Sequential voting with abstention

Dekel and Piccione [2000. Sequential voting procedures in symmetric binary elections. J. Polit. Economy 108, 34–55] have proven that information cascades do not necessarily affect the properties of information aggregation in sequential elections: under standard conditions, any symmetric equilibrium of a simultaneous voting mechanism is also an equilibrium of the correspondent sequential mechanism. We show that when voters can abstain, these results are sensitive to the introduction of an arbitrarily small cost of voting: the set of equilibria in the two mechanisms are generally disjoint; and the informative properties of the equilibrium sets can be ranked. If an appropriate q-rule is chosen, when the cost of voting is small the unique symmetric equilibrium of the simultaneous voting mechanism dominates all equilibria of the sequential mechanism.     

The (sub-)optimality of the majority rule

We consider collective choice from two alternatives. Ex-ante, each agent is uncertain about which alternative she prefers, and may be uncertain about the intensity of her preferences. An environment is given by a probability distribution over utility vectors that is symmetric across agents and neutral across alternatives. In many environments, the majority voting rule maximizes agents? ex-ante expected utilities among all anonymous and dominant-strategy implementable choice rules. But in some environments where the agents? utilities are stochastically correlated, other dominant-strategy choice rules are better for all agents. If utilities are stochastically independent across agents, majority voting is ex-ante optimal among all anonymous and incentive-compatible rules. We also compare rules from an interim-viewpoint.     

Majority rule when voters like to win

I analyze symmetric majority rule voting equilibria when voters wish to elect the better candidate and to vote for the winner. When voters care only about the winning candidate (the standard formulation) a unique responsive equilibrium exists. The addition of a desire to win creates multiple equilibria, some with unusual properties. In most of these equilibria information is not aggregated effectively, and I uncover the novel possibility of negative information aggregation in which information aggregated in equilibrium is used to select the worse rather than the better candidate.I then characterize the efficiency of optimal equilibria as the population becomes large and show that a discontinuity arises in the information aggregation capabilities of the majority rule voting mechanism: in elections without a dominant front-running candidate the better candidate is almost surely elected, whereas in races with a front-runner information cannot be effectively aggregated in equilibrium.     

Condorcet cycles in bipartite populations

Summary. Simple majority voting between pairs of alternatives is used to aggregate individual preferences. The occurence of Condorcet cycles is limited thanks to a principle of homogeneity on individual preferences. The restrictions induced on the domain of the latters are weak: among the n! possible orderings of n alternatives, more than one half are admissible within a domain. The resulting aggregated preference has then a neglectable probability of showing up cycles. We show moreover that the set of individual preferences can be `naturally' partitioned into two such domains. Received: June 17, 1996; revised version: April 15, 1997     

A Bayesian Model of Voting in Juries

We model voting in juries as a game of incomplete information, allowing jurors to receive a continuum of signals. We characterize the unique symmetric equilibrium of the game, and give a condition under which no asymmetric equilibria exist under unanimity rule. We offer a condition under which unanimity rule exhibits a bias toward convicting the innocent, regardless of the size of the jury, and give an example showing that this bias can be reversed. We prove a “jury theorem” for our general model: As the size of the jury increases, the probability of a mistaken judgment goes to zero for every voting rule except unanimity rule. For unanimity rule, the probability of making a mistake is bounded strictly above zero if and only if there do not exist arbitrarily strong signals of innocence. Our results explain the asymptotic inefficiency of unanimity rule in finite models and establishes the possibility of asymptotic efficiency, a property that could emerge only in a continuous model. Journal of Economic Literature Classification Numbers: C72, D72.     

A note on asymmetric and mixed strategy equilibria in the search-theoretic model of fiat money

Summary. The simple search-theoretic model of fiat money has three symmetric Nash equilibria: all agents accept money with probability 1; all agents accept money with probability 0; and all agents accept money with probability y in (0,1). Here I construct an asymmetric pure strategy equilibrium, payoff-equivalent to the symmetric mixed strategy equilibrium, where a fraction N in (0,1) of agents always accept money and 1-N never accept money. Counter to what has been conjectured previously, I find N > y. I also introduce evolutionary dynamics, and show that the economy converges to monetary exchange iff the initial proportion of agents accepting money exceeds N. Received: September 10, 1997; revised version: April 24, 1998     

VOTING AND SOCIAL PRESSURE UNDER IMPERFECT INFORMATION

We develop a model in which costly voting in a large, two‐party election is a sequentially rational choice of strategic, self‐interested players who can reward fellow voters by forming stronger ties in a network formation coordination game. The predictions match a variety of stylized facts, including explaining why an individual's voting behavior may depend on what she knows about her friends' actions. Players have imperfect information about others' voting behavior, and we find that some degree of privacy may be necessary for voting in equilibrium, enabling hypocritical but useful social pressure. Our framework applies to any costly prosocial behavior.     

