Related papers: Tournament limits: Degree distributions, score fun…
Tournaments are widely used models to represent pairwise dominance between candidates, alternatives, or teams. We study the problem of providing certified explanations for why a candidate appears among the winners under various tournament…
The core of a cooperative game on a set of players $N$ is one of the most popular concept of solution. When cooperation is restricted (feasible coalitions form a subcollection $\cF$ of $2^N$), the core may become unbounded, which makes it…
A 3-tournament is a complete 3-uniform hypergraph where each edge has a special vertex designated as its tail. A vertex set $X$ dominates $T$ if every vertex not in $X$ is contained in an edge whose tail is in $X$. The domination number of…
The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…
This paper introduces a declarative framework to specify and reason about distributions of data over computing nodes in a distributed setting. More specifically, it proposes distribution constraints which are tuple and equality generating…
In this paper, we characterize the extreme points of a class of multidimensional monotone functions. This result is then applied to large contests, where it provides a useful representation of optimal allocation rules under a broad class of…
An urn scheme is a probabilistic model in which balls are placed into urns sequentially and independently of each other. All balls share the same probability distribution for hitting the urns. In the simplest case, there is a finite number…
We consider the transformation reversing all arcs of a subset $X$ of the vertex set of a tournament $T$. The \emph{index} of $T$, denoted by $i(T)$, is the smallest number of subsets that must be reversed to make $T$ acyclic. It turns out…
Computational Social Choice (ComSoc) is a rapidly developing field at the intersection of computer science, economics, social choice, and political science. The study of tournaments is fundamental to ComSoc and many results have been…
We consider a random interval splitting process, in which the splitting rule depends on the empirical distribution of interval lengths. We show that this empirical distribution converges to a limit almost surely as the number of intervals…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
We introduce and analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while…
The classic Rock-Paper-Scissors game of size 3 and its extension, Rock-Paper-Scissors-Lizard-Spock, are modeled by directed graphs called tournaments. They can be further extended to any odd size. The extended games are regular tournaments…
We prove that there exists a constant $c > 0$ such that the vertices of every strongly $c \cdot kt$-connected tournament can be partitioned into $t$ parts, each of which induces a strongly $k$-connected tournament. This is clearly tight up…
In experimental applications of bounded-reasoning models, behavior is often summarized by distributions of "levels". We argue that such summaries conflate two conceptually distinct dimensions: a player's type, capturing beliefs about what…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
In a one-parameter model for evolution of random trees, which also includes the Barabasi-Albert random tree, almost sure behavior and the limiting distribution of the degree of a vertex in a fixed position are examined. Results about Polya…
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…
Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view…
We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and…