Related papers: Monotone Randomized Apportionment
The well-known Condorcet's Jury theorem posits that the majority rule selects the best alternative among two available options with probability one, as the population size increases to infinity. We study this result under an asymmetric…
A Ranked candidate voting method based on Phragmen's procedure is described that can be used to produce a top-down proportional candidate list. The method complies with the Droop proportionality criterion satisfied by Single Transferable…
The apportionment problem asks how to assign representation to states based on their populations. That is, given census data and a fixed number of seats, how many seats should each state be assigned? Various algorithms exist to solve the…
May's Theorem (1952), a celebrated result in social choice, provides the foundation for majority rule. May's crucial assumption of symmetry, often thought of as a procedural equity requirement, is violated by many choice procedures that…
The well-known Condorcet Jury Theorem states that, under majority rule, the better of two alternatives is chosen with probability approaching one as the population grows. We study an asymmetric setting where voters face varying…
The apportionment problem deals with the fair distribution of a discrete set of $k$ indivisible resources (such as legislative seats) to $n$ entities (such as parties or geographic subdivisions). Highest averages methods are a frequently…
Fairness in multiwinner elections is studied in varying contexts. For instance, diversity of candidates and representation of voters are both separately termed as being fair. A common denominator to ensure fairness across all such contexts…
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,…
We establish a link between multiwinner elections and apportionment problems by showing how approval-based multiwinner election rules can be interpreted as methods of apportionment. We consider several multiwinner rules and observe that…
Ranked-choice voting anomalies such as monotonicity paradoxes have been extensively studied through creating hypothetical examples and generating elections under various models of voter behavior. However, very few real-world examples of…
We study multiwinner elections with approval-based preferences. An instance of a multiwinner election consists of a set of alternatives, a population of voters---each voter approves a subset of alternatives, and the desired committee size…
Despite extensive theoretical research on proportionality in approval-based multiwinner voting, its impact on which committees and candidates can be selected in practice remains poorly understood. We address this gap by (i) analyzing the…
Proportional apportionment is the problem of assigning seats to parties according to their relative share of votes. Divisor methods are the de-facto standard solution, used in many countries. In recent literature, there are two algorithms…
Every representative democracy must specify a mechanism under which voters choose their representatives. The most common mechanism in the United States -- Winner takes all single-member districts -- both enables substantial partisan…
In approval-based budget division, a budget needs to be distributed to candidates based on the voters' approval ballots over these candidates. In the pursuit of a simple, consistent, and approximately fair rule for this setting, we…
A matching game is a cooperative profit game defined on an edge-weighted graph, where the players are the vertices and the profit of a coalition is the maximum weight of matchings in the subgraph induced by the coalition. A population…
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…
Arrow's Impossibility Theorem is a seminal result of Social Choice Theory that demonstrates the impossibility of ranked-choice decision-making processes to jointly satisfy a number of intuitive and seemingly desirable constraints. The…
We establish an equivalence between two seemingly different theories: one is the traditional axiomatisation of incomplete preferences on horse lotteries based on the mixture independence axiom; the other is the theory of desirable gambles…
We consider a model where a subset of candidates must be selected based on voter preferences, subject to general constraints that specify which subsets are feasible. This model generalizes committee elections with diversity constraints,…