Related papers: Symmetric majority rules
A canonical problem in social choice is how to aggregate ranked votes: given $n$ voters' rankings over $m$ candidates, what voting rule $f$ should we use to aggregate these votes into a single winner? One standard method for comparing…
We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of…
This study proposes a new efficiency requirement, a minimal almost weak Pareto principle, which says that x is socially better than y whenever the only one individual never prefers y to x, and all the others prefers x to y. Then, I show…
When selecting a subset of candidates (a so-called committee) based on the preferences of voters, proportional representation is often a major desideratum. When going beyond simplistic models such as party-list or district-based elections,…
We explore the relation between two natural symmetry properties of voting rules. The first is transitive-symmetry -- the property of invariance to a transitive permutation group -- while the second is the "unbiased" property of every voter…
The proportional veto principle, which captures the idea that a candidate vetoed by a large group of voters should not be chosen, has been studied for ranked ballots in single-winner voting. We introduce a version of this principle for…
We investigate the rank of random (symmetric) sparse matrices. Our main finding is that with high probability, any dependency that occurs in such a matrix is formed by a set of few rows that contains an overwhelming number of zeros. This…
In a context where a decision has to be taken collectively by several agents, the social choice problem consists in deciding whether there exists a socially acceptable rule that aggregates the individual preferences of the agents into a…
We study consensus processes on the complete graph of $n$ nodes. Initially, each node supports one from up to n opinions. Nodes randomly and in parallel sample the opinions of constant many nodes. Based on these samples, they use an update…
A social decision rule (SDR) is any non-empty set-valued map that associates any profile of individual preferences with the set of (winning) alternatives. An SDR is Condorcet-consistent if it selects the set of Condorcet winners whenever…
A population of heterogenous agents compeeting through a minority rule is investigated. Agents which frequently loose are selected for evolution by changing their strategies. The stationary composition of the population resulting for this…
We study a model of opinion formation where the opinions in conflict are not equivalent. This is the case when the subject of the decision is to respect a norm or a law. In such scenarios, one of the possible behaviors is to abide by the…
Within the ViSE (Voting in Stochastic Environment) model, we study the effectiveness of majority voting in various environments. As shown by the pit-of-losses paradox identified in previous work, majority decisions in apparently hostile…
The traditional axiomatic approach to voting is motivated by the problem of reconciling differences in subjective preferences. In contrast, a dominant line of work in the theory of voting over the past 15 years has considered a different…
A voter sits on each vertex of an infinite tree of degree $k$, and has to decide between two alternative opinions. At each time step, each voter switches to the opinion of the majority of her neighbors. We analyze this majority process when…
Within the model of social dynamics determined by collective decisions in a stochastic environment (the ViSE model), we consider the case of a homogeneous society consisting of classically rational economic agents. We obtain analytical…
We consider a dynamic collective choice problem where a large number of players are cooperatively choosing between multiple destinations while being influenced by the behavior of the group. For example, in a robotic swarm exploring a new…
In frequently repeated matching scenarios, individuals may require diversification in their choices. Therefore, when faced with a set of potential outcomes, each individual may have an ideal lottery over outcomes that represents their…
We consider distributed plurality consensus in a complete graph of size $n$ with $k$ initial opinions. We design an efficient and simple protocol in the asynchronous communication model that ensures that all nodes eventually agree on the…
Implicit bias is the unconscious attribution of particular qualities (or lack thereof) to a member from a particular social group (e.g., defined by gender or race). Studies on implicit bias have shown that these unconscious stereotypes can…