Related papers: What majority decisions are possible with possible…

Important decisions are likely made by groups of agents. Thus group decision making is very common in practice. Very transparent group aggregating rules are given by weighted voting, where each agent is assigned a weight. Here a proposal is…

Are there voting methods which (i) give everyone, including minorities, an equal share of effective power even if voters act strategically, (ii) promote consensus rather than polarization and inequality, and (iii) do not favour the status…

We study the properties of elections that have a given position matrix (in such elections each candidate is ranked on each position by a number of voters specified in the matrix). We show that counting elections that generate a given…

We investigate the dynamics of the majority-rule opinion formation model when voters experience differential latencies. With this extension, voters that just adopted an opinion go into a latent state during which they are excluded from the…

The \((n,k)\) game models a group of \(n\) individuals with binary opinions, say 1 and 0, where a decision is made if at least \(k\) individuals hold opinion 1. This paper explores the dynamics of the game with heterogeneous agents under…

We present a new model that describes the process of electing a group of representatives (e.g., a parliament) for a group of voters. In this model, called the voting committee model, the elected group of representatives runs a number of…

This paper studies choice situations in which a decision maker can choose multiple alternatives. Given a menu of available options, the decision maker selects a subset of the menu with certain probabilities. We employ an axiomatic approach…

In this work we generalize standard Decision Theory by assuming that two outcomes can also be incomparable. Two motivating scenarios show how incomparability may be helpful to represent those situations where, due to lack of information,…

Determination of the range of a variety of social choice correspondences: Plurality voting, the Borda rule, the Pareto rule, the Copeland correspondence, approval voting, and the top cycle correspondence

We consider a setting where one has to organize one or several group activities for a set of agents. Each agent will participate in at most one activity, and her preferences over activities depend on the number of participants in the…

To understand and summarize approval preferences and other binary evaluation data, it is useful to order the items on an axis which explains the data. In a political election using approval voting, this could be an ideological left-right…

This paper introduces a novel binary stability property for voting rules-called binary self-selectivity-by which a society considering whether to replace its voting rule using itself in pairwise elections will choose not to do so. In…

We study many-to-one matching problems between institutions and individuals, where each institution may be matched to multiple individuals. The matching market includes couples, who view pairs of institutions as complementary. Institutions'…

In this paper, we propose a framework to study a general class of strategic behavior in voting, which we call vote operations. We prove the following theorem: if we fix the number of alternatives, generate $n$ votes i.i.d. according to a…

This paper presents some fundamental collective choice theory for information system designers, particularly those working in the field of computer-supported cooperative work. This paper is focused on a presentation of Arrow's Possibility…

A continuous selection of polynomial functions is a continuous function whose domain can be partitioned into finitely many pieces on which the function coincides with a polynomial. Given a set of finitely many polynomials, we show that…

A cornerstone of social choice theory is Condorcet's paradox which says that in an election where $n$ voters rank $m$ candidates it is possible that, no matter which candidate is declared the winner, a majority of voters would have…

Election data represent a precious source of information to study human behavior at a large scale. In proportional elections with open lists, the number of votes received by a candidate, rescaled by the average performance of all…

This paper discusses the question of how many non-empty subsets of the set $[n] = \{ 1, 2, ..., n\}$ we can choose so that no chosen subset is the union of some other chosen subsets. Let $M(n)$ be the maximum number of subsets we can…

We prove that every Condorcet-consistent voting rule can be manipulated by a voter who completely reverses their preference ranking, assuming that there are at least 4 alternatives. This corrects an error and improves a result of [Sanver,…