Stochastic Voting Research Articles

Truth-revealing voting rules for large populations

We propose a new solution to the problem of strategic voting for large electorates. For any deterministic voting rule, we design a stochastic rule that asymptotically approximates it in the following sense: for a sufficiently large population of voters, the stochastic voting rule (i) incentivizes every voter to reveal her true preferences and (ii) produces the same outcome as the deterministic rule, with arbitrarily high probability. We then apply these results to obtain an implementation in Bayesian Nash equilibrium.

Vote-motivated candidates

We study stochastic voting models where the candidates are allowed to have any smooth, strictly increasing utility functions that translate vote shares into payoffs. We find that if a strict Nash equilibrium exists in a model with an infinite number of voters, then nearby equilibria should exist for similar large, but finite, electorates. If the votes are independent random events, then equilibria will not depend on the utility functions of the candidates. Our results have implications for existing models of redistributive politics and spatial competition, as the properties of pure-strategy equilibria in such games carry over to equilibria in games with arbitrary candidate preferences. On the other hand, candidate utility functions will matter if the individual voting decisions are correlated. In the presence of aggregate uncertainty, such as changing economic conditions or political scandals, the preferences of parties and candidates with respect to shares of votes will have an effect on political competition.

Truth-Revealing Voting Rules for Large Populations

Deterministic voting rules are notoriously susceptible to strategic voting. We propose a new solution to this problem for large electorates. For any deterministic voting rule, we can design a stochastic rule that asymptotically approximates it in the following sense: for a sufficiently large population of voters, the stochastic voting rule (i) incentivizes every voter to reveal her true preferences and (ii) produces the same outcome as the deterministic rule, with very high probability.

Strategic Ambiguity of Party Positions in Multi-Party Competition

Party competition is largely about making policy promises to voters. We argue that the clarity of the expressed policy position may be equally important. If blurred messages toward different audiences and therefore ambiguous positions can attract votes from different groups, parties have incentives to present ambiguous rather than clear-cut policy platforms. We present a formal model of multi-party competition with stochastic voting where party leaders make strategic choices on both the position and the level of ambiguity of their platforms. Leaders respond to the demands of two principals, the general public and party core constituencies. We derive two hypothesis on the location and ambiguity of party platforms and provide initial tests of these hypotheses in a comparative setting in 14 Western European democracies gathering data on voter and party left-right positions from Eurobarometer surveys and electoral manifestos. Ambiguity of party profiles is estimated using a variant of Wordscores on a newly established data set of electoral manifestos. We find that platforms become more ambiguous as the preferences of the two principals diverge. Our findings imply that ambiguity can be a winning strategy for parties, especially in settings with strong partisan lines.

Altruism, Noise, and the Paradox of Voter Turnout: An Experimental Study

This paper addresses the paradox of voter turnout, wherein observed voting participation rates are far greater than what rational choice theory would predict. Voters face multiple voting choices, stochastic voting costs, and candidates offering different economic platforms. A combination of two approaches attempts to resolve this paradox: quantal response equilibrium (QRE) analysis, which introduces noise into the decision-making process, and the possibility of ethical (altruism-motivated) voting. A series of laboratory experiments empirically tests the predictions of the resulting model. Participants in the experiments are also given opportunities for communicating online with their immediate neighbors, in order to enhance the chances that subjects would realize the possibility of ethical voting. The results show that ethical voting occurs but gains momentum only in the presence of a vocal advocate and even then it mostly dissipated by the second half of the session. The QRE-based model was able to explain some but not all of the overvoting that was observed, relative to the Nash equilibrium prediction. There is evidence to suggest that communication via the chat feature generated some of the voting and also some of the ethical voting.

The composition of government expenditure with alternative choicemechanisms

This paper investigates the choice of the composition of government expenditure using both positive and normative approaches. The former involves aggregation over selfish voters (simple majority voting and stochastic voting are examined), while the latter involves the choice by a single disinterested individual (considered to maximise a social welfare function). The approach allows direct comparisons of the choice mechanisms. The structures examined include a transfer payment combined with a pure public good, and a transfer payment with tax-financed education. Explicit solutions are obtained for the choice of expenditure components, and these are shown to depend on the proportional difference between the arithmetic mean and another measure of location of incomes, where the latter depends on the choice mechanism. In each case the expenditure composition depends on an inequality measure defined in terms of the proportional difference between a measure of location of the income distribution and the arithmetic mean, where the location measure depends on the decision mechanism.

Corporate Control with Cross-Ownership

Cross-ownership breaks the traditional rule of one-sided corporate control. Using a novel approach based on stochastic voting processes, this paper proposes a general method to determine control stakes in the presence of cross-ownership. It offers a generalization of the Banzhaf index, which allows coping with cross-ownership-inclusive ownership graphs. The original feature of this approach is its absolute sequentiality. We also operationalize this new approach by building an algorithm, which determines the shareholders’ respective control powers in any corporate structure. From a governance viewpoint, we emphasize that cross-ownership may act as a powerful device for shareholders’ expropriation. To make this point, we revisit the leading example of the German Allianz Group.

Three-candidate spatial competition when candidates have valence: stochastic voting

We study the effects of stochastic (probabilistic) voting on equilibrium locations, equilibrium vote shares and comparative statics in a setup with three heterogeneous candidates and a single-dimensional issue space. Comparing the equilibria with and without stochastic voting, we find that under an appropriate level of uncertainty about voter behavior, the model has a pure strategy Nash Equilibrium (PSNE) that is free from several non-plausible features of the PSNE under deterministic voting. This result is robust to extensions to asymmetric density and plurality maximization.

Probabilistic voting and platform selection in multi-party elections

The literature on stochastic voting to date has focused almost exclusively on models with only two candidates (or parties). This paper studies multiparty competition with stochastic voting. We look at two different models in which candidates aim to maximize their expected vote, as well as a model where the objective of candidates is rank minimization. The equilibria of these models are derived and characterized. We show that the properties of the equilibria are quite different from those derived in deterministic models. Furthermore, the analysis shows that deterministic voting models are not robust since the introduction of even a minute level of uncertainty leads to a drastic change in predictions. Consequently, we argue that the deterministic model provides a misleading benchmark. Stochastic models provide a much richer framework, and the nature of the uncertainty in voter choice is a key determinant of the qualtitative properties of the equilibria.

Equilibrium in spatial voting: The median voter result is an artifact

We study stochastic voting models where the candidates are allowed to have any smooth, strictly increasing utility functions that translate vote shares into payoffs. We find that if a strict Nash equilibrium exists in a model with an infinite number of voters, then nearby equilibria should exist for similar large, but finite, electorates. If the votes are independent random events, then equilibria will not depend on the utility functions of the candidates. Our results have implications for existing models of redistributive politics and spatial competition, as the properties of pure-strategy equilibria in such games carry over to equilibria in games with arbitrary candidate preferences. On the other hand, candidate utility functions will matter if the individual voting decisions are correlated. In the presence of aggregate uncertainty, such as changing economic conditions or political scandals, the preferences of parties and candidates with respect to shares of votes will have an effect on political competition.