GIANFRANCO GAMBARELLI

Misure di potere

N. 4/1987

Summary — The formation of majority coalitions in seldom explainable only in terms of the various participants coalitions, in fact, are often the result of human relations, feelings, adversions, external influences, psychological attitudes more than simple strenght ratios. The analysis of such processes can actually be quite interesting, in particular when it can lead to forecast the resulting configuration. This is then taken to be the essential grounds in view of achieving optimality in subsequent decisions as well as equity in problems of social rules and regulations. A first step toward such a forecast must necessarily be abstract and removed from the least quantifiable components. The gap will then have to be bridged by means of subsequent improvements of the proposed model. But the student will have always to be aware of the fact that the truth of the conclusions depends on the reliability of the hypotheses and on the credibility of the inference rules upon which the model is based. The power indices presented in this study fulfill the above mentioned preliminary steps: they assume unquestionably defined and numerically given values for the "weights" of the various coalitions’ members. In other words, these indices are based exclusively on weights such as shares, votes, seats and the like. Some of the best known power indices such as those proposed by Shapley-Shubik, Banzhaf-Coleman Schmeidler, Lemaire will be discussed together with. some of their common properties and applications The presentation will involve only minimal mathematical tools; while more technical considerations will be reported in the Appendix. Finally, further development with applications to current situations will also be suggested, such as for instance an alternative to proportional systems.