Pareto violations of parliamentary voting systems

It has been known for a long time that many binary voting rules can select a Pareto dominated outcome, that is an outcome such that there exists some other alternative which is preferred by every voter. In this paper, we show that some of these rules can select an outcome Pareto dominated in a much stronger sense. Furthermore, our main results are concerned with the evaluation of the likelihood of Pareto dominated outcomes under four social choice rules commonly used in Parliaments or in committees. Given a set of four alternatives and a set of n individuals, we assume anonymous profiles and using analytical methods we compute the proportion of profiles at which the Pareto criterion is violated. Our results show that one should not be especially worried about the existence of the possibility as such. We are grateful to two anonymous referees for very helpful remarks and suggestions.     

Playing for Your Own Audience: Extremism in Two‐Party Elections

This paper considers a two‐party election with a single‐dimensional policy space. We assume that each voter has a higher probability of observing the position of the party he is affiliated with than the position of the other party, an assumption that is consistent with the National Election Studies (NES) electoral data set. In equilibrium, the two parties locate away from the median, because the voters who dislike a party's platform observe its policy choice with a lower probability, and its own audience like policy choices that cater to its taste. As the asymmetry in voter information or the cost of voting increases, the parties adopt more extreme platforms, while if there are fewer extreme voters the opposite effect occurs. Making voters more symmetrically informed about the two parties' platforms increases the welfare of society, while asymmetric information acquisition by the voters is worse than no information acquisition at all.     

Information Manipulation in Election Campaigns

We provide a game‐theoretical model of manipulative election campaigns with two political candidates and a Bayesian voter. The latter is uncertain about how good the candidates are. Candidates take unobservable, costly actions to manipulate voter's opinion about their positions. We show that if the candidates differ in campaigning efficiency, and the voter receives the biased campaign messages with some noise, then the cost‐efficient candidate can win the election with higher probability than her opponent even when she is ex‐post an inferior choice for the voter. Our paper offers a novel informational justification for imposing limits on campaign spending and encouraging diversity in the supply of political information.     

Learning in Elections and Voter Turnout

Voter turnout in game theoretic models of voting has typically been difficult to predict because of the problem of multiple Nash equilibria ( Palfrey and Rosenthal 1983, 1985 ). Many of these equilibria require an extreme precision of beliefs among voters that is unlikely to be reached in real elections. At the same time, mechanisms like pre‐election polls exist to shape the beliefs of voters about expected turnout. We combine these two features in a model of voter learning in elections and characterize the asymptotically stable equilibria of both complete and incomplete information games in a simple symmetric setting with two candidates. We also show how the model can be used to qualitatively explain several phenomena observed in reality: increases in costs of voting affect turnout adversely but there may be persistence of turnout levels between elections even though costs and other parameters change. Increase in uncertainty increases turnout while increases in the size of the electorate decrease it, in line with intuition.     

Majority rule when voters like to win

I analyze symmetric majority rule voting equilibria when voters wish to elect the better candidate and to vote for the winner. When voters care only about the winning candidate (the standard formulation) a unique responsive equilibrium exists. The addition of a desire to win creates multiple equilibria, some with unusual properties. In most of these equilibria information is not aggregated effectively, and I uncover the novel possibility of negative information aggregation in which information aggregated in equilibrium is used to select the worse rather than the better candidate.I then characterize the efficiency of optimal equilibria as the population becomes large and show that a discontinuity arises in the information aggregation capabilities of the majority rule voting mechanism: in elections without a dominant front-running candidate the better candidate is almost surely elected, whereas in races with a front-runner information cannot be effectively aggregated in equilibrium.     

A passion for voting

We model expressive voting as a dynamic game with informed and ignorant voters. A voter has selective memory for actions and he is aware of it. We find a unique symmetric equilibrium with ignorant voting. Public signal in favor of one particular alternative creates the bandwagon and underdog effects. When the signal is sufficiently strong, the majority outcome is biased. This is a possible reason for persistence of public policies.     

