Implementing Strong and Lower Strong Positive Association Social Choice Rules by Social Procedures

Abstract

The main purpose of this paper is to show that the theory of social situations is fruitful in the area of implementation especially because it is “richer” and more flexible than “classical game theory”. For example, the theory of social situations unifies both the representation of the social environment and the solution concept and it is, therefore, possible to employ implementation procedures that involve both cooperative (“coalitional”) and noncooperative game forms. Another advantage of the theory of social situations is that it enables us to dispense with the requirement, inherent to “classical” noncooperative games, that the “set of outcomes” be a Cartesian product of the players’ sets of strategies. We exploit these features of the theory of social situations to implement social choice rules, using simple and intuitive procedures that satisfy “strong or lower strong positive association”.