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Even though proportional representation is a fundamental goal in multiwinner voting and a plethora of proportionality notions has been introduced, the normative justifications for choosing one notion over another remain poorly understood.…
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…
In multiagent settings where the agents have different preferences, preference aggregation is a central issue. Voting is a general method for preference aggregation, but seminal results have shown that all general voting protocols are…
We investigate how robust approval-based multiwinner voting rules are to small perturbations in the votes. In particular, we consider the extent to which a committee can change after we add/remove/swap one approval, and we consider the…
We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…
Maximum likelihood estimation furnishes powerful insights into voting theory, and the design of voting rules. However the MLE can usually be badly corrupted by a single outlying sample. This means that a single voter or a group of colluding…
Tsfasman-Boguslavsky Conjecture predicts the maximum number of zeros that a system of linearly independent homogeneous polynomials of the same positive degree with coefficients in a finite field can have in the corresponding projective…
The important Kemeny problem, which consists of computing median consensus rankings of an election with respect to the Kemeny voting rule, admits important applications in biology and computational social choice and was generalized recently…
The Borel--Kolmogorov paradox of conditioning with respect to events of prior probability zero has fascinated students and researchers since its discovery more than 100 years ago. Classical conditioning is only valid with respect to events…
We consider the problem of selecting an $n$-member committee made up of one of $m$ candidates from each of $n$ distinct departments. Using an algebraic approach, we analyze positional voting procedures, including the Borda count, as…
We present a relation-algebraic model of Condorcet voting and, based on it, relation-algebraic solutions of the constructive control problem via the removal of voters. We consider two winning conditions, viz. to be a Condorcet winner and to…
Pull voting is a classic method to reach consensus among $n$ vertices with differing opinions in a distributed network: each vertex at each step takes on the opinion of a random neighbour. This method, however, suffers from two drawbacks.…
This paper considers elections in which voters choose one candidate each, independently according to known probability distributions. A candidate receiving a strict majority (absolute or relative, depending on the version) wins. After the…
We study the problem of coalitional manipulation---where $k$ manipulators try to manipulate an election on $m$ candidates---under general scoring rules, with a focus on the Borda protocol. We do so both in the weighted and unweighted…
Previous studies have shown that Instant-Runoff Voting (IRV) is highly resistant to coalitional manipulation (CM), though the theoretical reasons for this remain unclear. To address this gap, we analyze the susceptibility to CM of three…
Sidorenko's conjecture states that the number of copies of any given bipartite graph in another graph of given density is asymptotically minimized by a random graph. The forcing conjecture further strengthens this, claiming that any…
This paper provides conditions on the observation probability distribution in Bayesian localization and optimal filtering so that the conditional mean estimate satisfies convex stochastic dominance. Convex dominance allows us to compare the…
The maximum independent set problem is a classic optimization problem that has also been studied quite intensively in the distributed setting. While the problem is hard to approximate in general, there are good approximation algorithms…
Motivated by the difficulty of specifying complete ordinal preferences over a large set of $m$ candidates, we study voting rules that are computable by querying voters about $t < m$ candidates. Generalizing prior works that focused on…
In this paper, we study the metric distortion of deterministic social choice rules that choose a winning candidate from a set of candidates based on voter preferences. Voters and candidates are located in an underlying metric space. A voter…