Equilibrium Agenda Formation

We develop a definition of equilibrium for agenda formation in general voting settings. The definition is independent of any protocol. We show that the set of equilibrium outcomes for any Pareto efficient voting rule is uniquely determined, and in fact coincides with that of the outcomes generated by considering all full agendas. Under voting by successive elimination (or amendment), the set of equilibrium outcomes corresponds with the Banks set. We also examine the implications in several specific settings and show that studying equilibrium agendas can lead to sharp predictions, in contrast with well-known ``chaos'' theorems.agenda, equilibrium, voting, agenda formation

A foundation for strategic agenda voting

We offer complete characterizations of the equilibrium outcomes of two prominent agenda voting institutions that are widely used in the democratic world: the amendment, also known as the Anglo-American procedure, and the successive, or equivalently the Euro-Latin procedure. Our axiomatic approach provides a proper understanding of these voting institutions, and allows comparisons between them, and with other voting procedures.Strategic Voting, Agendas, Committees, Institutions, Axioms

Condorcet admissibility: Indeterminacy and path-dependence under majority voting on interconnected decisions

Judgement aggregation is a model of social choice where the space of social alternatives is the set of consistent evaluations (`views') on a family of logically interconnected propositions, or yes/no-issues. Unfortunately, simply complying with the majority opinion in each issue often yields a logically inconsistent collection of judgements. Thus, we consider the Condorcet set: the set of logically consistent views which agree with the majority in as many issues as possible. Any element of this set can be obtained through a process of diachronic judgement aggregation, where the evaluations of the individual issues are decided through a sequence of majority votes unfolding over time, with earlier decisions possibly imposing logical constraints on later decisions. Thus, for a fixed profile of votes, the ultimate social choice can depend on the order in which the issues are decided; this is called path dependence. We investigate the size and structure of the Condorcet set ---and hence the scope and severity of path-dependence ---for several important classes of judgement aggregation problems.judgement aggregation; diachronic; path-dependence; indeterminacy; Condorcet; median rule; majoritarian

Breaking the Brexit Impasse: Achieving a Fair, Legitimate and Democratic Outcome

Unanimity on the question of UK exit from the EU is not within reach, but this does not mean that the House of Commons or the population at large can not find a way out of the current Brexit impasse that is fair and legitimate. We discuss different voting procedures which satisfy some important principles of democracy and which can select the option that can win a majority against all other alternatives in a head-to-head majority vote. We argue that strategic considerations play an important role and we propose a procedure that works well and can help break the impasse when voters act strategically. The procedure requires (1) that all options with some minimum support are on the agenda, (2) that voting takes place in multiple rounds and (3) that in each round the alternative with the least support is eliminated until in the last round only two alternatives are left and the majority winner is selected. We discuss how this procedure can be modified to take into account that some voters may vote non-strategically and how it, in practice, could be used either in the House of Commons or in a new referendum.</jats:p

Computational aspects of voting: a literature survey

Preference aggregation is a topic of study in different fields such as philosophy, mathematics, economics and political science. Recently, computational aspects of preference aggregation have gained especial attention and “computational politics” has emerged as a marked line of research in computer science with a clear concentration on voting protocols. The field of voting systems, rooted in social choice theory, has expanded notably in both depth and breadth in the last few decades. A significant amount of this growth comes from studies concerning the computational aspects of voting systems. This thesis comprehensively reviews the work on voting systems (from a computing perspective) by listing, classifying and comparing the results obtained by different researchers in the field. This survey covers a wide range of new and historical results yet provides a profound commentary on related work as individual studies and in relation to other related work and to the field in general. The deliverables serve as an overview where students and novice researchers in the field can start and also as a depository that can be referred to when searching for specific results. A comprehensive literature survey of the computational aspects of voting is a task that has not been undertaken yet and is initially realized here. Part of this research was dedicated to creating a web-depository that contains material and references related to the topic based on the survey. The purpose was to create a dynamic version of the survey that can be updated with latest findings and as an online practical reference

Going twice to the polls?: Optimality of two-stage voting procedures

A Masters Thesis, presented as part of the requirements for the award of a Research Masters Degree in Economics from NOVA – School of Business and EconomicsTwo-stage voting systems are commonly used, not only in political elections but in many other types of contests such as the Academy of Motion Pictures Arts and Sciences (AMPAS) awards. These methods are nonetheless more costly than single-stage ones. In this paper we will compare the performance of di¤erent one-stage and two-stage voting systems. In particular, we will analyse the impact of the introduction of a second stage in the ability of electing the Condorcet winner and rejecting the Condorcet loser. Through simulation, we will conclude that under two-stage systems with only two nominees in the second stage, the likelihood of respecting the Condorcet criteria increases signi cantly. However, with three nominees in the second stage, results are ambiguous, depending on the degree of homogeneity of preferences

Eliminating the Weakest Link: Making Manipulation Intractable?

Successive elimination of candidates is often a route to making manipulation intractable to compute. We prove that eliminating candidates does not necessarily increase the computational complexity of manipulation. However, for many voting rules used in practice, the computational complexity increases. For example, it is already known that it is NP-hard to compute how a single voter can manipulate the result of single transferable voting (the elimination version of plurality voting). We show here that it is NP-hard to compute how a single voter can manipulate the result of the elimination version of veto voting, of the closely related Coombs' rule, and of the elimination versions of a general class of scoring rules.Comment: To appear in Proceedings of Twenty-Sixth Conference on Artificial Intelligence (AAAI-12

Nonmanipulable Selections from a Tournament

A tournament is a binary dominance relation on a set of alternatives. Tournaments arise in many contexts that are relevant to AI, most notably in voting (as a method to aggregate the preferences of agents). There are many works that deal with choice rules that select a desirable alternative from a tournament, but very few of them deal directly with incentive issues, despite the fact that game-theoretic considerations are crucial with respect to systems populated by selfish agents. We deal with the problem of the manipulation of choice rules by considering two types of manipulation. We say that a choice rule is emph{monotonic} if an alternative cannot get itself selected by losing on purpose, and emph{pairwise nonmanipulable} if a pair of alternatives cannot make one of them the winner by reversing the outcome of the match between them. Our main result is a combinatorial construction of a choice rule that is monotonic, pairwise nonmanipulable, and onto the set of alternatives, for any number of alternatives besides three