5 research outputs found
Empirical Evaluation of Real World Tournaments
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 published about tournament solution sets and reasoning in
tournaments. Theoretical results in ComSoc tend to be worst case and tell us
little about performance in practice. To this end we detail some experiments on
tournaments using real wold data from soccer and tennis. We make three main
contributions to the understanding of tournaments using real world data from
English Premier League, the German Bundesliga, and the ATP World Tour: (1) we
find that the NP-hard question of finding a seeding for which a given team can
win a tournament is easily solvable in real world instances, (2) using detailed
and principled methodology from statistical physics we show that our real world
data obeys a log-normal distribution; and (3) leveraging our log-normal
distribution result and using robust statistical methods, we show that the
popular Condorcet Random (CR) tournament model does not generate realistic
tournament data.Comment: 2 Figure
Election with Bribed Voter Uncertainty: Hardness and Approximation Algorithm
Bribery in election (or computational social choice in general) is an
important problem that has received a considerable amount of attention. In the
classic bribery problem, the briber (or attacker) bribes some voters in
attempting to make the briber's designated candidate win an election. In this
paper, we introduce a novel variant of the bribery problem, "Election with
Bribed Voter Uncertainty" or BVU for short, accommodating the uncertainty that
the vote of a bribed voter may or may not be counted. This uncertainty occurs
either because a bribed voter may not cast its vote in fear of being caught, or
because a bribed voter is indeed caught and therefore its vote is discarded. As
a first step towards ultimately understanding and addressing this important
problem, we show that it does not admit any multiplicative -approximation
algorithm modulo standard complexity assumptions. We further show that there is
an approximation algorithm that returns a solution with an additive-
error in FPT time for any fixed .Comment: Accepted at AAAI 201