and thus is rounded down to "Poor". The median of B is "Fair". Thus, B is elected Majority Judgment winner for the reversed ballots. Conclusion B is the Majority Judgment winner using the normal ballots and also using the ballots with reversed ratings. Thus, Majority Judgment fails the Reversal symmetry criterion. However, note that using another rounding method could prevent the failure to Reversal symmetry. Also, note that this situation is unlikely to arise in practical elections with many voters because it involves a "tie" of sorts - some candidate (A in this case) gets exactly the same number of votes above and below a certain value ("fair" in this case). Minimax This example shows that the Minimax method violates the Reversal symmetry criterion. Assume four candidates A, B, C and D with 14 voters with the following preferences: Since all preferences are strict rankings (no equals are present), all three Minimax methods (winning votes, margins and pairwise opposite) elect the same winners. Now, the winners are determined for the normal and the reversed order. Normal order In the following the Minimax winner for the ballots in normal order is determined. The results would be tabulated as follows: [X] indicates voters who preferred the candidate listed in the column caption to the candidate listed in the row caption [Y] indicates voters who preferred the candidate listed in the row caption to the candidate listed in the column caption Result: The candidates A, B, and C form a cycle with clear defeats. D benefits from that since its two losses are relatively close and therefore D's biggest defeat is the closest of all candidates. Thus, D is elected Minimax winner. Reversed order In the following the Minimax winner for the ballots in reversed order is determined. The results would be tabulated as follows: Result: Still, the candidates A, B, and C form a cycle with clear defeats and D benefits from that. Therefore D's biggest defeat is the closest of all candidates. Thus, D is elected Minimax winner. Conclusion D is the Minimax winner using the normal preference order and also using the ballots with reversed preference orders. Thus, Minimax fails the Reversal symmetry criterion. Plurality voting This example shows that Plurality voting violates the Reversal symmetry criterion. Assume three candidates A, B and C and 4 voters with the following preferences: Note that reversing all the ballots, leads to the