CHAPTER 5 – SOPHISTICATED VOTING

Publisher Summary Given a game form and a fixed profile, a dominating strategy of a particular agent i is an optimal decentralized behavior for this agent whatever the information he or she possesses on the other agents' preferences. If i is completely informed of the whole profile or if he is only aware of his own preference ordering, he will still use his dominating strategy as long as cooperation with the rest of the society is not possible. This is how strategy-proof game forms achieve full decentralization of collective decisions—not creating any incentive for individual agents to acquire information about their respective opinions. This chapter discusses a rich class of dominance solvable game forms, namely voting by binary choices. The chapter reviews a family of dominance-solvable game forms that sophisticatedly implement several Condorcet-type social choice functions. A sophisticated social choice function is one that is sophisticatedly implemented by some finite dominance solvable game form—requiring finiteness of the message space is consistent with the assumption, throughout the chapter, that A and N are both finite.