Related papers: Monotone Randomized Apportionment
In this article, we introduce mixture representations for likelihood ratio ordered distributions. Essentially, the ratio of two probability densities, or mass functions, is monotone if and only if one can be expressed as a mixture of…
Peer reviews, evaluations, and selections are a fundamental aspect of modern science. Funding bodies the world over employ experts to review and select the best proposals from those submitted for funding. The problem of peer selection,…
We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for $n$-sided dice with pairwise ordering induced by the probability, relative to $1/2$, that a throw from one die is…
The study of proportionality in multiwinner voting with approval ballots has received much attention in recent years. Typically, proportionality is captured by variants of the Justified Representation axiom, which say that cohesive groups…
Respecting minority opinions is vital in solving social problems. However, minority opinions are often ignored in general majority rules. To build consensus on pluralistic values and make social choices that consider minority opinions, we…
We study the problem of fairly allocating indivisible goods to groups of agents. Agents in the same group share the same set of goods even though they may have different preferences. Previous work has focused on unanimous fairness, in which…
The basic idea of voting protocols is that nodes query a sample of other nodes and adjust their own opinion throughout several rounds based on the proportion of the sampled opinions. In the classic model, it is assumed that all nodes have…
We consider elections where the voters come one at a time, in a streaming fashion, and devise space-efficient algorithms which identify an approximate winning committee with respect to common multiwinner proportional representation voting…
We study a mathematical model of voting contest with $m$ voters and $n$ candidates, with each voter ranking the candidates in order of preference, without ties. A Condorcet winner is a candidate who gets more than $m/2$ votes in pairwise…
We consider object allocation problems with capacities (see, e.g., Abdulkadiroglu and Sonmez, 1998; Basteck, 2025) where objects have to be assigned to agents. We show that if a lottery rule satisfies ex-post non-wastefulness and…
Proportional representation (PR) is often discussed in voting settings as a major desideratum. For the past century or so, it is common both in practice and in the academic literature to jump to single transferable vote (STV) as the…
The Majority Rule is applied to a topology that consists of two coupled random networks, thereby mimicking the modular structure observed in social networks. We calculate analytically the asymptotic behaviour of the model and derive a phase…
A large amount of literature in social choice theory deals with quantifying the probability of certain election outcomes. One way of computing the probability of a specific voting situation under the Impartial Anonymous Culture assumption…
The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party to a smaller number $m$…
In this paper, we study the problem of Participatory Budgeting (PB) with approval ballots, inspired by Multi-Winner Voting schemes. We present generalized preference aggregation methods for participatory budgeting, especially for finding…
We develop a framework that leverages the smoothed complexity analysis by Spielman and Teng to circumvent paradoxes and impossibility theorems in social choice, motivated by modern applications of social choice powered by AI and ML. For…
We prove that under the Jefferson--D'Hondt method of apportionment, given certain distributional assumptions regarding mean rounding residuals, as well as absence of correlations between party vote shares, district sizes (in votes), and…
Citizens' assemblies are a form of democratic innovation in which a randomly selected panel of constituents deliberates on questions of public interest. We study a novel goal for the selection of panel members: maximizing the entropy of the…
The Condorcet Jury Theorem or the Miracle of Aggregation are frequently invoked to ensure the competence of some aggregate decision-making processes. In this article we explore an estimation of the prior probability of the thesis predicted…
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…