Condorcet Jury Theorem: An example in which informative voting is rational but leads to inefficient information aggregation

Recent research on the Condorcet Jury Theorem has proven that informative voting (that is, voting according to one’s signal) is not necessarily rational. With two alternatives, rational voting typically leads to the election of the correct alternative, in spite of the fact that not all voters vote informatively. We prove that with three alternatives, there are cases in which informative voting is rational and yet leads to the election of a wrong alternative.     

PROXIMITY AND VOTING FOR PROFESSIONAL SPORTING STADIUMS: THE PATTERN OF SUPPORT FOR THE SEAHAWK STADIUM REFERENDUM

This paper evaluates voting behavior on the Seahawk Stadium referendum in the State of Washington. For our empirical strategy, we implement both the linear probability model and a group logit model, which gives greater weight to voting areas with greater number of votes cast. We find that voting support was lowest among those living closest to the proposed stadium site, while voting support was highest among those within “easy access” of the stadium. This nonlinear distance effect differs from the typical “proximity” effect found in most professional sporting stadiums in the United States; however, it is consistent with a referendum‐voting outcome for a professional soccer stadium in Germany and public projects such as national forests. (JEL R53, H71, L83)     

Manipulation through political endorsements

We study elections with three candidates under plurality voting. A candidate is a Condorcet loser if the majority of the voters place that candidate at the bottom of their preference rankings. We first show that a Condorcet loser might win the election in a three-way race. Next we introduce to the model an endorser who has private information about the true probability distribution of the preferences of the voters. Observable endorsements facilitate coordination among voters who may otherwise split their votes and lead to the victory of the Condorcet loser. When the endorser has an ideological bias towards one of the candidates, the coordination impact of endorsements remains unaltered, moreover the endorser successfully manipulates the outcome of the election in favor of his bias, even if his ideological bias is known by the voters. The results are true for any endorsement cost and any magnitude of bias as long as the electorate is large enough.     

A note on plurality distortion in large committees

Simple plurality voting allows the somewhat surprising possibility that a majority of a committee or an electorate may prefer one of the defeated alternatives to the plurality winner. This paradox is distinct from Condorcet's paradox and has received less attention in the literature. Recently, however, the frequency of the Borda effect anticipated under different cultures has been computed and some empirical results have also been reported. Here results are obtained for both impartial and partial cultures using a class of Polya urn models. Emphasis is on asymptotic investigations and results valid for large committees.     

Inconsistency of estimate of the degree of freedom of multivariate student-t disturbances in linear regression models

A moment estimator for the degree of freedom of the jointly multivariate student-t distribution of the disturbances in a linear regression model has been suggested by Singh [Economic letters (1988) 27, 47–53]. In this paper we will show that the distribution of the moment estimate is independent of the true value of the degree of freedom and the estimate converges to infinite in probability as the sample size goes to infinite. Our results show that the moment estimate does not provide any information on the degree of freedom.     

Bandwagons and Momentum in Sequential Voting

In this paper I show that an equilibrium exists to the sequential voting game in which a bandwagon begins with probability 1. These bandwagons are driven by a combination of beliefs and the desire of voters to vote for the winning candidate. Significantly, in this equilibrium the pivot probability for each voter is non-zero, even in an infinite population. Consequently, the bandwagons do not always start after one (or at most two) favourable decisions (as do economic cascades) and varying levels of informative voting are observed, consistent with observations from sequential voting in U.S. presidential primaries. Further, voters are exposed to counterintuitive incentives, referred to as "buyers' remorse", that have been attributed to real primary voters.
I also derive equilibrium behaviour in this environment when voting is simultaneous and compare the quality of information aggregation within each mechanism. I relate the conclusions to U.S. presidential primaries and find they are consistent with a common conclusion about the front-loading of the primary process: that in tight elections (with no front-runner) simultaneous voting is preferred, whereas in lopsided elections sequential voting is preferred. The superior performance of sequential voting in lopsided races is precisely because bandwagons occur.     

RECURRENT BUBBLES*

We study rational bubbles in a standard linear asset price model. We first consider a class of bubble processes driven by multiplicative i.i.d. shocks. We show that a bubble process in this class either diverges to infinity with probability one, converges to zero with probability one, or keeps fluctuating forever with probability one, depending on investors' “confidence” in expected bubble growth. We call a bubble process having the last property “recurrent.” We develop sufficient conditions for a bubble process to be recurrent when it is driven by non‐i.i.d. shocks, when the risk‐free interest rate is not constant, and when the process is driven by non‐i.i.d. shocks and the risk‐free interest rate is not constant. In the last case we demonstrate via simulation that there can be a prolonged period in which both the bubble and the interest rate stay close to zero.