Scoring rules and implementation in iteratively undominated strategies

We characterize voting procedures according to the solution that they implement when voters cast ballots strategically, applying iteratively undominated strategies. In elections with three candidates, the Borda Rule is the unique positional scoring rule that satisfies unanimity (U) (i.e., elects a candidate whenever it is unanimously preferred) and is majoritarian after eliminating a worst candidate (MEW)(i.e., if there is a unanimously disliked candidate, the majority-preferred among the other two is elected). In the larger class of direct mechanism scoring rules, Approval Voting is characterized by a single axiom – it is majoritarian after eliminating a Pareto dominated candidate (MEPD)(i.e., if there is a Pareto-dominated candidate, the majority-preferred among the other two is elected). However, it fails a desirable monotonicity property: a candidate that is elected for some preference profile, may lose the election once she gains further in popularity. In contrast, the Borda Rule is the unique direct mechanism scoring rule that satisfies U, MEW and monotonicity (MON). Finally, there exists no direct mechanism scoring rule that satisfies both MEPD and MON or Condorcet consistency (CON).