Reversal symmetry: Difference between revisions
Add STAR voting
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Note, that every voting system that satisfies the Reversal symmetry criterion, would have to lead to a tie in this example (as in every example in which the set of reversed ballots is the same as the set of normal ballots).
=== [[STAR voting]] ===
The following example shows that [[STAR voting]] violates the Reversal symmetry criterion.
{| class="wikitable"
|-
! # of voters !! Preferences
|-
| 2 || A (3 points) > C (1 point) > B (0 points)
|-
| 1 || C (3 points) > B (1 point) > A (0 points)
|-
| 2 || B (3 points) > A (1 point) > C (0 points)
|}
This is an A>C>B>A cycle, and the scores are:
{| class="wikitable"
|-
! Candidate !! Score
|-
| A || 8
|-
| B || 7
|-
| C || 5
|}
Before reversal, A and B advance to the automatic runoff, and then B beats A pairwise and wins.
If each voter rates each candidate 5-x points instead of x, then the A>C>B>A cycle is reversed to A>B>C>A and A is now the candidate with the lowest total rating. Thus B and C advance to the automatic runoff, where B beats C pairwise and wins.
In both the normal and reversed case, B is the winner, demonstrating the reversal symmetry failure.
==References==
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