Optimizing the Efficiency of Weighted Voting Games

• Published in: Czech Economic Review Vol. 5; no. 3; pp. 306 - 323
• Main Author: Doležel, Pavel
• Format: Journal Article
• Language: English
• Published: Univerzita Karlova v Praze - Institut ekonomických studií 2011; Charles University in Prague - Institute of Economic Studies
• Subjects: Economy; efficiency of voting; integer programming; IAC models; Weighted voting game
• ISSN: 1802-4696

Having a group of voters endowed with weights, the simple weighted voting game (or system) represents a system of approving propositions in which the approved is only a proposition that is accepted by voters weighted to a number that is at least equal to a prescribed number called a quota. We call the system simple if there is only one set of weights and one quota, as opposed to the multi-rule systems that have more weights assigned to each voter and with more quotas. This paper presents an analysis of the efficiency of simple weighted voting systems. It assumes the Impartial Anonymous Culture (the probability of a single voter voting for a proposition is 1=2 and voters act independently). This culture is used for the general evaluationof voting systems, when no specific information about propositions and voters’ preferences are known, or when the voters’ preferences and proposition characteristics are not willing to be reflected in the voting system itself, keeping in mind its non-pragmatics, fairn ess and generality. The efficiency of a simple weighted voting system is defined as the probability of a proposition being approved. This paper focuses on efficiency maximization and minimization with respect to weights. We prove a theorem which enables the computing of the efficiency maximum and efficiency minimum with respect to weights, given the number of voters and quota in linear time.