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.The authors thank Martin Osborne and Maurice Salles for useful comments and suggestions. The first author would also like to thank the Bankard Fund for financial support.     

The spatial model with non-policy factors: a theory of policy-motivated candidates

The theoretical literature on two candidate elections is dominated by symmetric contests and vote-maximizing candidates. These models fail to capture two important features of real elections. First, most elections pit a stronger candidate against a weaker one. Second, candidates care not only about holding office, but also about policy outcomes. Ignoring any one of these features means we will fail to capture an important dynamic—strong candidates must balance their desire to change policy with their need to win the election. We provide conditions for the existence of an equilibrium in the spatial model with non-policy factors, when candidates are policy motivated. We provide a characterization of ‘regular’ equilibria and show that there exists at most one regular equilibrium. We provide conditions that guarantee that all equilibria are regular. We derive comparative statics for the model and show that increasing a candidate’s non-policy advantage causes that candidate to move towards his ideal point.     

Electoral competition in 2-dimensional ideology space with unidimensional commitment

We study a model of electoral competition between two candidates with two orthogonal issues, where candidates are office motivated and committed to a particular position in one of the dimensions, while having the freedom to select (credibly) any position on the other dimension. We analyse two settings: one where both candidates are committed to the same dimension, and the other where each candidate is committed to a different dimension. We focus on characterisation and existence of pure strategy Nash equilibria when the core is empty. We show that if the distribution of voters’ ideal policies is continuously differentiable and has a bounded support, then an equilibrium exists if the candidates are differentiated enough. Our results for the case where the candidates have a common committed issue have implications for the literature on valence.     

A group majority voting model of public good provision

A model of public good provision by majority rule selection incorporating the behavior of rational group voting is formulated. Two probability maximizing candidates are assumed. If voters are risk averse in public sector preferences, then a unique symmetric (both candidates offering identical platforms) equilibrium exists. If certain additional conditions hold on the group cost functions of political support, this equilibrium will lie at the public good levels which maximizes the sum of voter utility. It is further demonstrated that it is unlikely for those conditions to be satisfied and therefore more realistic asymmetric equilibria with positive voter turnout is predicted.This paper is based on an essay of a dissertation submitted to Tulane University under the supervision and invaluable assistance of Steven Slutsky, Jonathan Hamilton, and William Oakland. The advice of Gerald Whitney, Michaels Johnson, and an anonymous referee is also gratefully acknowledged. All errors remain the authors.     

Citizen candidates under uncertainty

In this paper I add uncertainty about the total vote count to a “citizen candidate” model of representative democracy. I show that in a society with a large electorate, where the outcome of the election is uncertain and where winning candidates receive a large reward from holding office, there will be a two-candidate equilibrium and no equilibria with a single candidate. This work has benefited from valuable comments by Paul Healy, Morgan Kousser, Alejandro Saporiti, Al Slivinski, participants in a seminar in Princeton, and especially by Matt Jackson and Tom Palfrey. Their contribution is gratefully acknowledged.     

A voluntary participation game through a unit-by-unit cost share mechanism of a non-excludable public good

The strategic analysis of voluntary participation in the public good provision has shown two distinct results. First, when the provision of public goods is binary, there are Nash equilibria supporting efficient allocations, and these are Strong Nash equilibria of the game. On the other hand, a model of a continuous public good (Saijo–Yamato, J Econ Theory 84:227–242, 1999) showed that the participation of all agents is not an equilibrium in many situations. This article considers the provision of a discrete and multi-unit public good, and examines a unit-by-unit participation game. Namely, people are asked to participate in each unit of public good provision, and those who chose to participate share the marginal cost of public good. In this game of public good provision, there are subgame-perfect equilibria that are Pareto efficient. We also use the refinement concepts to eliminate inefficient subgame-perfect equilibria and also to characterize the efficient subgame-perfect equilibria.     

THE OPTIMAL DEFENSE OF NETWORKS OF TARGETS

This paper examines a game‐theoretic model of attack and defense of multiple networks of targets in which there exist intranetwork strategic complementarities among targets. The defender's objective is to successfully defend all the networks and the attacker's objective is to successfully attack at least one network of targets. Although there are multiple equilibria, we characterize correlation structures in the allocations of forces across targets that arise in all equilibria. For example, in all equilibria the attacker utilizes a stochastic “guerrilla warfare” strategy in which a single random network is attacked. (JEL C72, D74)     

THE EXPECTATIONAL STABILITY OF UNDEREMPLOYMENT EQUILIBRIA

External economies of scale can generate multiple equilibria in perfect-foresight models. With multiple equilibria comes the problem of indeterminacy: At which equilibrium will the economy arrive? Another implication of these models is that “animal spirits” may drive the economy between equilibria, say from a low-employment to a high-employment equilibrium and back. I show a learning algorithm can be used to eliminate the indeterminacy of these models. Socially inferior low-employment steady states are ruled out. Stable low-employment steady states may exist, but are not unambiguously inferior because of the presence of both positive and negative externalities.     

