On the performance of voting systems in spatial voting simulations

We study the performance of voting systems in terms of minimizing the overall social disutility of making a collective choice in an univariate voting space with ideological voting and perfect information. In order to obtain a distribution of the performance indicator for each of the 12 systems chosen for this study—Baldwin’s Method, Black’s Method, The Borda Count, Bucklin’s Grand Junction System, Coombs’ Method, Dodgson’s System, Instant Run-Off Voting, Plurality, Simpson’s MinMax, Tideman’s Ranked Pairs, Schulze’s Beatpath Method, and Two-Round Majority—we simulate elections using an Agent-Based Computational approach under several different distributions for voters and candidates positioning, with up to 15 available candidates. At each iteration, voters generate complete and strict ordinal utility functions over the set of available candidates, based on which each voting system computes a winner. We define the performance of a system in terms of its capability of choosing among the available candidates the one that minimizes aggregate voter disutility. As expected, the results show an overall dominance of Condorcet completion methods over the traditional and more widely used voting systems, regardless of the distributions of voter and candidate positions.     

Voting power in municipal annexation elections

In many American states, municipal annexation and consolidation require concurrent majority votes of all affected jurisdictions. The effectiveness and fairness of this voting procedure have been criticized on the grounds that a small minority of voters can frustrate the preferences of the overall majority. This paper investigates the extent to which the relative ability of voters in large and small jurisdictions to influence voting outcomes in procedures requiring concurrent majorities is influenced by jurisdictional size. The Banzhaf index, which counts the number of case4s in which a given voter could reverse the overall group decision by changing positions on an issue, is applied to this problem of concurrent voting majorities. Mathematical analysis indicates that the ratio of power between voters in small and large jurisdictions approximately equals the inverse of the square root of the ratio of their population size.     

On the structure of voting systems between two alternatives

Voting systems between two alternatives have been widely studied in the literature of Social Choice. One of the results given by Fishburn (The theory of social choice. Princeton University Press, Princeton, 1973) allows us to characterize anonymous, neutral and monotonic voting systems by means of functions satisfying adequate conditions. From among all kinds of functions, the class of affine functions is highly interesting because from them it is possible to obtain the voting systems most used in practice. In this paper we analyze the structure of the set of these functions and we show that this set is convex and its extreme points are the functions that generate the following voting systems: simple majority, absolute majority, unanimous majority and Pareto majority. Moreover, we suggest a simple method for choosing a voting system when two alternatives are under consideration.     

Weighted representative democracy

We propose a new system of democratic representation. Any voter can choose any legislator as her representative; thus, different legislators can represent different numbers of voters. Decisions in the legislature are made by weighted majority voting, where the weight of each legislator is determined by the number of voters she represents. We show that, if the size of the electorate is very large, then with very high probability, the decisions obtained in the legislature agree with those which would have been reached by a popular referendum decided by simple majority vote.     

Voter turnout in a multidimensional policy space

Many factors influence the likelihood of citizens turning out to vote. In this paper we focus our attention on issue voting, that is, on the likelihood that different policies offered by politicians affect the probability of voting. If voters consider both the benefits and the costs of voting, rational voters will only vote when politicians offer differentiated policies. In a multidimensional policy space this implies that citizens only vote when they perceive enough difference on the issues they care about the most. We investigate the role of voter abstention due to indifference in a unidimensional and a multidimensional policy setting using data from the US National Election Studies for 1972–2000 and find support for our predictions: voters perceiving a small difference between the platforms of the Democratic and Republican parties are less likely to vote; and voters who perceive the two parties as more different on a larger number of issues are significantly more likely to vote.     

An indifference trap of voting

In this paper strategic situations of voting and abstentions are analysed in a three-candidate voting model where voters are indifferent to various alternatives and candidates are interested in winning the election and seeing their most preferred alternative being realized. A specific decision problem is analysed, described by an Indifference Trap Game, with respect to, e.g., the corresponding Nash equilibria, perfect equilibria, and maximin solution. A second-best outcome is contained in the choice set of all three solutions while the Nash equilibrium concept is compatible with the Pareto efficient outcomes of the game.An alternative scenario where candidates suffer from incumbency but voters still are indifferent to some alternatives also supports the second-best outcome. Again, various solutions concepts are applied. We conclude that indifferent voters imply an eminent coordination problem for the candidates in the given voting game which, in general, ends up in inefficient outcomes. The inherent complexity of the decision situation cannot be sufficiently reduced to single out one and only one outcome.     

A comparison of measures to validate scales in voting advice applications

Quality & Quantity - Voting advice applications (VAAs) are online tools providing voting advice to their users. This voting advice is based on the match between the answers of the user and the...     

