- Reversal symmetry
Reversal symmetry is a
voting system criterion that is stated as follows: If a candidate A is the unique winner, and the individual preferences of each voter are inverted, then candidate A must not be elected. Methods that satisfy reversal symmetry include theSchulze method and theBorda count . Methods that fail reversal symmetry includeBucklin voting ,instant-runoff voting andCondorcet method s that fail theCondorcet loser criterion like Minimax.For cardinal voting systems which can be meaningfully reversed,
approval voting andrange voting satisfy the criterion.Example
Consider a preferential system where 11 voters express their preferences as:
*5 voters prefer A then B then C
*4 voters prefer B then C then A
*2 voters prefer C then A then BWith the Borda count A would get 23 points (5×3+4×1+2×2), B would get 24 points, and C would get 19 points, so B would be elected. In instant-runoff, C would be eliminated in the first round and A would be elected in the second round by 7 votes to 4.Now reversing the preferences:
*5 voters prefer C then B then A
*4 voters prefer A then C then B
*2 voters prefer B then A then CWith the Borda count A would get 21 points (5×1+4×3+2×2), B would get 20 points, and C would get 25 points, so this time C would be elected. In instant-runoff, B would be eliminated in the first round and A would as before be elected in the second round, this time by 6 votes to 5.
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