Multicameral voting cohesion games

This work links two research branches regarding cooperative games: multi-cameral games and a priori coalitions. Regarding the former, many parliaments are based on a bicameral system where bills have to be approved by both chambers. The parties’ power indices are affected by it. In fact one certain political party for one certain coalition can be crucial in one chamber and not in the other. Usually the problem can be solved by building a unified game, related to two or more chambers, where the global power indices can be calculated. Concerning cohesion games, some coalitions among parties might be possible, but have a low probability of materializing if the parties involved have very different ideologies. It is necessary to take this into consideration when we compute the relative power indices. In this work, a model is built that takes into consideration both topics. An automatic calculation algorithm is elaborated and is applied to the current situations in Belgium, the Czech Republic, France, Italy, the Netherlands, Poland and Romania, considering the location of the parties on the left-right axis. This model is then applied globally to the European Union. In this work the model is applied to Politics, but its applications are not limited to that field. For instance, in Finance it can be applied to describe agreements for debt restructuring and corporate mergers.

[1]  W. Gamson.  Coalition Formation at Presidential Nominating Conventions , 1962, American Journal of Sociology.

[2]  Forming Coalitions and Measuring Voting Power , 1982 .

[3]  Jesús Mario Bilbao,et al.  Generating Functions for Computing the Myerson Value , 2002, Ann. Oper. Res..

[4]  Gianfranco Gambarelli.  Transforming Games from Characteristic into Normal Form , 2007, IGTR.

[5]  Taylor Alan,et al.  Weighted Voting, Multicameral Representation, and Power , 1993 .

[6]  G. Owen.  Modification of the Banzhaf-Coleman Index for Games with a Priori Unions , 1981 .

[7]  Philip Wolfe,et al.  Contributions to the theory of games , 1953 .

[8]  Lawrence E. Blume,et al.  Mathematics for Economists , 1994 .

[9]  L. Shapley.  A Value for n-person Games , 1988 .

[10]  R. J. Aumann,et al.  Cooperative games with coalition structures , 1974 .

[11]  Theodore Caplow,et al.  Two Against One: Coalitions in Triads. , 1970 .

[12]  Jesús Mario Bilbao,et al.  Computing power indices in weighted multiple majority games , 2003, Math. Soc. Sci..

[13]  D. Marc Kilgour.  A Shapley Value for Cooperative Games with Quarrelling , 1974 .

[14]  G. Gambarell.  A new approach for evaluating the Shapely value , 1990 .

[15]  Jesús Mario Bilbao,et al.  Voting power in the European Union enlargement , 2002, Eur. J. Oper. Res..

[16]  William A. Gamson,et al.  A theory of coalition formation , 1961 .

[17]  J. M. Bilbao,et al.  Generating functions for computing power indices efficiently , 2000 .

[18]  Roger B. Myerson,et al.  Graphs and Cooperation in Games , 1977, Math. Oper. Res..

[19]  T. Caplow.  A Theory of Coalitions in the Triad , 1956 .

[20]  Marida Bertocchi,et al.  Modelling techniques for financial markets and bank management , 1996 .

[21]  Martin Shubik,et al.  A Method for Evaluating the Distribution of Power in a Committee System , 1954, American Political Science Review.

[22]  L. Shapley,et al.  VALUES OF LARGE GAMES. 6: EVALUATING THE ELECTORAL COLLEGE EXACTLY , 1962 .

[23]  T. König.  Bicameralism and Party Politics in Germany: An Empirical Social Choice Analysis , 2001 .

[24]  J. Deegan,et al.  A new index of power for simplen-person games , 1978 .

[25]  L. Penrose.  The Elementary Statistics of Majority Voting , 1946 .

[26]  G. Owen.  VALUES OF GAMES WITH A PRIORI UNIONS , 1977 .

[27]  W. Riker.  The first power index , 1986 .

[28]  T. Caplow.  Further Development of a Theory of Coalitions in the Triad , 1959, American Journal of Sociology.