Maximin choice of voting rules for committees

In the context of a probabilistic voting model with dichotomous choice, we investigate the consequences of choosing among voting rules according to the maximin criterion. A voting rule is the minimum number of voters who vote favorably on a change from the status quo required for it to be adopted. We characterize the voting rules that satisfy the maximin criterion as a function of the distribution of voters’ probabilities to favor change from the status quo. We prove that there are at most two maximin voting rules, at least one is Pareto efficient and is often different to the simple majority rule. If a committee is formed only by “conservative voters” (i.e. voters who are more likely to prefer the status quo to change) then the maximin criterion recommends voting rules that require no more voters supporting change than the simple majority rule. If there are only “radical voters”, then this criterion recommends voting rules that require no less than half of the total number of votes.Received: June 2003, Accepted: September 2004, JEL Classification: D71Salvador Barberá, Carmen Beviá, Mirko Cardinale, Wioletta Dziuda, Joan Esteban, Mahmut Erdem, Bernard Grofman, Matthew Jackson, Kai Konrad, Raul Lopez, Jordi Massó, Hugh Mullan, Shmuel Nitzan, Ana Pires do Prado, Elisabeth Schulte, Arnold Urken and two anonymous referees provided helpful comments. Finally, I also acknowledge financial support from Capes, Brazilian Ministry of Education and Spanish Ministry of Science and Technology (Project BEC2002-02130).     

A Note on the Probability of Having a Strong Condorcet Winner

In an election, a strong Condorcet winner is a candidate who is top-ranked by more than 50% of the voters. The purpose of this note is to provide some algebraic representations for the probability of having a strong Condorcet winner in three-candidate elections. Three alternative procedures for generating voting situations are considered: the Impartial Culture condition, the Impartial Anonymous Culture condition and the Maximal Culture condition. It turns out that the conclusions we obtain strongly depend on the way for generating voting situations.     

Modeling undecided voters to forecast elections: From bandwagon behavior and the spiral of silence perspective

Forecasting election results has been a highly attractive activity among political and social scientists. Different forecasting methods have been proposed, but those based on public opinion polls are the most common. However, there are challenges to using opinion polls, especially because they neglect undecided voters. Due to the significant number of undecided participants and their impact on voting outcomes, we analyze the potential behavior of undecided voters by considering opinion polls and sentiment based on voter expectation from the perspective of the bandwagon effect and the spiral of silence. We establish a hierarchical Bayesian forecasting model to predict voting results, and apply it to the 2016 United States presidential election and the 2016 Brexit referendum. The results of our model suggest that voting outcomes are more predictable when fully utilizing the impact of undecided voters. The results indicate that integrating aggregated polls into the hierarchical Bayesian framework is a strong predictor for forecasting outcomes, and they provide evidence for the influence of sentiment based on voter expectation in forecasting election results.     

Epistemic democracy with correlated voters

We develop a general theory of epistemic democracy in large societies, which subsumes the classical Condorcet Jury Theorem, the Wisdom of Crowds, and other similar results. We show that a suitably chosen voting rule will converge to the correct answer in the large-population limit, even if there is significant correlation amongst voters, as long as the average covariance between voters becomes small as the population becomes large. Finally, we show that these hypotheses are consistent with models where voters are correlated via a social network, or through the DeGroot model of deliberation.     

Bargaining through Approval

The paper considers two-person bargaining under Approval Voting. It first proves the existence of pure strategy equilibria. Then it shows that this bargaining method ensures that both players obtain at least their mean utility level in equilibrium. Finally it proves that, provided that the players are partially honest, the mechanism triggers sincerity and ensures that no alternative Pareto dominates the outcome of the game.     

A simple voting scheme generates all binary relations on finite sets

A simple head-to-head voting scheme in which voters hold complete and transitive preferences over alternatives generates all binary relations on finite sets. The minimal number of voters required to generate a binary relation provides a measure of complexity for binary relations. Complexity so defined tells us, by how much a given binary relation fails to qualify as a total preorder.     

A political economy model of road pricing

In this paper, we use a simple majority voting model to study the introduction of urban congestion tolls. The model allows for different types of uncertainty and considers different uses of the toll revenues. The following results are obtained. First, we show that individual uncertainty with respect to modal substitution costs may imply that a majority votes against road pricing ex ante, although a majority would have been in favor after its introduction ex post. Moreover, if a majority is against road pricing ex ante, there will also be no majority for organizing an experiment that would take away the individual uncertainty. Second, political uncertainty with respect to the use of the revenues corroborates the finding that ex ante more voters will be against the introduction of tolls. Third, both types of uncertainty suggest that fewer voters are against road pricing when toll revenues are used to subsidize public transport than when they are redistributed to all voters. Importantly, the results of this paper are consistent with a number of recent empirical observations on efforts to introduce road pricing, including the systematic rejection of road pricing in referenda, the more favorable attitudes towards road pricing after than before its introduction, and tying the toll revenues to support public transport.     

