Analysis of inefficiencies in systems with many independent agents

Abstract

Finally, we examine the quality of social choice functions, which map agents' orderings over a set of alternatives to a single winning alternative. We assume that every agent has costs over all of the alternatives and that these costs form a metric space. However, the social choice mechanisms may not have access to these costs, especially since they may be unknown to the agents themselves. As a result, we cannot simply select the alternative that minimizes the total agent cost. Instead, we assume that the social choice functions only have access to the agents' ordinal preferences that are induced by the metric space. We examine the distortion, which is the worst-case ratio of the quality of the alternative selected by the social choice mechanism and the quality of the optimal alternative. Bounding the distortion acts as a method for determining the quality of the social choice function itself. We provide distortion bounds for a variety of deterministic and randomized mechanisms, such as plurality, Copeland, and randomized dictatorship.