Related papers: Plurality in Spatial Voting Games with constant $\…
We study the problem of fair sequential decision making given voter preferences. In each round, a decision rule must choose a decision from a set of alternatives where each voter reports which of these alternatives they approve. Instead of…
We analyse strategic, complete information, sequential voting with ordinal preferences over the alternatives. We consider several voting mechanisms: plurality voting and approval voting with deterministic or uniform tie-breaking rules. We…
We study the design of voting rules in the metric distortion framework. It is known that any deterministic rule suffers distortion of at least $3$, and that randomized rules can achieve distortion strictly less than $3$, often at the cost…
We consider multiwinner elections in Euclidean space using the minimax Chamberlin-Courant rule. In this setting, voters and candidates are embedded in a $d$-dimensional Euclidean space, and the goal is to choose a committee of $k$…
We consider voting on multiple independent binary issues. In addition, a weighting vector for each voter defines how important they consider each issue. The most natural way to aggregate the votes into a single unified proposal is…
Distortion-based analysis has established itself as a fruitful framework for comparing voting mechanisms. m voters and n candidates are jointly embedded in an (unknown) metric space, and the voters submit rankings of candidates by…
Let L be a positive line bundle over a projective complex manifold X. Consider the space of holomorphic sections of the tensor power of order p of L. The determinant of a basis of this space, together with some given probability measure on…
The voting systems known as Alternative Vote (AV) and Single Transferable Vote (STV) are extensively used for elections in Australia, possibly more than in any other jurisdiction. Often proposed as superior alternatives to Plurality and…
We prove the three candidate Plurality is Stablest Conjecture of Khot-Kindler-Mossel-O'Donnell from 2005 for correlations $\rho$ satisfying $-1/43<\rho<1/10$: the Plurality function is the most noise stable three candidate election method…
We examine two aspects of the mathematical basis for two-tier voting systems, such as that of the Council of the European Union. These aspects concern the use of square-root weights and the choice of quota. Square-root weights originate in…
We consider synchronous iterative voting, where voters are given the opportunity to strategically choose their ballots depending on the outcome deduced from the previous collective choices.We propose two settings for synchronous iterative…
Multi-winner voting is the process of selecting a fixed-size set of representative candidates based on voters' preferences. It occurs in applications ranging from politics (parliamentary elections) to the design of modern computer…
We present arguments in favour of the inequalities $var(X_n^2|X \in B_v(\rho)) \le 2\lambda_n E[X_n^2|X \in B_v(\rho)]$, where $X \sim N_v(0,\Lambda)$ is a normal vector in $v\ge 1$ dimensions, with zero mean and covariance matrix $\Lambda…
A subset $A$ of a vector space $X$ is called $\alpha$-lineable whenever $A$ contains, except for the null vector, a subspace of dimension $\alpha$. If $X$ has a topology, then $A$ is $\alpha$-spaceable if such subspace can be chosen to be…
In the apportionment problem, a fixed number of seats must be distributed among parties in proportion to the number of voters supporting each party. We study a generalization of this setting, in which voters can support multiple parties by…
Multi-winner approval elections are seen in a variety of settings ranging from academic societies and associations to public elections. In such elections, it is often the case that ballot-length restrictions are enforced; that is, where…
An important aspect of AI design and ethics is to create systems that reflect aggregate preferences of the society. To this end, the techniques of social choice theory are often utilized. We propose a new social choice function motivated by…
We consider iterative voting models and position them within the general framework of acyclic games and game forms. More specifically, we classify convergence results based on the underlying assumptions on the agent scheduler (the order of…
We introduce a novel definition for a small set R of k points being "representative" of a larger set in a metric space. Given a set V (e.g., documents or voters) to represent, and a set C of possible representatives, our criterion requires…
The {\em Maximal} points in a set S are those that aren't {\em dominated} by any other point in S. Such points arise in multiple application settings in which they are called by a variety of different names, e.g., maxima, Pareto optimums,…