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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…
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…
Sequential voting rules have played a crucial role in shaping decisions within parliamentary and legislative frameworks. After observing that the existing sequential rules fail several fundamental axioms, Horan and Sprumont [2022] proposed…
We analyze the susceptibility of instant runoff voting (IRV) to a lesser-studied paradox known as a \emph{reinforcement paradox}, which occurs when candidate $X$ wins under IRV in two distinct elections but $X$ loses in the combined…
Reinforcement Learning from AI Feedback (RLAIF) relies on LLM judges as preference measurement instruments, yet these instruments are fundamentally limited by random measurement errors -- stochastic fluctuations that manifest as preference…
We introduce the model of line-up elections which captures parallel or sequential single-winner elections with a shared candidate pool. The goal of a line-up election is to find a high-quality assignment of a set of candidates to a set of…
We show how hidden interesting subelections can be discovered in ordinal elections. An interesting subelection consists of a reasonably large set of voters and a reasonably large set of candidates such that the former have a consistent…
In perpetual voting, multiple decisions are made at different moments in time. Taking the history of previous decisions into account allows us to satisfy properties such as proportionality over periods of time. In this paper, we consider…
In approval-based committee (ABC) elections, the goal is to select a fixed-size subset of the candidates, a so-called committee, based on the voters' approval ballots over the candidates. One of the most popular classes of ABC voting rules…
When selecting a subset of candidates (a so-called committee) based on the preferences of voters, proportional representation is often a major desideratum. When going beyond simplistic models such as party-list or district-based elections,…
We revisit the recent breakthrough result of Gkatzelis et al. on (single-winner) metric voting, which showed that the optimal distortion of 3 can be achieved by a mechanism called Plurality Matching. The rule picks an arbitrary candidate…
Voting can abstractly model any decision-making scenario and as such it has been extensively studied over the decades. Recently, the related literature has focused on quantifying the impact of utilizing only limited information in the…
Voting rules may implement the will of the society when all eligible voters vote, and only them. However, they may fail to do so when sybil (fake or duplicate) votes are present and when only some honest (non sybil) voters actively…
We consider the dynamics of the voter model and of the monomer-monomer catalytic process in the presence of many ``competing'' inhomogeneities and show, through exact calculations and numerical simulations, that their presence results in a…
In this article, we study a model of random permutations, which we call random standardized permutations, based on a sequence of i.i.d. random variables. This model generalizes others, such as the riffle-shuffle and the major-index-biased…
In the standard arrovian framework and under the assumption that individual preferences and social outcomes are linear orders on the set of alternatives, we study the rules which satisfy suitable symmetries and obey the majority principle.…
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 investigate a variation of the classical voter model in which the set of influencing agents depends on an individual's current opinion. The initial population consists of a random sample of equally sized sub-populations for each state,…
The major finding, of this article, is an ensemble method, but more exactly, a novel, better ranked voting system (and other variations of it), that aims to solve the problem of finding the best candidate to represent the voters. We have…
We propose six axioms concerning when one candidate should defeat another in a democratic election involving two or more candidates. Five of the axioms are widely satisfied by known voting procedures. The sixth axiom is a weakening of…