Sincere versus sophisticated voting when legislators vote sequentially

Elsewhere (Groseclose and Milyo 2010), we examine a game where each legislator has preferences over (i) the resulting policy and (ii) how he or she votes. The latter preferences are especially important when the legislator is not pivotal. We show that when the game follows the normal rules of legislatures—most important, that legislators can change their vote after seeing how their fellow legislators have voted—then the only possible equilibrium is one where all legislators ignore their policy preferences. That is, each legislator votes as if he or she is not pivotal. The result, consistent with empirical studies of Congress, suggests that legislators should tend to vote sincerely, rather than sophisticatedly. In this paper we examine how outcomes change if we change the rules for voting. Namely, instead of a simultaneous game, we consider a game where legislators vote sequentially in a pre-determined order. We show that, opposite to the simultaneous game, an alternative wins if and only if a majority of legislators’ policy preferences favor that alternative. Our results suggest that if Congress adopted this change in rules, then sophisticated voting would become frequent instead of rare.     

Strategy-proofness on Euclidean spaces

 In this paper we characterize strategy-proof voting schemes on Euclidean spaces. A voting scheme is strategy-proof whenever it is optimal for every agent to report his best alternative. Here the individual preferences underlying these best choices are separable and quadratic. It turns out that a voting scheme is strategy-proof if and only if (α) its range is a closed Cartesian subset of Euclidean space, (β) the outcomes are at a minimal distance to the outcome under a specific coordinatewise veto voting scheme, and (γ) it satisfies some monotonicity properties. Neither continuity nor decomposability is implied by strategy-proofness, but these are satisfied if we additionally impose Pareto-optimality or unanimity. Received: 18 October 1993/Accepted: 2 February 1996     

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.     

The structure of coalitional power under probabilistic voting procedures

We consider probabilistic voting procedures which map each feasible set of alternatives and each utility profile to a social choice lottery over the feasible set. It is shown that if we impose: (i) a probabilistic collective rationality condition known as regularity; (ii) probabilistic counterpart of Arrow's independence of irrelevant alternatives and citizens' sovereignty; (iii) a probabilistic positive association condition called monotonicity; then the coalitional power structure under a probabilistic voting procedure is characterized by weak random dictatorship. Received: 1 March 1999/Accepted: 21 May 2001     

VOTING EXPRESSIVELY

We address a common criticism directed toward models of expressive voting that they are ad hoc in nature. To that end, we propose a foundation for expressive behavior that is based on a novel theory of social preferences under risk. Under our proposal, expressive considerations in behavior arise from the particular way in which risky social prospects are assessed by decision‐makers who want to interpret their choices as moral. To illustrate the scope of our framework, we use it to address some key questions in the literature on expressive voting: why, for expressive considerations, might voters vote against their self‐interest in large elections and why might such elections exhibit a moral bias. Specifically, we consider an electoral set‐up with two alternatives and explain why, when the size of the electorate is large, voters may want to vote for the alternative they deem morally superior even if this alternative happens to be strictly less preferred, in an all‐inclusive sense, than the other. (JEL D01, D03, D81, D72, A13)     

Some Further Results on the Manipulability of Social Choice Rules

A typology of electoral environments in which strategic manipulation of voting rules can occur is proposed. From this typology, six different concepts of equilibria (or quasi-equilibria) are defined, including the usual ones. Then, focusing on three alternative elections, we derive some analytical representations for the vulnerability of a large number of voting rules to strategic manipulation by considering successively each type of equilibrium. Our results show that the hierarchy of the rules changes when the voting framework is modified. However, some rules are clearly dominated and some others (among which the Borda and the Nanson rules) appear to be uniquely the best in some specific contexts.     

Rationalizations of Condorcet-consistent rules via distances of hamming type

In voting, the main idea of the distance rationalizability framework is to view the voters’ preferences as an imperfect approximation to some kind of consensus. This approach, which is deeply rooted in the social choice literature, allows one to define (“rationalize”) voting rules via a consensus class of elections and a distance: a candidate is said to be an election winner if she is ranked first in one of the nearest (with respect to the given distance) consensus elections. It is known that many classic voting rules can be distance-rationalized. In this article, we provide new results on distance rationalizability of several Condorcet-consistent voting rules. In particular, we distance-rationalize the Young rule and Maximin using distances similar to the Hamming distance. It has been claimed that the Young rule can be rationalized by the Condorcet consensus class and the Hamming distance; we show that this claim is incorrect and, in fact, this consensus class and distance yield a new rule, which has not been studied before. We prove that, similarly to the Young rule, this new rule has a computationally hard winner determination problem.     

