A Complete Geometric Representation of Four-Player Weighted Voting Systems

A Complete Geometric Representation of Four-Player Weighted Voting Systems

The relatively new weighted voting theory applies to many important organizations such as the United States Electoral College and the International Monetary Fund. Various power indexes are used to establish a relationship between weights and influence; in 1965, the Banzhaf Power Index was used to show that areas of Nassau County were unrepresented in the county legislature. It is of interest to...

Mathematics of Voting – Weighted Voting Systems

A geometric and combinatorial view of weighted voting

A natural partial ordering exists on all weighted games and, more broadly, on all linear games. We describe several properties of the partially ordered sets formed by these games and utilize this perspective to enumerate proper linear games with one generator. We introduce a geometric approach to weighted voting by considering the convex polytope of all possible realizations of a weighted game ...

A representation for some groups, a geometric approach

‎In the present paper‎, ‎we are going to use geometric and topological concepts‎, ‎entities and properties of the‎ ‎integral curves of linear vector fields‎, ‎and the theory of differential equations‎, ‎to establish a representation for some groups on $R^{n} (ngeq 1)$‎. ‎Among other things‎, ‎we investigate the surjectivity and faithfulness of the representation‎. At the end‎, ‎we give some app...

Weighted voting systems: reliability versus rapidity

Gregory Levitin Reliability Department, Planning, Development and Technology Division, Bait Amir, Israel Electric Corporation Ltd., P.O. Box 10, Haifa, 31000 Israel E-mail: [email protected] Abstract The weighted voting system (WVS) consists of n units that each provide a binary decision (0 or 1) or abstain from voting. Each unit has its own individual weight. System output is 1 if the cumulati...