Strategic Voting over Strategic Proposals, Second Version

Prior research on “strategic voting” has reached the conclusion that unanimity rule is uniquely bad: it results in destruction of information, and hence makes voters worse off. We show that this conclusion depends critically on the assumption that the issue being voted on is exogenous, i.e., independent of the voting rule used. We depart from the existing literature by endogenizing the proposal that is put to a vote, and establish that under many circumstances unanimity rule makes voters better off. Moreover, in some cases unanimity rule also makes the proposing individual better off even when he has diametrically opposing preferences. In this case, unanimity is the Pareto dominant voting rule. Voters prefer unanimity rule because it induces the proposing individual to make a more attractive proposal. The proposing individual prefers unanimity rule because the acceptance probabilities for moderate proposals are higher.Strategic voting; agenda setting; multilateral bargaining

Persuading voters

In a symmetric information voting model, an individual (information controller) can influence voters’ choices by designing the information content of a public signal. We characterize the controller’s optimal signal. With a non-unanimous voting rule, she exploits voters’ heterogeneity by designing a signal with realizations targeting di↵erent winning-coalitions. Consequently, under simple-majority voting rule, a majority of voters might be strictly worse o↵ due to the controller’s influence. We characterize voters’ preferences over electoral rules, and provide conditions for a majority of voters to prefer a supermajority (or unanimity) voting rule, in order to induce the controller to supply a more informative signal

Persuading voters

In a symmetric information voting model, an individual (politician) can influence voters' choices by strategically designing a policy experiment (public signal). We characterize the politician's optimal experiment. With a non-unanimous voting rule, she exploits voters' heterogeneity by designing an experiment with realizations targeting different winning coalitions. Consequently, under a simple-majority rule, a majority of voters might be strictly worse off due to the politician's influence. We characterize voters' preferences over electoral rules and provide conditions for a majority of voters to prefer a supermajority (or unanimity) voting rule, in order to induce the politician to supply a more informative experiment

On anonymous and weighted voting systems

Many bodies around the world make their decisions through voting systems in which voters have several options and the collective result also has several options. Many of these voting systems are anonymous, i.e., all voters have an identical role in voting. Anonymous simple voting games, a binary vote for voters and a binary collective decision, can be represented by an easy weighted game, i.e., by means of a quota and an identical weight for the voters. Widely used voting systems of this type are the majority and the unanimity decision rules. In this article, we analyze the case in which voters have two or more voting options and the collective result of the vote has also two or more options. We prove that anonymity implies being representable through a weighted game if and only if the voting options for voters are binary. As a consequence of this result, several significant enumerations are obtained.This research was partially supported by funds from the Spanish Ministry of Science and Innovation grant PID2019-I04987GB-I00. We are grateful to the associate editor and two anonymous referees whose interesting comments allowed us to improve the paper.Peer ReviewedPostprint (author's final draft

Tops-Only Domains

In this paper we consider the standard voting model with a finite set of alternatives A and n voters and address the following question : what are the characteristics of domains D that induce the property that every strategy-proof social choice function f : Dn -> A satisfying unanimity, has the tops-only property? We first impose a minimal richness condition which ensures that for every alternative a, there exists an admissible ordering where a is maximal. We identify conditions on D that are sufficient for strategy-proofness and unanimity to imply tops onlyness in the general case of n voters and in the special case, n = 2. We provide an algorithm for constructing tops-only domains from connected graphs with elements of A as nodes. We provide several applications of our results. Finally, we relax the minimal richness assumption and partially extend our results.Voting, social choice, tops-only domain

The Principle of Unanimity and Voluntary Consent in Social Choice

A discrete version of the author\u27s incentive-compatible Auction Mechanism for public goods is applied to the problem of social choice (voting) among distinct mutually exclusive alternatives. This Auction Election is a bidding mechanism characterized by (1) unanimity, (2) provision for the voluntary compensation of voters harmed by a winning proposition, and (3) incentives for \u27reasonable\u27 bidding by excluding members of a collective from maximal increase in benefit if they fail to agree on the proposition with largest surplus. Four of five experiments with six voters, bidding privacy, monetary rewards, and cyclical majority rule structure choose the best of three propositions

Approval-Based Shortlisting

Shortlisting is the task of reducing a long list of alternatives to a (smaller) set of best or most suitable alternatives from which a final winner will be chosen. Shortlisting is often used in the nomination process of awards or in recommender systems to display featured objects. In this paper, we analyze shortlisting methods that are based on approval data, a common type of preferences. Furthermore, we assume that the size of the shortlist, i.e., the number of best or most suitable alternatives, is not fixed but determined by the shortlisting method. We axiomatically analyze established and new shortlisting methods and complement this analysis with an experimental evaluation based on biased voters and noisy quality estimates. Our results lead to recommendations which shortlisting methods to use, depending on the desired properties

Quantum voting and violation of Arrow's Impossibility Theorem

We propose a quantum voting system, in the spirit of quantum games such as the quantum Prisoner's Dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's Impossibility Theorem. Arrow's Theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's Theorem. A quantum version of majority rule, we show, violates this Quantum Arrow Conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.Comment: Version accepted by Phys. Rev. A. Added background and references about game theory and about Arrow's Theorem. Added an opportunity for further research. For citation purposes: The second author's family name is "Yunger Halpern" (not "Halpern"

Voting with Coarse Beliefs

The classic Gibbard-Satterthwaite theorem says that every strategy-proof voting rule with at least three possible candidates must be dictatorial. Similar impossibility results hold even if we consider a weaker notion of strategy-proofness where voters believe that the other voters' preferences are i.i.d.~(independent and identically distributed). In this paper, we take a bounded-rationality approach to this problem and consider a setting where voters have "coarse" beliefs (a notion that has gained popularity in the behavioral economics literature). In particular, we construct good voting rules that satisfy a notion of strategy-proofness with respect to coarse i.i.d.~beliefs, thus circumventing the above impossibility results