A Complete Geometric Representation of Four-Player Weighted Voting Systems

Zhengjia Jiang
2013 Journal of Mathematics Research  
This paper seeks to expand voting power theory, a branch of game theory that applies to many important organizations. Typically, weighted voting systems are displayed using the algebraic representation, consisting of a quota and a weight vector. A newer idea, however, is the geometric representation. This representation maps all normalized weighted voting systems onto a simplex and thus can be called a complete representation of weighted voting systems. The concept of the region, sets of
more » ... eristically identical weighted voting systems, will be introduced, greatly simplifying the analysis of weighted voting systems. In this paper, four-player weighted voting systems are solved completely using the geometric representation. The geometric representation will be shown to be a useful alternative to the algebraic representation.
doi:10.5539/jmr.v5n1p122 fatcat:wzxfd6nskbhafixcym3jq3bbhu