Recognizing majority-rule equilibrium in spatial voting games

It is provably difficult (NP-complete) to determine whether a given point can be defeated in a majority-rule spatial voting game. Nevertheless, one can easily generate a point with the property that if any point cannot be defeated, then this point cannot be defeated. Our results suggest that majority-rule equilibrium can exist as a purely practical matter: when the number of voters and the dimension of the policy space are both large, it can be too difficult to find an alternative to defeat the status quo. It is also computationally difficult to determine the radius of the yolk or the Nakamura number of a weighted voting game.We are grateful to Norman Schofield and an anonymous referee for many helpful suggestions.The first author was supported in part by a Presidential Young Investigator Award from the National Science Foundation (ECS-8351313) and by the Office of Naval Research (N00014-85-K-0147). The third author was supported in part by a Presendential Young Investigator Award from the National Science Foundation (ECS-8451032).     

Equitable agendas: agendas ensuring identical sincere and sophisticated voting decisions

 Sophisticated voting under amendment procedure using majority rule usually results in a decision that is distinct from the decision obtained through sincere voting. In this article it is shown that the underlying majority tournament (determined by the voters’ preferences) admits an agenda so that the sincere and sophisticated decisions are identical if and only if the initial strong component of the tournament is not a 3-cycle. As a result, most tournaments, in an asymptotic sense, admit an agenda so that the sincere and sophisticated decisions are identical. Received: 31 August 1993/Accepted: 28 August 1995     

Committees with Farsighted Voters: A New Interpretation of Stable Sets

The interpretation of von Neumann–Morgenstern stable sets in voting games has been debated by most political scientists. The present paper addresses the issue in a model that consists of an infinite sequence of repetitions of the standard committee game. The analysis of equilibrium processes leads to the following conclusion: when voters are farsighted, an alternative is the limit of an absorbing equilibrium process if and only if it belongs to some stable set of the underlying committee game. While the traditional interpretation of the core implicitly assumes myopic voters, we also demonstrate that the core of a strong committee is the unique limit of all absorbing equilibrium processes, provided that voters are arbitrarily patient. We finally proceed to an analysis of the Condorcet Paradox in this dynamic context.     

Hierarchy of players in swap robust voting games

Ordinarily, the process of decision making by a committee through voting is modeled by a monotonic game the range of whose characteristic function is restricted to {0, 1}. The decision rule that governs the collective action of a voting body induces a hierarchy in the set of players in terms of the a-priori influence that the players have over the decision making process. In order to determine this hierarchy in a swap robust game, one has to either evaluate a power index (e.g., the Shapley–Shubik index, the Banzhaf–Coleman index) for each player or conduct a pairwise comparison between players, whereby a player i is ranked higher than another player j if there exists a coalition in which i is more desirable as a coalition partner than j. In this paper, we outline an alternative mechanism to determine the ranking of players in terms of their a-priori power. This simple and elegant method uses only minimal winning coalitions, rather than the entire set of winning coalitions.     

Scoring rule voting games and dominance solvability

This article studies the dominance solvability (by iterated deletion of weakly dominated strategies) of general scoring rule voting games when there are three alternatives. The scoring rules we study include Plurality rule, Approval voting, Borda rule, and Relative Utilitarianism. We provide sufficient conditions for dominance solvability of general scoring rule voting games. The sufficient conditions that we provide for dominance solvability are in terms of one statistic of the game: sufficient agreement on the best alternative or on the worst alternative. We also show that the solutions coincide with the set of Condorcet Winners whenever the sufficient conditions for dominance solvability are satisfied. Approval Voting performs the best in terms of our criteria.     

Annexations and alliances: When are blocs advantageous a priori?

For any simple voting game (SVG), we consider the question posed in the title from two different points of view as to what voting power means. We also distinguish between blocs imposed by annexation and those formed voluntarily, and present some general theoretical results concerning these notions. We illustrate our theoretical findings with examples using both toy SVGs and the Qualified Majority Voting rule of the Council of Ministers of the European Community (CMEC). We show that when voting power is understood as influence (I-power), forming a voluntary bloc may be advantageous even if its voting power is smaller than the sum of the original powers of its members; and it may be disadvantageous even if its voting power is greater than that sum. Received: 9 February 2000/Accepted: 19 October 2000     

Impartiality,friendship-networks and voting behavior: Evidence from voting patterns in the Eurovision Song Contest

