Power Indices Without the Transfer Axiom

Authors: 
Anna B. Khmelnitskaya
Abstract: 

We show that for voting systems containing at least three voters the set of all marginalist, efficient, and monotonic power indices possessing the -player property coincide with the set of random-order power indices, and thereby the last statement spreads to simple games the result of Khmelnitskaya concerning an axiomatization without the linearity assumption for random-order values for the entire class of TU games. We also give evidence that every marginalist, efficient, and symmetric power index is just the Shapley-Shubik power index what provides an axiomatization for the latter similar to that of Young for the Shapley value; in symmetric case there is no restriction for a number of players to be not less than three. Keywords: Simple game; Power index; Axiomatic characterization; Efficiency; Marginalism

Date: 
January, 1999
Published in: 
In H. de Swart (ed.) Logic, Game Theory and Social Choice. Proceedings of the International Conference LGS (1999) Tilburg University Press: 208-213
Number: 
189