Related papers: Approximately Strategyproof Tournament Rules: On L…
Scheduling a sports tournament is a complex optimization problem, which requires a large number of hard constraints to satisfy. Despite the availability of several such constraints in the literature, there remains a gap since most of the…
We study deliberative social choice, where voters engage in small-group discussions to output collective preferences that are then aggregated by a social choice rule. We introduce a simple deliberation-via-matching protocol. In this…
Rule k is a localized approximation algorithm that finds a small connected dominating set in a graph. We estimate the expected size of the Rule k dominating set for the model of random unit disk graphs constructed from n random points in an…
Classical voting rules assume that ballots are complete preference orders over candidates. However, when the number of candidates is large enough, it is too costly to ask the voters to rank all candidates. We suggest to fix a rank k, to ask…
We investigate a new tournament format that consists of a series of individual knockout tournaments; we call this new format a Serial Knockout Competition (SKC). This format has recently been adopted by the Professional Darts Corporation.…
The determinant of a tournament $T$ is defined as the determinant of the skew-adjacency matrix of $T$. For a positive odd integer $k$, let $\mathcal{D}_k$ be the set of tournaments whose all subtournaments have determinant at most $k^2$.…
The Chamberlin-Courant and Monroe rules are fundamental and well-studied rules in the literature of multi-winner elections. The problem of determining if there exists a committee of size k that has a Chamberlin-Courant (respectively,…
A $k$-majority tournament $T$ on a finite set of vertices $V$ is defined by a set of $2k-1$ linear orders on $V$, with an edge $u \to v$ in $T$ if $u>v$ in a majority of the linear orders. We think of the linear orders as voter preferences…
We consider the classic Multi-Armed Bandit setting to understand the exploration/exploitation tradeoffs made by different search heuristics. Since many search heuristics work by comparing different options (in evolutionary algorithms called…
We introduce the dueling teams problem, a new online-learning setting in which the learner observes noisy comparisons of disjoint pairs of $k$-sized teams from a universe of $n$ players. The goal of the learner is to minimize the number of…
We study tournaments where winning a rank-dependent prize requires passing a minimum performance standard. We show that, for any prize allocation, the optimal standard is always at a mode of performance that is weakly higher than the global…
A tournament graph is a complete directed graph, which can be used to model a round-robin tournament between $n$ players. In this paper, we address the problem of finding a champion of the tournament, also known as Copeland winner, which is…
Aboulker, Aubian, Charbit, and Lopes (2023) defined the clique number of a tournament to be the minimum clique number of one of its backedge graphs. Here we show that if $T$ is a tournament of sufficiently large clique number, then $T$…
We prove that every Condorcet-consistent voting rule can be manipulated by a voter who completely reverses their preference ranking, assuming that there are at least 4 alternatives. This corrects an error and improves a result of [Sanver,…
In this thesis we prove a variety of theorems on tournaments. A \emph{prime} tournament is a tournament $G$ such that there is no $X \subseteq V(G)$, $1 < |X| < |V(G)|$, such that for every vertex $v \in V(G) \minus X$, either $v \ra x$ for…
This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…
In this paper we have used one 2 variable Boolean function called Rule 6 to define another beautiful transformation named as Extended Rule-6. Using this function we have explored the algebraic beauties and its application to an efficient…
We present a new problem called the incomplete Traveling Tournament problem, which introduces the well known Traveling Tournament Problem into the realm of incomplete round-robin tournaments. We focus on the case where teams can face each…
Sumner's universal tournament conjecture states that any tournament on $2n-2$ vertices contains any directed tree on $n$ vertices. In this paper we prove that this conjecture holds for all sufficiently large $n$. The proof makes extensive…
The traveling tournament problem (TTP) is to minimize the total traveling distance of all teams in a double round-robin tournament. In this paper, we focus on TTP-2, in which each team plays at most two consecutive home games and at most…