Quaternary dichotomous voting rules

In this article, we provide a general model of “quaternary” dichotomous voting rules (QVRs), namely, voting rules for making collective dichotomous decisions (to accept or reject a proposal), based on vote profiles in which four options are available to each voter: voting (“yes”, “no”, or “abstaining”) or staying home and not turning out. The model covers most of actual real-world dichotomus rules, where quorums are often required, and some of the extensions considered in the literature. In particular, we address and solve the question of the representability of QVRs by means of weighted rules and extend the notion of “dimension” of a rule.     

Systematic analysis of multiple voting rules

For a class of voting rules, which includes Approval and Cumulative Voting, it is shown how to find and analyze all possible outcomes that arise with a specified profile, and, conversely, how to start with a potential region and determine whether there exist supporting profiles. The geometry of these regions is determined by the “Reversal symmetry” portion of a profile; i.e., components of the Asucc Bsucc C, Csucc Bsucc A{Asucc Bsucc C, Csucc Bsucc A} type.     

Optimal voting rules for two-member tenure committees

A tenure committee first votes on whether to hire a candidate; if it does, it receives an informative performance signal, and then votes on whether to tenure the candidate; rejection at either stage returns the committee to a candidate pool, endogenising the value of the outside option. A candidate’s fate depends only on the behaviour of two ‘weather-vane’ committee members. Committee members may vote against favoured candidates if the weather-vane is opposed; enthusiastic assessments by one of these weather-vanes may harm a candidate’s chances by increasing others’ thresholds for hiring him; sunk time costs may lead voters who voted against hiring to vote for tenuring him, even after a poor probationary performance. For two member committees that are patient and perceptive, the optimal voting rule is a (weak) majority at the hiring stage and unanimity at the tenure stage; when such committees are impatient or imperceptive, the double (weak) majority rule is optimal. Perversely, the performance of a patient, imperceptive committee improves as its perceptiveness further declines. Consistent with practice, falling threshold rules are not optimal. Results on optimal voting rules are also presented in limit cases as committee members’ beliefs become more correlated. Finally, we compare the model to a discrete-time European options model.     

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

     

Subgame perfect implementation of voting rules via randomized mechanisms

We characterize completely ordinal and onto choice rules that are subgame perfect of Nash equilibrium (SPE) implementable via randomized mechanisms under strict preferences. The characterization is very operationalizable, and allows us to analyse SPE implementability of voting rules. We show that no scoring rule is SPE implementable. However, the top-cycle and the uncovered correspondences as well as plurality with runoff and any strongly Condorcet consistent voting rule can be SPE implemented. Therefore our results are favourable to majority based voting rules over scoring rules. Nevertheless, we show that many interesting Condorcet consistent but not strongly Condorcet consistent rules, such as the Copeland rule, the Kramer rule and the Simpson rule, cannot be SPE implemented.     

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.     

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.     

Independence of clones as a criterion for voting rules

Independence of clones is a generalization of the condition of not being subject to the perverse consequences of vote splitting that arise under plurality voting. A new voting rule that is at least almost always independent of clones is obtained by the following algorithm: Require the collective ranking of the candidates to be consistent with the paired comparisons decided by the largest and second largest margins, and then, if possible, with the paired comparison decided by the third largest margin, and so on. The advantages of this ranked pairs rule over previously proposed voting rules that are independent of clones is that it possesses Condorcet consistency, non-negative responsiveness, and resolvability (the property that every tie be within one vote of being broken).I am indebted to Jaques Crémer, Amoz Kats, Martin Ricketts, Thomas Schwartz and an anonymous referee for helpful suggestions.     

On the manipulability of approval voting and related scoring rules

We characterize all preference profiles at which the approval (voting) rule is manipulable, under three extensions of preferences to sets of candidates: by comparison of worst candidates, best candidates, or by comparison based on stochastic dominance. We perform a similar exercise for k-approval rules, where voters approve of a fixed number k of candidates. These results can be used to compare (k-)approval rules with respect to their manipulability. Analytical results are obtained for the case of two voters, specifically, the values of k for which the k-approval rule is minimally manipulable—has the smallest number of manipulable preference profiles—under the various preference extensions are determined. For the number of voters going to infinity, an asymptotic result is that the k-approval rule with k around half the number of candidates is minimally manipulable among all scoring rules. Further results are obtained by simulation and indicate that k-approval rules may improve on the approval rule as far as manipulability is concerned.     