DISEQUILIBRIUM EXCHANGE IN BARTER AND MONETARY ECONOMIES

This article compares the relative performances of barter and monetary arrangements at fixed disequilibrium prices. The decentralized functioning of the two systems is described, and their "fix-price" equilibria compared. It is shown that, while the fix-price equilibria will be more difficult to obtain in the barter economy, they are more efficient than in the monetary economy where disequilibrium "effective demand failures" appear.     

STABILIZATION POLICY CAN LEAD TO CHAOS

Nonlinearities in economies, as elsewhere, can generate chaotic equilibria. The presence of Pareto-inferior chaotic equilibria might seem reason enough to use stabilization policy to select preferable equilibria. However, I show that a stabilization policy with feedback can itself lead to chaotic dynamics. Thus the existence of nonlinearities in the economy does not by itself justify monetary or fiscal policies aimed at reducing economic instability. Current evidence cannot distinguish whether monetary policy stabilizes a nonlinear economy, creates nonlinear dynamics in the economy, or both.     

Implementation in perfect equilibria

This paper considers implementation when the feasible outcomes are lotteries over a finite set of alternatives. The following weak condition is sufficient for implementation in trembling hand perfect equilibria (with three or more players): if all but one player agree on which alternative is the best, this alternative is (among those that are) chosen by the social choice rule, and if all but one player agree on which alternative is the worst, this alternative is not chosen. Many interesting social choice rules that are not Nash implementable satisfy this condition. On the other hand, there are social choice rules that are implementable in Nash equilibria but not in perfect equilibria.I am grateful to Luis Corchón, Eric Maskin, William Thomson, seminar participants at Harvard and Rochester, and two anonymous referees for helpful comments and suggestions. This research was supported by grants from the Royal Swedish Academy of Sciences and the Bank of Sweden Tercentenary Foundation.     

Repeated electoral competition over nonlinear income tax schedules

We consider a repeated electoral competition game between two parties, each representing a constituent with a given income level. Parties are unable to commit to a policy before the election; they choose a nonlinear income tax schedule once elected. In each period, citizens cast a vote either for the incumbent or for the challenger. We first show that there exist (pure strategy) subgame perfect equilibria where both parties choose the most-preferred tax schedule of their constituent, subject to the constraint that they are reelected. We characterize a specific class of these BPR (Best Policy with Reelection) equilibria in which one of the parties plays its constituent’s unconstrained optimal tax function. Equilibrium tax schedules are always piecewise linear. Depending on the income levels of the two parties’ constituents, we obtain either classical left-vs-right equilibria (where the poor vote for one party and the rich for the other one) or ends-against-the-middle equilibria (where both poor and rich vote for one party while the middle class votes for the other party). In both types of equilibria, both parties propose the same tax schedule to a subset of the population.     

Financing the Campaigns of Women Candidates and Their Opponents

Abstract

Contrary to research from the 1970s, evidence since the 1980s suggests that women candidates compete evenly for campaign funds with male candidates. The existing evidence is less complete at the state legislative level than it is in congressional elections. The data presented here draw upon the campaign finance reports of state legislative candidates from three states from 1982 to 1990. The results suggest that women candidates usually raise more than similarly situated male candidates, but this does not result in an actual advantage because their male opponents also raise more than other male candidates. The patterns over time do not indicate that women candidates gained parity with male candidates during the 1980s but rather began that decade equal to men in campaign finance.     

LEADERSHIP BY EXAMPLE IN THE WEAK‐LINK GAME

We investigate the effects of leadership in a four‐player weak‐link game. A weak‐link game is a coordination game with multiple Pareto‐ranked Nash equilibria. Because the more efficient equilibria involve a degree of strategic uncertainty groups typically find it difficult to coordinate on more efficient equilibria. We wanted to see whether leadership by example, in the form of one player acting publicly before the rest of the group, could help groups do better. Our results suggest that leadership can increase efficiency but is far from being a guarantee of success. Specifically, in a significant number of groups we observed successful leadership and increased efficiency, but in most groups efficiency was low despite the efforts of leaders. We did not find any difference between voluntary leaders and leaders that are randomly assigned. (JEL C72, H41)     

Linear cost share equilibria and the veto power of the grand coalition

We consider pure exchange economies with finitely many private goods involving the choice of a public project. We discuss core-equivalence results in the general framework of non-Euclidean representation of the collective goods. We define a contribution scheme to capture the fraction of the total cost of providing the project that each blocking coalition is expected to cover. We show that for each given contribution scheme defined over the wider class of Aubin coalitions, the resulting core is equivalent to the corresponding linear cost share equilibria. We also characterize linear cost share equilibria in terms of the veto power of the grand coalition. It turns out that linear cost share equilibria are exactly those allocations that cannot be blocked by the grand coalition with reference to auxiliary economies with the same space of agents and modified initial endowments and cost functions. Unlike the Aubin-type equivalence and results presented in Diamantaras and Gilles (Soc Choice Welf 15:121–139, 1998), this characterization does not depend on a particular contribution scheme.     

