The paradox of voting intelligently

Classical economic models predict far less voting than happens in practice. Expressive voting may partly explain the divergence, but some who are generally uninterested in politics and thus unlikely to take elections as an important form of personal expression nevertheless vote. One possible explanation is that these voters overestimate the instrumental, outcome-changing consequences of voting; such systematic misperception may be more likely among those with less cognitive capacity. Analysis of responses to the American National Election Studies confirms this hypothesis: while intelligence and interest both increase the likelihood of voting, the combination enhances the likelihood of turnout still further.     

The product paradox of voting power

We consider a system made up of two committees, with overlapping membership but with different rules for passing decisions; the passage of a joint resolution requires separate approval by each committee. We show that it is possible for one voter a to be stronger (have greater voting power) than another voter b in both of the two committees, while in the two-committee system (considered as a single composite entity) b is stronger than a. We argue that this apparently paradoxical phenomenon is inherent in the structure of the decision-making system in question, rather than being an artefact of any particular index used to measure voting power.     

Less is more: The paradox of choice in voting behavior

How does the number of candidates competing in an election affect voting behavior? In theory, as the number of candidates running for office increase, citizens’ utility from voting also increases. With more candidates, voters are more likely to have candidates that are close to their ideal points. Practically, however, more candidates also means a higher cognitive burden for voters who must learn more during campaigns in order to find their “ideal” candidate. In this paper, we examine how choice set size affects voting behavior. Using a survey experiment, we show that subjects presented with many options learn less about candidates, are more likely to vote based on meaningless heuristics, and are more likely to commit voting errors, when compared with subjects who choose between only a few candidates.     

Campaign allocations under probabilistic voting

We develop a probabilistic voting model where candidates compete by advertising in different media markets. Ads are viewed by everyone within a market and cannot be targeted to subgroups such as one candidate??s partisans. Candidates estimate the distribution of voter preference intensities in a market, and campaign ads then shift this distribution. Individuals with any intensity vote with some probability for each candidate. We derive comparative static implications of changes in a variety of factors on the advertising decisions of each candidate. Using campaign advertising data from 2002, we find these results to be consistent with actual campaign allocation behavior.     

Multiparty spatial competition with probabilistic voting

I develop a general model of multiparty competition in which parties model voters' choices by means of probabilistic choice rules. The model is specified in terms of an issue salience coefficient which varies with the importance voters attach to issues, as opposed to unmeasured nonissue motivations. I show that when the policy salience coefficient is sufficiently low, then both vote-maximizing and rank-maximizing parties have a dominant strategy: to adopt the “most popular platform,” which maximizes voter utilities over the entire electorate. This most popular platform therefore represents a convergent equilibrium when all parties are vote- or rank-maximizing. Numerical estimates suggest that this equilibrium result holds for degrees of issue voting which exceed the parameters behavioral researchers have estimated for various historical elections.     

Equilibrium in multicandidate probabilistic spatial voting

This paper presents a multicandidate spatial model of probabilistic voting in which voter utility functions contain a random element specific to each candidate. The model assumes no abstentions, sincere voting, and the maximization of expected vote by each candidate. We derive a sufficient condition for concavity of the candidate expected vote function with which the existence of equilibrium is related to the degree of voter uncertainty. We show that, under concavity, convergent equilibrium exists at a “minimum-sum point” at which total distances from all voter ideal points are minimized. We then discuss the location of convergent equilibrium for various measures of distance. In our examples, computer analysis indicates that non-convergent equilibria are only locally stable and disappear as voter uncertainty increases.     

Policy divergence in multicandidate probabilistic spatial voting

Existing models of multicandidate spatial competition with probabilistic voting typically predict a high degree of policy convergence, yet in actual elections candidates advocate quite divergent sets of policies. What accounts for this disparity between theory and empirical observation? I introduce two variations on the basic probabilistic vote model which may account for candidate policy divergence: 1) a model which incorporates candidate-specific variables, so that candidates may enjoy nonpolicy-related electoral advantages (or disadvantages); 2) a model which allows nonzero correlations between the random terms associated with voters' candidate utilities, thereby capturing situations where voters view two or more candidates as similar on nonpolicy grounds. I report candidate equilibrium analyses for each model, which show far greater policy divergence than exists under the standard probabilistic vote model. I then analyze the strategic logic which underlies these results.

     

Pareto optimality of policy proposals with probabilistic voting

This paper studies the Pareto optimality properties of policy proposals and electoral outcomes when there is probabilistic voting. Theorem 1 proves that, when the position of one candidate is taken as fixed, the other candidate will propose a Pareto optimal alternative. This implies that whenever there is an electoral equilibrium (in pure strategies) the electoral outcome is Pareto optimal. It also implies that, even if there is no such equilibrium, the electoral outcomes from a sequence of elections will be Pareto optimal (except, possibly, for an initial status quo).     

Frequency of paradox in a common n-winner voting scheme

This paper investigates the extent to which a commonly used electoral scheme — voting for n candidates when there are n vacancies to fill — is likely to lead, in practice, to paradoxical results. Two types of paradox are investigated. One occurs when an increase in the number of vacancies causes a candidate to drop from the list of winners. The second occurs when the Condorcet candidate fails to win. Using a Monte Carlo study, we show that the likelihood of paradox can be substantial and depends critically on the degree of homogeneity of voters' preferences and on the number of voters.     

Interest groups,campaign contributions,and probabilistic voting

This essay develops a simple model to analyze the impact of campaign contributions on electoral-policy decisions of candidates for office. Interest groups here are firms that select contributions under the assumption that candidates' policies and opposing groups' donations remain unaltered. Candidates, however, recognize that their policy choices affect contributions. Campaign contributions are used by candidates to affect policy-oriented voters' perceptions of candidates' positions. In this framework the introduction of campaign contributions may affect candidates' electoral policies, and if they do then they benefit surely exactly one of the two interest groups.     

The inevitability of the “paradox of redistribution” in the allocation of voting weights

In voting bodies, when voting weights are reallocated, it may be observed that the voting power of some members, as measured by the Shapley-Shubik and Banzhaf power indices, increases while their voting weight decreases. By a simple constructive proof, this paper shows that such a “paradox of redistribution” can always occur in any voting body if the number of voters, n, is sufficiently large. Simulation results show that the paradox is quite frequent (up to 30 percent) and increases with n (at least for small n). Examples are given where the Banzhaf and Shapley-Shubik indices are not consistent in demonstrating the paradox.