A class of voting procedures based on repeated ballots and elimination of one candidate in each round is shown to always induce an outcome in the top cycle and is thus Condorcet consistent, when voters behave strategically. This is an important class as it covers multi-stage, sequential...

We consider a multi-awards generalization of King Solomon's problem: $k$ identical and indivisible awards should be distributed among $n$ agents, $k<n$, with the top $k$ valuation agents receiving the awards. Agents have complete information about each others' valuations. Glazer and Ma (1989) analyzed the single-prize (i.e., $k=1$) version of this problem. We show that in the `more than two agents' problem the mechanism of Glazer and Ma admits inefficient equilibria and thus fails to solve Solomon's problem. So, first we modify their mechanism to rule out inefficient equilibria and implement efficient prize allocation in subgame perfect equilibrium when there are at least three agents. Then it is shown that a simple repeated application of our modified mechanism will distribute $k\;(>1)$ prizes efficiently in subgame perfect equilibria without any monetary transfers in equilibrium. Finally, in the multi-awards case we relax the...</n$,>