Acyclic Games and Iterative Voting

We consider iterative voting models and position them within the general framework of acyclic games and game forms. More specifically, we classify convergence results based on the underlying assumptions on the agent scheduler (the order of players) and the action scheduler (which better-reply is played). Our main technical result is providing a complete picture of conditions for acyclicity in several variations of Plurality voting. In particular, we show that (a) under the traditional lexicographic tie-breaking, the game converges for any order of players under a weak restriction on voters' actions; and (b) Plurality with randomized tie-breaking is not guaranteed to converge under arbitrary agent schedulers, but from any initial state there is \emph{some} path of better-replies to a Nash equilibrium. We thus show a first separation between restricted-acyclicity and weak-acyclicity of game forms, thereby settling an open question from [Kukushkin, IJGT 2011]. In addition, we refute another conjecture regarding strongly-acyclic voting rules.Comment: some of the results appeared in preliminary versions of this paper: Convergence to Equilibrium of Plurality Voting, Meir et al., AAAI 2010; Strong and Weak Acyclicity in Iterative Voting, Meir, COMSOC 201

A conditional defense of plurality rule: generalizing May's theorem in a restricted informational environment

May's theorem famously shows that, in social decisions between two options, simple majority rule uniquely satisfies four appealing conditions. Although this result is often cited in support of majority rule, it has never been extended beyond decisions based on pairwise comparisons of options. We generalize May's theorem to many-option decisions where voters each cast one vote. Surprisingly, plurality rule uniquely satisfies May's conditions. This suggests a conditional defense of plurality rule: If a society's balloting procedure collects only a single vote from each voter, then plurality rule is the uniquely compelling electoral procedure. To illustrate the conditional nature of this claim, we also identify a richer informational environment in which approval voting, not plurality rule, is supported by a May-style argument

On Societies Choosing Social Outcomes, and their Memberships : Strategy-proofness

April 2017, Volume 48, Issue 4, pp 857-875The work of G. Bergantiños is partially supported by research Grants ECO2014-52616-R from the Spanish Ministry of Science and Competitiveness, GRC 2015/014 from "Xunta de Galicia", and 19320/PI/14 from " Fundaci ón Séneca de la Región de Murcia". J. Massó acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2015-0563) and Grant ECO2014-53051, and from the Generalitat de Catalunya, through Grant SGR2014-515. The paper was partly written while J. Massó was visiting the Department of Economics at Stanford University; he wishes to acknowledge its hospitality as well as financial support from the Ministerio de Educación, Cultura y Deporte through project PR2015-00408. The work of A. Neme is partially supported by the Universidad Nacional de San Luis, through Grant 319502, and by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), through Grant PIP 112-200801-00655.We consider a society whose members have to choose not only an outcome from a given set of outcomes but also the subset of agents that will remain members of the society. We assume that each agent is indifferent between any two alternatives (pairs of final societies and outcomes) provided that the agent does not belong to any of the two final societies, regardless of the chosen outcome. Under this preference domain restriction we characterize the class of all strategy-proof, unanimous and outsider independent rules as the family of all serial dictator rules