Implementability via Protective Equilibria*

Social choice functions choose the ‘best’ outcome corresponding to each profile of individual preferences. Implementing a given social choice function is to make sure that the relationship it establishes between individual preferences and ‘best’ outcomes always holds. One possible way of implementing a given rule is to first ascertain what individual preferences are, and then find their image. However, since information on an individual’s preference is private to the individual, this method will not work unless the individual is motivated to reveal his actual preference. A particularly clear-cut case arises under rules for which revealing one’s own preference is always a dominant strategy. In this case, no individual would ever gain by revealing preferences other than those by which he actually evaluates social outcomes, and such rules would be implementable provided individuals are rational. Moreover, implementation could be decentralized, since computation of one’s own preferences does not require any knowledge about the preferences and/or the strategies of others. Unfortunately, the Gibbard/Satterthwaite theorem shows that truthful revelation of preferences is always a dominant strategy only under trivial social choice functions. Thus, in general, the possibility of implementing a social choice function is subject to a number of qualifications. A social choice functionfcan be viewed as the outcome function of a gameform where individual strategies are the possible