Related papers: A note on the voting problem

Multiwinner voting rules are used to select a small representative subset of candidates or items from a larger set given the preferences of voters. However, if candidates have sensitive attributes such as gender or ethnicity (when selecting…

Let $p_{k}$ denote the $k$-th prime and $d(p_{k}) = p_{k} - p_{k - 1}$, the difference between consecutive primes. We denote by $N_{\epsilon}(x)$ the number of primes $\leq x$ which satisfy the inequality $d(p_{k}) \leq (\log p_{k})^{2 +…

In the context of single-winner ranked-choice elections between $m$ candidates, we explore the tradeoff between two competing goals in every democratic system: the majority principle (maximizing the social welfare) and the minority…

We present yet another algebraic proof of the unimodality of the binomial coefficients.

We first consider the problem of learning $k$-parities in the on-line mistake-bound model: given a hidden vector $x \in \{0,1\}^n$ with $|x|=k$ and a sequence of "questions" $a_1, a_2, ...\in \{0,1\}^n$, where the algorithm must reply to…

Let $k\ge 2$ and $\Pi(n)=\prod_{i=1}^k(a_in+b_i)$ for some integers $a_i, b_i$ ($1\le i\le k$). Suppose that $\Pi(n)$ has no fixed prime divisors. Weighted sieves have shown for infinitely many integers $n$ that $\Omega(\Pi(n))\le r_k$…

In real-world elections where voters cast preference ballots, voters often provide only a partial ranking of the candidates. Despite this empirical reality, prior social choice literature frequently analyzes fairness criteria under the…

We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for $n$-sided dice with pairwise ordering induced by the probability, relative to $1/2$, that a throw from one die is…

In an approval-based committee election, the task is to select a committee of up to $k$ candidates from a set of $m$ candidates based on the preferences of $n$ voters, each of whom approves a subset of the candidates. A central open…

In approval voting, individuals vote for all platforms that they find acceptable. In this situation it is natural to ask: When is agreement possible? What conditions guarantee that some fraction of the voters agree on even a single…

In a party-based election system, the voters are grouped into parties and all voters of a party are assumed to vote according to the party preferences over the candidates. Hence, once the party preferences are declared the outcome of the…

In elections, a set of candidates ranked consecutively (though possibly in different order) by all voters is called a clone set, and its members are called clones. A clone structure is a family of all clone sets of a given election. In this…

We prove that there is no preferential voting method satisfying the Condorcet winner and loser criteria, positive involvement (if a candidate $x$ wins in an initial preference profile, then adding a voter who ranks $x$ uniquely first cannot…

Let $V$ be a set of $n$ points in $\mathbb{R}^d$, called voters. A point $p\in \mathbb{R}^d$ is a plurality point for $V$ when the following holds: for every $q\in\mathbb{R}^d$ the number of voters closer to $p$ than to $q$ is at least the…

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 view voting rules as classifiers that assign a winner (a class) to a profile of voters' preferences (an instance). We propose to apply techniques from formal explainability, most notably abductive and contrastive explanations, to…

We study voting rules with respect to how they allow or limit a majority from dominating minorities: whether a voting rule makes a majority powerful, and whether minorities can veto the candidates they do not prefer. For a given voting…

Consider elections where the set of candidates is partitioned into parties, and each party must nominate exactly one candidate. The Possible President problem asks whether some candidate of a given party can become the winner of the…

Let $V$ be a multiset of $n$ points in $\mathbb{R}^d$, which we call voters, and let $k\geq 1$ and $\ell\geq 1$ be two given constants. We consider the following game, where two players $\mathcal{P}$ and $\mathcal{Q}$ compete over the…

Many hardness results in computational social choice make use of the fact that every directed graph may be induced as the pairwise majority relation of some preference profile. However, this fact requires a number of voters that is almost…