Whose Opinion Counts? Political Processes and the Implementation Problem

We augment the mechanism used in Nash implementation with a political process that collects the opinions of a subset of individuals with a xed probability distribution. The outcome is a function of only the collected opinions. We show that the necessary - and sometimes sufficient - condition for implementation by a specic political process can be either weaker or stronger than Maskin monotonicity. We study three such processes: oligarchy, oligarchic democracy and random sampling. Oligarchy collects only the opinions of the oligarchs (a strict subset of the individuals). We present a Nash implementable social choice rule (SCR) that cannot be implemented by any oligarchy. Oligarchic democracy "almost always" collects the opinions of the oligarchs but sometimes, there is a referendum (i.e., everyone's opinions are collected). We show that in economic environments, every Nash implementable SCR can be implemented by oligarchic democracy in which any three individuals act as oligarchs. In random sampling, a sample of opinions are collected randomly. We show that in economic environments, every Nash implementable SCR can be implemented by randomly sampling opinions of 4 individuals. We also provide necessary and sufficient conditions for implementation when the planner has the exibility to choose any political process.