Voting on redistribution with tax evasion

This paper analyzes voting on a linear income tax whose proceeds are redistributed lump sum to the taxpayers. Individuals can evade taxes, which leads to penalties if evasion is detected. Since preferences satisfy neither single peakedness nor single crossing, a voting equilibrium may not exist. When an equilibrium does exist, there are several possible outcomes. There may be ‘conventional’ equilibria where the rich are expropriated by the poor and middle class. There may be equilibria without full expropriation where redistribution is limited by the threat of evasion. Finally, there may be equilibria where redistribution goes from the middle class to the rich and poor.     

HIERARCHICAL TRADE

Commodity trading is typically organized hierarchically: Large‐scale trade takes place at the global price system while individuals trade at local price systems within their countries. Agencies or trading houses establish the link between these different market places. In this paper, we devise a framework to study this type of hierarchical trade. We identify the free trade and the autarky equilibrium as polar cases. We show that no other two‐stage market equilibria exist if the commodity space is two‐dimensional. An example demonstrates that other, so‐called intermediate equilibria exist for three‐dimensional commodity spaces. We then provide an explicit construction of special classes of intermediate equilibria. Moreover, we study the consequences when some countries control the agency that organizes trade at the global level and we analyze the role of international goods arbitrage. Finally, we show that profit‐maximizing agencies may not promote free trade outcomes. (JEL D43, D50, F10)     

WOMEN CANDIDATES IN THE NEWS: AN EXAMINATION OF GENDER DIFFERENCES IN U.S. SENATE CAMPAIGN COVERAGE

By covering male and female candidates differently, the newsmedia may influence the success of female candidates for publicoffice. A content analysis was conducted to assess potentiallyimportant differences in the newspaper coverage of a sampleof male and female U.S. Senate candidates in the elections of1982–86. The results of the study show that female candidates for the U.S. Senate are treated differently by the press.Female candidates receive less news coverage and the coveragethey do receive concentrates more on their viability and lesson their issue positions. Furthermore, female candidates' viabilitycoverage is more negative than that of their male counterparts.Given these gender differences in press treatment, we wouldexpect voters' recognition of male candidates to exceed thatof female candidates and we would also expect evaluations offemale candidates to be tied more closely to their perceivedviabil ity. Because female candidates are often considered noncompetitiveby the press, this attention to the horserace may lead votersto develop more negative evaluations of female candidates. Theseresults suggest that current patterns of press coverage mayserve as a critical obstacle for women running for the U.S.Senate.     

Condorcet efficiency: A preference for indifference

The Condorcet winner in an election is the candidate who would be able to defeat all other candidates in a series of pairwise elections. The Condorcet efficiency of a voting procedure is the conditional probability that it will elect the Condorcet winner, given that a Condorcet winner exists. The study considers the Condorcet efficiency of weighted scoring rules (WSR's) on three candidates for large electorates when voter indifference between candidates is allowed. It is shown that increasing the proportion of voters who have partial indifference will increase the probability that a Condorcet winner exists, and will also increase the Condorcet efficiency of all WSR's. The same observation is observed when the proportion of voters with complete preferences on candidates is reduced. Borda Rule is shown to be the WSR with maximum Condorcet efficiency over a broad range of assumptions related to voter preferences. The result of forcing voters to completely rank all candidates, by randomly breaking ties on candidates that are viewed as indifferent, leads to a reduction in the probability that a Condorcet winner exists and to a reduction in the Condorcet efficiency of all WSR's. Received: 31 July 1999/Accepted: 11 February 2000     

Special majority rules and the existence of voting equilibria

This paper is concerned with voting rules in which one alternative defeats a second alternative if and only if it is preferred to the second alternative by a pre-specified proportion of the individuals who have strict preferences on the pair. In particular, the paper focuses on the potential of two alternative lower bounds (for the proportion used) as tools for studying the existence of voting equilibria (i.e., for studying the existence of alternatives which cannot be defeated). It establishes that there are certain important contexts where one of the two bounds does not directly reveal whether any voting equilibria exist, but the other one does.