Symmetry and impartial lotteries

A prize is to be randomly assigned to some agent, so each agent designates one of his peers on a ballot. The ballots determine the lottery which selects the winner, and impartiality requires that no agent’s report impacts his own chance of winning. The primary results are (1) a characterization of all impartial rules which treat agents symmetrically as voters and (2) a characterization of all impartial rules which treat agents symmetrically as candidates. Each rule in either class randomly selects from a finite set of simple rules. Corollaries include a known constant rule impossibility, a new dictatorship impossibility, and the first axiomatic characterization of the rule which randomly selects one of the ballots using the uniform distribution proposed by Holzman and Moulin (2013).