Tournament Methods in Choice Theory

Choice procedures using the notion of tournament matrix are investigated in the framework of general choice theory. Tournament procedures of multicriterial choice are introduced and studied. New characteristic conditions for describing some tournament and other essentially nonclassical choice functions are obtained. The comparison of tournament and graph-dominant choice mechanisms is established

Tournament Methods in Choice Theory

Choice procedures using the notion of tournament matrix are investigated in the framework of general choice theory. Tournament procedures of multicriterial choice are introduced and studied. New characteristic conditions for describing some tournament and other essentially nonclassical choice functions are obtained. The comparison of tournament and graph-dominant choice mechanisms is established

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

On the additivity of preference aggregation methods

The paper reviews some axioms of additivity concerning ranking methods used for generalized tournaments with possible missing values and multiple comparisons. It is shown that one of the most natural properties, called consistency, has strong links to independence of irrelevant comparisons, an axiom judged unfavourable when players have different opponents. Therefore some directions of weakening consistency are suggested, and several ranking methods, the score, generalized row sum and least squares as well as fair bets and its two variants (one of them entirely new) are analysed whether they satisfy the properties discussed. It turns out that least squares and generalized row sum with an appropriate parameter choice preserve the relative ranking of two objects if the ranking problems added have the same comparison structure.Comment: 24 pages, 9 figure

How Models Fail. A Critical Look at the History of Computer Simulations of the Evolution of Cooperation

Simulation models of the Reiterated Prisoner's Dilemma have been popular for studying the evolution of cooperation since more than 30 years now. However, there have been practically no successful instances of empirical application of any of these models. At the same time this lack of empirical testing and confirmation has almost entirely been ignored by the modelers community. In this paper, I examine some of the typical narratives and standard arguments with which these models are justified by their authors despite the lack of empirical validation. I find that most of the narratives and arguments are not at all compelling. None the less they seem to serve an important function in keeping the simulation business running despite its empirical shortcomings

Class tournament as an assessment method in physics courses : a pilot study

Testing knowledge is an integral part of a summative assessment at schools. It can be performed in many different ways. In this study we propose assessment of physics knowledge by using a class tournament approach. Prior to a statistical analysis of the results obtained over a tournament organized in one of Polish high schools, all its specifics are discussed at length, including the types of questions assigned, as well as additional self- and peer-evaluation questionnaires, constituting an integral part of the tournament. The impact of the tournament upon student improvement is examined by confronting the results of a post-test with pre-tournament students’ achievements reflected in scores earned in former, tests written by the students in experimental group and their colleagues from control group. We also present some of students’ and teachers’ feedback on the idea of a tournament as a tool of assessment. Both the analysis of the tournament results and the students’ and teachers’ opinions point to at least several benefits of our approach