The cost of principles: analyzing power in compatibility weighted voting games
نویسندگان
چکیده
We propose Compatibility Weighted Voting Games, a variant of Weighted Voting Games in which some pairs of agents are compatible and some are not. In a Weighted Voting Game each agent has a weight, and a set of agents can form a winning coalition if the sum of their weights is at least a given quota. Whereas the original Weighted Voting Game model assumes that all agents are compatible, we consider a model in which the agents’ compatibility is described by a compatibility graph. We consider power indices, which measure the power of each agent to affect the outcome of the game, and show that their computation is tractable under certain restrictions (chiefly that the agents’ compatibilities have spectral structure). Through simulations we investigate the effect an agent’s compatibility restrictions has on its power.
منابع مشابه
Analyzing Power in Weighted Voting Games with Super-Increasing Weights
Weighted voting games (WVGs) are a class of cooperative games that capture settings of group decision making in various domains, such as parliaments or committees. Earlier work has revealed that the effective decision making power, or influence of agents in WVGs is not necessarily proportional to their weight. This gave rise to measures of influence for WVGs. However, recent work in the algorit...
متن کاملA 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...
متن کاملCombinatorial and computational aspects of multiple weighted voting games
Weighted voting games are ubiquitous mathematical models which are used in economics, political science, neuroscience, threshold logic, reliability theory and distributed systems. They model situations where agents with variable voting weight vote in favour of or against a decision. A coalition of agents is winning if and only if the sum of weights of the coalition exceeds or equals a specified...
متن کاملBoolean combinations of weighted voting games
Weighted voting games are a natural and practically important class of simple coalitional games, in which each agent is assigned a numeric weight, and a coalition is deemed to be winning if the sum of weights of agents in that coalition meets some stated threshold. We study a natural generalisation of weighted voting games called Boolean Weighted Voting Games (BWVGs). BWVGs are intended to mode...
متن کاملManipulation of Weighted Voting Games and the Effect of Quota
The Shapley-Shubik, Banzhaf, and Deegan-Packel indices are three prominent power indices for measuring voters’ power in weighted voting games. We consider two methods of manipulating weighted voting games, called annexation and merging. These manipulations allow either an agent, called an annexer to take over the voting weights of some other agents, or the coming together of some agents to form...
متن کامل