The Aggregate and the Representation of its Parts

Abstract

The main concern of this contribution is to review the approach Condorcet applied to problems of aggregation and representation. The modern viewpoint usually chosen for these topic is mainly driven by social choice theory. Here the viewpoint was altered and the problems and solutions were presented in a setting which uses cooperative game theory. After the introductory notes on Condorcet's basic ideas, we follow one logical path for an initial analysis of rules (Section 3). We present some new facts on the solutions to stand-offs. After connecting the logical approach and the social choice approach in Section 4, we discuss the probabilistic models introduced by Condorcet (Section 5). In Section 6 we provide additional structural insight, which can be derived from the game theoretic viewpoint. Based on the results of the previous sections, in Section 7 we analyse representation procedures. We develop a major tool for representation, namely the minimal representation of a weighted majority game. We discuss its construction and provide examples based on the results of the German Bundestag election in the year 2005.