WEA 2006: Experimental Algorithms pp 73-84

# Some Advances in the Theory of Voting Systems Based on Experimental Algorithms

• Josep Freixas
• Xavier Molinero
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4007)

## Abstract

In voting systems, game theory, switching functions, threshold logic, hypergraphs or coherent structures there is an important problem that consists in determining the weightedness of a voting system by means of trades among voters in sets of coalitions. The fundamental theorem by Taylor and Zwicker [8] establishes the equivalence between weighted voting games and k-trade robust games for each positive integer k. Moreover, they also construct, in [9], a succession of games G k based on magic squares which are (k – 1)-trade robust but not k-trade robust, each one of these games G k has k 2 players.

The goal of this paper is to provide improvements by means of different experiments to the problem described above. In particular, we will classify all complete games (a basic class of games) of less than eight players according to whether they are: a weighted voting game or a game which is (k – 1)-trade robust but not k-trade robust for all values of k. As a consequence it will we showed the existence of games with less than k 2 players which are (k – 1)-trade robust but not k-trade robust. We want to point out that the classifications obtained in this paper by means of experiments are new in the mentioned fields.

## Keywords

Vote System Characteristic Invariant Recursive Function Simple Game Winning Coalition
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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