What is the extent to which a country's political institutions impact aggregate voting behavior in a comparative perspective? More specifically, are citizens in some countries more inclined vote on the basis of ‘quality’ or ‘merit’ over ‘friendship’ or ‘loyalty’, and if so, why? This paper seeks to address how the extent to which a country's political institutions are impartial (treats all citizens equally, free from corruption, strong rule of law) impact aggregate citizen behavior. When political institutions are more (less) impartial, success in society is more often on the basis of merit (patrimonial ties). This test cases is voting in the Eurovision Song Contest (ESC) from 1975 to 2012 among pairs and blocs of ‘voting friends’. The theory elucidates that given that certain pairs or blocs exhibit systematic voting bias for one another over time, the bias will be considerably less among impartial states than those with highly partial institutions. Using several measures of ‘friendship’, I find strong empirical evidence for this claim, even when controlling for myriad alternative factors and taking into account various voting regimes. The analysis gives us new insights on how political institutions condition aggregate citizen behavior in general and that although there is much bias in ESC voting, not all bias is equal among friend-countries.     

Voting rules as statistical estimators

We adopt an ‘epistemic’ interpretation of social decisions: there is an objectively correct choice, each voter receives a ‘noisy signal’ of the correct choice, and the social objective is to aggregate these signals to make the best possible guess about the correct choice. One epistemic method is to fix a probability model and compute the maximum likelihood estimator (MLE), maximum a posteriori (MAP) estimator or expected utility maximizer (EUM), given the data provided by the voters. We first show that an abstract voting rule can be interpreted as MLE or MAP if and only if it is a scoring rule. We then specialize to the case of distance-based voting rules, in particular, the use of the median rule in judgement aggregation. Finally, we show how several common ‘quasiutilitarian’ voting rules can be interpreted as EUM.     

Are Condorcet procedures so bad according to the reinforcement axiom?

A Condorcet social choice procedure elects the candidate that beats every other candidate under simple majority when such a candidate exists. The reinforcement axiom roughly states that given two groups of individuals, if these two groups select the same alternative, then this alternative must also be selected by their union. Condorcet social choice procedures are known to violate this axiom. Our goal in this paper is to put this important voting theory result into perspective. We then proceed by evaluating how frequently this phenomenon is susceptible to occur.     

Sophisticated voting rules: the case of two tournaments

A voting rule maps voter preferences into outcomes, and is called sophisticated if there exists a voting tree whose sophisticated outcomes coincide with the voting rule for every voter preference. As yet, no complete characterization of such rules is available. In this paper, we provide an important step toward this characterization by completely solving the problem when there are two possible sets of voter preferences.The second author was supported by the Office of Naval Research, Grant N00014-92-J-1387.     

Voting barriers and solutions: the experiences of people with disabilities during the Dutch national election in 2017

Exercising the right to vote at elections is frequently denied to people with disabilities. In this study, we examined the voting behaviour of individuals with physical or learning impairments and the barriers they encountered during the national elections in 2017 in the Netherlands. A survey design was chosen to allow large-scale questioning of both target groups. Over 90% of people with physical impairments voted and respondents found that voting was accessible. Voter turnout among people with learning impairments was much lower (46%). They experienced difficulty to prepare themselves and at the polling station. The Netherlands seems well on the way to achieving an inclusive environment for people with physical impairments. Recommendations are given about accessibility for all and for exploring alternative methods of voting such as proxy voting and tailoring information and procedures to the needs of people with learning impairments.     

On the voting power of an alliance and the subsequent power of its members

Even, and in fact chiefly, if two or more players in a voting game have on a binary issue independent opinions, they may have interest to form a single voting alliance giving an average gain of influence for all of them. Here, assuming the usual independence of votes, we first study the alliance voting power and obtain new results in the so-called asymptotic limit for which the number of players is large enough and the alliance weight remains a small fraction of the total of the weights. Then, we propose to replace the voting game inside the alliance by a random game which allows new possibilities. The validity of the asymptotic limit and the possibility of new alliances are examined by considering the decision process in the Council of Ministers of the European Union.     

First and second best voting rules in committees

A committee of people with common preferences but different abilities in identifying the best alternative (e.g., a jury) votes in order to decide between two alternatives. The first best voting rule is a weighted voting rule that takes the different individual competences into account, and is therefore not anonymous, i.e., the voters’ identities matter. Under this rule, it is rational for the committee members to vote according to their true opinions, or informatively. This is not necessarily true for an anonymous voting rule, under which members may have an incentive to vote non-informatively. Thus, strategic, sophisticated voters may vary their voting strategies according to the voting rule rather than naively voting informatively. This paper shows that the identity of the best anonymous and monotone (i.e., quota) voting rule does not depend on whether the committee members are strategic or naive or whether some are strategic and some are naive. One such rule, called the second best rule, affords the highest expected utility in all cases.

“Wasn’t he sweet?” said Yossarian. “Maybe they should give him three votes.” Joseph Heller, Catch-22