Tied at the top: Difference between revisions
→Notes
No edit summary |
(→Notes) |
||
Line 11:
25 A>B| >C
40 B>C| >A
Line 18 ⟶ 17:
There is an A>B>C>A cycle, with the approvals being A 60, B 65, and C 75. C is elected for having the most approvals in the Smith set. The easiest way for A-top voters to get someone they prefer to C under regular Smith//Approval is for at least 11 of them to swap A and B, making B a [[Condorcet winner]]. With a modification of the tied at the top rule, they could instead vote A=B, and this would yield a matchup of 49 votes for A, 40 for B, and 11 tied votes. Since the 11 tied votes is greater than the margin of 9 votes, the matchup could simply be dropped, meaning that B becomes a CW because B pairwise beats C.
Note that C-top voters can vote C=A to make A have no pairwise defeats too, so A and B would tie, having a 50/50 chance of winning, which is better from C-top voters' perspectives. Then, B-top voters, if they wished to, could vote B=C to remove C's only pairwise defeat, resulting in all 3 candidates having a 1/3rd chance of winning.
[[Category:Single-winner voting methods]]
| |||