May’s theorem in an infinite setting

We generalize May’s theorem to an infinite setting, preserving the elementary character of the original theorem. We define voting scenarios and generalized voting scenarios, and prove appropriate versions of May’s theorem. The case of generalized voting scenarios specialized to a countably infinite set of voters and the collections of all coalitions that have asymptotic density, shows that majority rule is the only aggregation rule that satisfies neutrality, irrelevance of null coalitions, anonymity, and positive responsiveness.     

Campaign dynamics of cognitive accessibility of political judgments: measuring the impact of campaigns and campaign events using response latencies in two German rolling cross section studies

Do campaigns matter? Based on two rolling cross-section computer-assisted telephone surveys conducted in the run-up to the 2009 and 2013 German Federal Election, we test whether we can detect campaign effects on the accessibility of voters’ judgments: how do response latencies of political judgments evolve over the course of campaigns? The study uses response latencies, i.e. the standardized time it takes respondents to answer a survey question, as a proxy measurement of cognitive accessibility of political judgments. If campaigns do help voters to make up their minds, we should be able to observe changes at the implicit level of response latencies. Do people answer questions about their voting behavior and political attitudes faster as Election Day comes closer? Our results suggest that attitudes towards candidates and voting intentions become more cognitively accessible during campaigns whereas the accessibility of party identification is conditional on the contextual features of campaigns. In addition we find specific short-term effects of TV debates.     

Can People Explain Their Own Vote? Introspective Questions as Indicators of Salience in the 1995 Quebec Referendum on Sovereignty

Most scholars doubt that voters are able to explain their own vote. We argue that introspective questions whereby respondents are invited to tell, in their own words, the reasons why they vote the way they do, provide useful information on which considerations are most salient in their voting decisions. We show that open-ended questions about reasons for voting Yes or No in the 1995 Quebec referendum on sovereignty help us to sort out subgroups of voters for whom a given consideration is more salient.     

Voting over selective immigration policies with immigration aversion

Selective immigration policies set lower barriers to entry for skilled workers. However, simple economic intuition suggests that skilled majorities should welcome unskilled immigrants and protect skilled natives. This paper studies the voting over a selective policy in a two-country, three-factor model with skilled and unskilled labor, endogenous migration decisions, costly border enforcement and aversion to immigration. Results show that heterogeneity in capital distribution forces skilled voters to form a coalition with unskilled voters, who become pivotal. The voting outcome is therefore biased towards the preferences of the latter, and consists in a selective protectionism. Finally, immigration aversion helps to explain why skilled majorities do not bring down entry barriers against unskilled workers.     

Voter decisions on eminent domain and police power reforms

One unresolved issue arising from the use of eminent domain power involves how the perceived benefits and costs of eminent domain power affect people’s positions on the reform of eminent domain and police power law. The paper addresses this issue by estimating a voting model that explains voters’ decisions on eminent domain and police power reform referenda in the US. Estimates indicate that eminent domain referendum outcomes hinged on voters’ fundamental values and ideology, and voters’ immediate self-interest. Voters’ fundamental values and ideology affects referendum outcomes insofar as educational attainment in a county has a statistically significant effect on support for reform. Despite the greater incidence of eminent domain in low income and poorer communities, success of reform referenda in this study was found to be greater in counties with higher incomes and lower unemployment rates. This implies that whatever asymmetry exists in the exercise of eminent domain law across income groups does not affect voter reaction to eminent domain reforms. Moreover, counties with high unemployment rates consider the larger potential benefits from urban renewal projects in vote decision-making providing a link between self-interest and voting behavior.     

Dynamics in the fragmentation of political party systems

Fragmentation is an important dimension of political party systems. It concerns the proliferation of minor parties and the willingness of voters to vote for them. Past research relates party fragmentation to the voting system in a country; by Duverger's hypothesis, fragmentation should be highest in counties with proportional representation. The entropy measure is used to quantify fragmentation. The upper limit of fragmentation is analyzed in 24 countries, and the patterns of change in fragmentation are identified with mathematical difference equations, testing the idea that voters and parties evolve toward an equilibrium in fragmentation. The highest level of fragmentation is found comparable with a psychological limit on human information processing. In 17 of 22 countries, fragmentation moves toward an equilibrium, regardless of the type of voting system, and countries with higher equilibrium levels usually evolve more slowly. The results affirm the stability of democratic governments but raise questions about voters' strategies and suggest that some voters may try to control fragmentation when they vote.