Define the predictability number α(G) of a tournament T to be the largest supermajority threshhold 1 2 < α ≤ 1 for which T could represent the pairwise voting outcomes from some population of voter preference orders. We establish that the predictability number always exists and is rational. Only acyclic tournaments have predictability 1; the Condorcet voting paradox tournament has predictabilit...

We introduce the Tournament Rank Probability Score (TRPS) as a measure to evaluate and compare pre-tournament predictions, where predictions of full tournament results are required be available before begins. The TRPS handles partial ranking teams, gives credit that only slightly wrong, can modified with weights stress importance particular features prediction. Thus, Prediction is more flexible...

This paper investigates the effects of a number of replacement strategies for use in steady state genetic algorithms. Some of these (deleting the oldest, worst or random members, or deletion by “Kill Tournament”) are well known from the literature. The last, “conservative” replacement was developed for use in timevarying problems and combines a Replace–Oldest strategy with modified selection to...

This paper presents an experimental study of different variants of tournament selection, and proposes a new DISPAR-tournament (Disjoint Sets Parallel tournament) operator for population reduction to be used in parallel implementations of evolution strategies and other evolutionary algorithms.

Tournament selection is a useful and robust selection mechanism commonly used by genetic algorithms. The selection pressure of tournament selection directly varies with the tournament size | the more competitors , the higher the resulting selection pressure. This article develops a model, based on order statistics, that can be used to quantitatively predict the resulting selection pressure of a...

For a tournament $H$ with $h$ vertices, its typical density is $h!2^{-\binom{h}{2}}/aut(H)$, i.e. this the expected of in random tournament. A family ${\mathcal F}$ $h$-vertex tournaments {\em dominant} if for all sufficiently large $n$, there exists an $n$-vertex $G$ such that each element larger than by constant factor. Characterizing dominant families challenging already small $h$. Here we c...

We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, encompassing the top cycle, the uncovered set, the Banks set, the minimal covering set, and the tournament equilibrium set. Moreover, the hi...

A tournament is unimodular if the determinant of its skew-adjacency matrix $1$. In this paper, we give some properties and constructions tournaments. $T$ with $S$ invertible $S^{-1}$ a tournament. spectral characterization tournaments given. Lastly, show that every $n$-tournament can be embedded in by adding at most $n - \lfloor\log_2(n)\rfloor$ vertices.

A tournament is a complete graph with its edges directed, and colouring a tournament means partitioning its vertex set into transitive subtournaments. For some tournaments H there exists c such that every tournament not containing H as a subtournament has chromatic number at most c (we call such a tournament H a hero); for instance, all tournaments with at most four vertices are heroes. In this...