Related papers: Refining Tournament Solutions via Margin of Victor…
We analyze different methods of sorting and selecting a set of objects by their intrinsic value, via pairwise comparisons whose outcome is uncertain. After discussing the limits of repeated Round Robins, two new methods are presented: The…
The margin of victory is easy to compute for many election schemes but difficult for Instant Runoff Voting (IRV). This is important because arguments about the correctness of an election outcome usually rely on the size of the electoral…
We consider the classical statistical learning/regression problem, when the value of a real random variable Y is to be predicted based on the observation of another random variable X. Given a class of functions F and a sample of independent…
We explore a new way to evaluate generative models using insights from evaluation of competitive games between human players. We show experimentally that tournaments between generators and discriminators provide an effective way to evaluate…
Challenge the Champ is a simple tournament format, where an ordering of the players -- called a seeding -- is decided. The first player in this order is the initial champ, and faces the next player. The outcome of each match decides the…
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…
This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…
A 2.75-approximation algorithm is proposed for the unconstrained traveling tournament problem, which is a variant of the traveling tournament problem. For the unconstrained traveling tournament problem, this is the first proposal of an…
Round robin tournaments are omnipresent in sport competitions and beyond. We propose two new integer programming formulations for scheduling a round robin tournament, one of which we call the matching formulation. We analytically compare…
A directed graph where there is exactly one edge between every pair of vertices is called a {\em tournament}. Finding the "best" set of vertices of a tournament is a well studied problem in social choice theory. A {\em tournament solution}…
We consider the problem of inferring an unknown ranking of $n$ items from a random tournament on $n$ vertices whose edge directions are correlated with the ranking. We establish, in terms of the strength of these correlations, the…
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…
As alternatives to the time-to-first-event analysis of composite endpoints, the {\it net benefit} (NB) and the {\it win ratio} (WR) -- which assess treatment effects using prioritized component outcomes based on clinical importance -- have…
We propose a new tournament structure that combines the popular knockout tournaments and the round-robin tournaments. As opposed to the extremes of divisive elimination and no elimination, our tournament aims to eliminate the participants…
We introduce a simple one-parameter game derived from a model describing the properties of a directed polymer in a random medium. At his turn, each of the two players picks a move among two alternatives in order to maximize his final score,…
An {\it inversion} of a tournament $T$ is obtained by reversing the direction of all edges with both endpoints in some set of vertices. Let ${\rm inv}_k(T)$ be the minimum length of a sequence of inversions using sets of size at most $k$…
Single-elimination (SE) tournaments are a popular format used in competitive environments and decision making. Algorithms for SE tournament manipulation have been an active topic of research in recent years. In this paper, we initiate the…
We consider the manipulability of tournament rules which map the results of $\binom{n}{2}$ pairwise matches and select a winner. Prior work designs simple tournament rules such that no pair of teams can manipulate the outcome of their match…
A fundamental property of choice functions is stability, which, loosely speaking, prescribes that choice sets are invariant under adding and removing unchosen alternatives. We provide several structural insights that improve our…
In this paper we bring a novel approach to the theory of tournament rankings. We combine two different theories that are widely used to establish rankings of populations after a given tournament. First, we use the statistical approach of…