures influence both voter turnout and the candidates' political positions. In general, lowering the net expense of voting reduces political polarization. If the net expense of voting is made very low, then candidates no longer have an incentive to take partisan positions to motivate turnout and will converge at the median voter's ideal point. For small changes in the net expense of voting, however, decreasing the cost of voting and penalties for not voting (two common measures) can result in drastically different political outcomes. Counter intuitively, measures that make voting cheaper might not increase turnout: since these measures decrease the difference between the candidates' political positions, they also decrease the benefit of voting.     

Would letting people vote for multiple candidates yield policy moderation?

We investigate whether letting people vote for multiple candidates would yield policy moderation. We do so in a setting that takes three key features of elections into account, namely, strategic voting, endogenous candidacy and policy motivation on the part of the candidates. We consider two classes of voting rules. One class consists of the voting rules where each voter casts several equally-weighed votes for the different candidates. The other class consists of the voting rules where each voter rank-orders the candidates. We identify conditions under which these voting rules yield policy moderation. We also show that these voting rules may yield policy extremism instead of policy moderation if one (or several) of the conditions is not satisfied! Finally, we find that amongst these voting rules the extent of policy moderation is maximal under the Borda Count if we consider only equilibria where all candidates are serious contenders. However, this result does not carry over to spoiler equilibria, where Approval Voting can yield more moderate policy outcomes than the Borda Count.     

Italy’s demographic trap: Voting for childcare subsidies and fertility outcomes

In this paper we study how population aging impacts the age distribution of the voting electorate and voters’ choices over childcare subsidies. We build a computable general equilibrium framework populated by heterogeneous agents who, over the course of their life-cycle, make endogenous and age-dependent fertility choices. The model is calibrated to match economic and population outcomes of the Italian economy. Child support favors young and fertile cohorts but can also impact all population subgroups through changes in prices, income taxation and population growth. A probabilistic voting model is used to measure voting outcomes over a range of childcare subsidy levels and tax policies. Our findings show that childcare subsidies have a positive impact on the total fertility rate and are welfare improving when financed with both capital and labor income taxation and in combination with lower pension contribution rates. A 10 percent increase in the level of subsidies can increase the population growth rate by an average of 0.47–0.70 percentage points. We find that voting choices of different population subgroups, while depending on the tax used to finance new expenditure, lead to lower levels of childcare subsidies, lower fertility rates and to a demographic ‘trap’.     

Compulsory versus voluntary voting: An experimental study

We report on an experiment comparing compulsory and voluntary voting institutions in a voting game with common preferences. Rational choice theory predicts sharp differences in voter behavior between these two institutions. If voting is compulsory, then voters may find it rational to vote insincerely, i.e., against their private information. If voting is voluntary so that abstention is allowed, then sincere voting in accordance with a voter's private information is always rational while participation may become strategic. We find strong support for these theoretical predictions in our experimental data. Moreover, voters adapt their decisions to the voting institution in place in such a way as to make the group decision accuracy differences between the two voting institutions negligible. The latter finding may serve to rationalize the co-existence of compulsory and voluntary voting institutions in nature.     

A foundation for strategic agenda voting

We offer complete characterizations of the equilibrium outcomes of two prominent agenda voting institutions that are widely used in the democratic world: the amendment, also known as the Anglo-American procedure, and the successive, or equivalently the Euro-Latin procedure. Our axiomatic approach provides a proper understanding of these voting institutions, and allows comparisons between them, and with other voting procedures.     

Non-consequentialist voting

Standard theory assumes that voters’ preferences over actions (voting) are induced by their preferences over electoral outcomes (policies, candidates). But voters may also have non-consequentialist (NC) motivations: they may care about how they vote even if it does not affect the outcome. When the likelihood of being pivotal is small, NC motivations can dominate voting behavior. To examine the prevalence of NC motivations, we design an experiment that exogenously varies the probability of being pivotal yet holds constant other features of the decision environment. We find a significant effect, consistent with at least 12.5 percent of subjects being motivated by NC concerns.     

Emigrants’ missing votes

What are the causal effects of emigration on election outcomes in the country of origin? Large emigration of high-skilled emigrants can lead to changes in the distribution of political preferences, which affect voting outcomes. Using administrative migration and voting data, we show that emigration from Poland following its accession to the European Union in 2004 caused an increase in vote shares for right-wing parties, while decreasing the vote share for left-wing parties due to emigrants’ missing left-leaning votes. To account for endogenous migration patterns, we construct an innovative instrument that measures the distance to the closest open EU border. Our results highlight that emigration enhances stayers’ trust in right-wing governments and increases stayers’ voting for parties with pro-European positions. Exploiting a change in voting rules over time allows to disentangle different mechanisms. These results have important implications for the design of voting policies.