A characterization of strategy-proof voting rules for separable weak orderings

We consider the problem of choosing a subset of a finite set of indivisible objects (public projects, facilities, laws, etc.) studied by Barberà et al. (1991). Here we assume that agents preferences are separable weak orderings. Given such a preference, objects are partitioned into three types, goods, bads, and nulls. We focus on voting rules, which rely only on this partition rather than the full information of preferences. We characterize voting rules satisfying strategy-proofness (no one can ever be better off by lying about his preference) and null-independence (the decision on each object should not be dependent on the preference of an agent for whom the object is a null). We also show that serially dictatorial rules are the only voting rules satisfying efficiency as well as the above two axioms. We show that the separable domain is the unique maximal domain over which each rule in the first characterization, satisfying a certain fairness property, is strategy-proof. I am grateful to Professor William Thomson for helpful comments and suggestions. I also thank Professor John Duggan, Christopher Chambers, and seminar participants in Department of Economics, University of Rochester. I thank anonymous referees for their detailed comments and suggestions that helped me a great deal to develop the earlier version of this paper. All remaining errors are mine.     

A note on the Condorcet Jury Theorem with supermajority voting rules

Social Choice and Welfare -     

Majority voting rules and the union success rate in national labor relations board representation elections

This paper simulates how the union success rate in representation elections would be affected if the NLRB reverted from its current simple-majority voting rule to its original majority-in-unit voting rule. Such a rule change would have altered 21 percent of decertification and 16 percent of certification victories over the period 1977–81, resulting in the loss of 180,400 actual or potential bargaining unit members for the union movement. Abstentions play an important role in election outcomes. Under the present voting rule unions have no clear advantage to “get out the vote” in decertification elections, but a clear disadvantage in certification elections. Under a majority-in-unit rule unions hold an advantage when they “get out the vote” in all representation elections. I would like to thank Mike Bognanno, Jim Dworkin, Paul Schumann, two reviewers, and the editor for helpful comments and David Wilson for excellent research assistance. I would also like to thank the NLRB for providing the election data tape.     

Strategic, sincere, and heuristic voting under four election rules: an experimental study

We report on laboratory experiments on voting. In a setting where subjects have single-peaked preferences, we find that the rational choice theory provides very good predictions of actual individual behavior in one-round and approval voting elections but fares poorly in explaining vote choice under two-round elections. We conclude that voters behave strategically as far as strategic computations are not too demanding, in which case they rely on simple heuristics (under two-round voting) or they just vote sincerely (under single transferable vote).     

Yes-no voting

Yes-No (Y-N) voting is a voting method for choosing a governing coalition in a parliament after the seating of its members. Each member can designate a party to be Y (it must be included in the governing coalition), N (it must be excluded from the governing coalition), or neither (it may be either in or out of the governing coalition). The majority coalition acceptable to the most voters, because it includes all parties that these voters designate Y and no parties that they designate N, is given the first opportunity to form a government. Possible combinations of majority coalitions that a member might vote for are derived, including ones based on consistent and interval voting strategies. Examples illustrate a number of different phenomena, such as when a rational voter might not be loyal to his or her party by designating it Y.     

Fairness and voting

In this paper we present a two-period model in which we examine how concern about fairness might affect voter behavior. We show that in the first period politicians choose the median voter’s position even if this does not correspond to their bliss points and neither they nor the voters can commit to a particular action. Moreover, concern about fairness creates substantial incumbency advantages. Our results hold even if voters care very little about fairness.     

The objective and subjective rationalization of war

Perhaps the most engaging theories in historical sociology have been those pertaining to the rationalization of Western society. In particular, both Max Weber and Michelle Foucault point to the unique nature of societal rationalization in the early modern period, a thorough-going upheaval both in forms of social organization and in individual subjectivity. These correlative changes led to the nature of the modern state and its citizens. One example used by both is the rationalization of warfare. Close attention to the question of rationalization and the history of infantry warfare, however, suggests that far from representing a watershed change from non-rationalized to rationalized war, the early-modern period was more like other rapid expansions of armies based on recruitment of commoners, and had little to do with the distinctive characteristics of the emerging nation-states.     

Stability of voting games

This paper generalizes the result of Le Breton and Salles (1990) about stable set (far-sighted core of order 1) for voting games to far-sighted core of arbitrary order. Let m be the number of alternatives, n be the number of voters and G(n,k) be a proper symmetric simple game in which the size of a winning coalition is greater or equal to k. It is shown that the far-sighted core of order d for G(n,k) is nonempty for all preference profiles and for all n and k with n/(n–k)=v ¹ iff m(d+1)(v–1).This paper is part of my dissertation. I am grateful to my thesis advisor Leonid Hurwicz for his guidance and encouragement. I would like to thank Edward Green, Lu Hong, James Jordan, Andrew McLennan, Herve Moulin and Marcel Richter for their very helpful suggestions. Especially a referee and Maurice Salles made many good comments. Of course, any errors that remain are the sole responsibility of the author.