Related papers: The Inversion Paradox and Ranking Methods in Tourn…
Answering a pair of questions of Conrey, Gabbard, Grant, Liu, and Morrison, we prove that a triplet of dice drawn from the multiset model are intransitive with probability $1/4+o(1)$ and the probability a random pair of dice tie tends…
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}…
In the contest design problem, there are $n$ strategic contestants, each of whom decides an effort level. A contest designer with a fixed budget must then design a mechanism that allocates a prize $p_i$ to the $i$-th rank based on the…
Competitive tournaments appear in sports, politics, population ecology, and animal behavior. All of these fields have developed methods for rating competitors and ranking them accordingly. A tournament is intransitive if it is not…
With the aid of mathematical modelling (basic tool is the random walk with absorbing barriers) we derive subsequent formulas to study the effect of different versions of possible rules. For different rules the probability of winning a game,…
We examine ``tournament'' second-price auctions in which $N$ bidders compete for the right to participate in a second stage and contend against bidder $N+1$. When the first $N$ bidders are committed so that their bids cannot be changed in…
We investigate the problem of computing the probability of winning in an election where voter attendance is uncertain. More precisely, we study the setting where, in addition to a total ordering of the candidates, each voter is associated…
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…
In voting with ranked ballots, each agent submits a strict ranking of the form $a \succ b \succ c \succ d$ over the alternatives, and the voting rule decides on the winner based on these rankings. Although this ballot format has desirable…
We study a game-theoretic information retrieval model in which strategic publishers aim to maximize their chances of being ranked first by the search engine while maintaining the integrity of their original documents. We show that the…
The occurrence of Simpson's paradox (SP) in $2\times 2$ contingency tables has been well studied. The present work comprehensively revisits this problem using a combination of philosophical reflections, causal considerations, and…
We identify a new type of paradoxical behavior in dice, where the sum of independent rolls produces a deceptive sequence of dominance relations. We call these ``anti-inductive dice". Consider a game with two players and two non-identical…
This paper describes Simpson's paradox, and explains its serious implications for randomised control trials. In particular, we show that for any number of variables we can simulate the result of a controlled trial which uniformly points to…
We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend…
We propose a new model of provenance, based on a game-theoretic approach to query evaluation. First, we study games G in their own right, and ask how to explain that a position x in G is won, lost, or drawn. The resulting notion of game…
The transitivity of preferences is one of the basic assumptions used in the theory of games and decisions. It is often equated with rationality of choice and is considered useful in building rankings. Intransitive preferences are considered…
Inverse reinforcement learning is the problem of inferring a reward function from an optimal policy or demonstrations by an expert. In this work, it is assumed that the reward is expressed as a reward machine whose transitions depend on…
Let T = (V,A) be a (finite) tournament and k be a non negative integer. For every subset X of V is associated the subtournament T[X] = (X,A\cap (X \timesX)) of T, induced by X. The dual tournament of T, denoted by T\ast, is the tournament…
Ranking of agents competing with each other in complex systems may lead to paradoxes according to the pre-chosen different measures. A discussion is presented on such rank-rank, similar or not, correlations based on the case of European…
Consider a round-robin tournament on n teams, where a winner must be (possibly randomly) selected as a function of the results from the ${n \choose 2}$ pairwise matches. A tournament rule is said to be k-SNM-${\alpha}$ if no set of k teams…