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.
This research was supported by the Spanish Ministerio de Ciencia y Tecnología programme TIC2002-00190 (AEDRI II) and TIN2005-05446 (ALINEX), and Grant BFM 2003–01314 of the Ministerio de Ciencia y Tecnología and the European Regional Development Fund.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Carreras, F., Freixas, J.: Complete simple games. Mathematical Social Sciences 32, 139–155 (1996)
Freixas, J.: The dimension for the European Union Council under the Nice rules. European Journal of Operational Research 156(2), 415–419 (2004)
Freixas, J., Puente, M.A.: Complete games with minimum. Annals of Operations Research 84, 97–109 (1998)
Freixas, J., Zwicker, W.S.: Weighted voting, abstention, and multiple levels of approval. Social Choice and Welfare 21, 399–431 (2003)
Isbell, J.R.: A class of simple games. Duke Mathematics Journal 25, 423–439 (1958)
Kilgour, D.M.: A formal analysis of the amending formula of Canada’s Constitution. Act. Canadian Journal of Political Science 16, 771–777 (1983)
Taylor, A.D.: Mathematics and Politics. Springer, New York (1995)
Taylor, A.D., Zwicker, W.S.: A characterization of weighted voting. Proceedings of the American mathematical society 115, 1089–1094 (1992)
Taylor, A.D., Zwicker, W.S.: Simple games and magic squares. Journal of combinatorial theory, ser. A 71, 67–88 (1995)
Taylor, A.D., Zwicker, W.S.: Simple games: desirability relations, trading, and pseudoweightings. Princeton University Press, New Jersey (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Freixas, J., Molinero, X. (2006). Some Advances in the Theory of Voting Systems Based on Experimental Algorithms. In: Àlvarez, C., Serna, M. (eds) Experimental Algorithms. WEA 2006. Lecture Notes in Computer Science, vol 4007. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11764298_7
Download citation
DOI: https://doi.org/10.1007/11764298_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34597-8
Online ISBN: 978-3-540-34598-5
eBook Packages: Computer ScienceComputer Science (R0)