Plurality Mechanisms, Virtual Implementation, and Condorcet-Decisiveness

We investigate implementation of social choice functions as mappings from states to lotteries under complete information. We assume that for every agent, any pair of distinct states induces distinct preferences. A social choice function is called Condorcet-decisive if it always enforces the Condorcet winner among its range. We introduce plurality mechanisms, where each agent makes a single announcement and the lottery associated with the opinion announced by the largest number of agents is enforced. We show that a social choice function is virtually implementable via plurality mechanisms combined with constrained random dictatorship, if and only if it is Condorcet-decisive.