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We consider the problem of finding the $k^{th}$ highest element in a totally ordered set of $n$ elements (select), and partitioning a totally ordered set into the top $k$ and bottom $n-k$ elements (partition) using pairwise comparisons.…
We consider a spatial voting model where both candidates and voters are positioned in the $d$-dimensional Euclidean space, and each voter ranks candidates based on their proximity to the voter's ideal point. We focus on the scenario where…
There is a growing need for discrete choice models that account for the complex nature of human choices, escaping traditional behavioral assumptions such as the transitivity of pairwise preferences. Recently, several parametric models of…
Population protocols are a model of distributed computing where $n$ agents, each a simple finite-state machine, interact in pairs to solve a common task against a (adversarial) interaction scheduler. This model was intensively studied in…
Given pairwise comparisons between multiple items, how to rank them so that the ranking matches the observations? This problem, known as rank aggregation, has found many applications in sports, recommendation systems, and other web…
As from time to time it is impractical to ask agents to provide linear orders over all alternatives, for these partial rankings it is necessary to conduct preference completion. Specifically, the personalized preference of each agent over…
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…
In the theory of voting, the Plurality rule for preferences that come in the form of linear orders selects the alternatives most frequently appearing in the first position of those orders, while the Anti-Plurality rule selects the…
A preference order or ranking aggregated from pairwise comparison data is commonly understood as a strict total order. However, in real-world scenarios, some items are intrinsically ambiguous in comparisons, which may very well be an…
A Condorcet voting scheme chooses a winning candidate as one who defeats all others in pairwise majority rule. We provide a review which includes the rigorous mathematical treatment for calculating the limiting probability of a Condorcet…
How much influence can a coordinated coalition exert in a multiwinner Top-$k$ election under a positional scoring rule? We study the maximum displacement problem: with coalition size $m$, how many of the current top-$k$ winners can be…
We study popular matchings in three classical settings: the house allocation problem, the marriage problem, and the roommates problem. In the popular matching problem, (a subset of) the vertices in a graph have preference orderings over…
We study electoral campaign management scenarios in which an external party can buy votes, i.e., pay the voters to promote its preferred candidate in their preference rankings. The external party's goal is to make its preferred candidate a…
We study the following metric distortion problem: there are two finite sets of points, $V$ and $C$, that lie in the same metric space, and our goal is to choose a point in $C$ whose total distance from the points in $V$ is as small as…
Aggregating multiple input rankings into a consensus ranking is essential in various fields such as social choice theory, hiring, college admissions, web search, and databases. A major challenge is that the optimal consensus ranking might…
We study the top-$K$ ranking problem where the goal is to recover the set of top-$K$ ranked items out of a large collection of items based on partially revealed preferences. We consider an adversarial crowdsourced setting where there are…
I provide simplified proofs for each of the following fundamental theorems regarding selection principles: 1. The Quasinormal Convergence Theorem, due to the author and Zdomskyy, asserting that a certain, important property of the space of…
The Possible Winner problem asks, given an election where the voters' preferences over the candidates are specified only partially, whether a designated candidate can become a winner by suitably extending all the votes. Betzler and Dorn [1]…
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…
In this paper, we experimentally compare major approval-based multiwinner voting rules. To this end, we define a measure of similarity between two equal-sized committees subject to a given election. Using synthetic elections coming from…