Minimax
This example shows that the Minimax method violates the Independence of irrelevant alternatives criterion. Assume four candidates A, B and C and 13 voters with the following preferences:
| # of voters | Preferences |
|---|---|
| 2 | B > A > C |
| 4 | A > B > C |
| 3 | B > C > A |
| 4 | C > A > B |
Since all preferences are strict rankings (no equals are present), all three Minimax methods (winning votes, margins and pairwise opposite) elect the same winners.
The results would be tabulated as follows:
| X | ||||
| A | B | C | ||
| Y | A | 5 8 |
7 6 |
|
| B | 8 5 |
4 9 |
||
| C | 6 7 |
9 4 |
||
| Pairwise election results (won-tied-lost): | 1-0-1 | 1-0-1 | 1-0-1 | |
| worst pairwise defeat (winning votes): | 7 | 8 | 9 | |
| worst pairwise defeat (margins): | 1 | 3 | 5 | |
| worst pairwise opposition: | 7 | 8 | 9 | |
- indicates voters who preferred the candidate listed in the column caption to the candidate listed in the row caption
- indicates voters who preferred the candidate listed in the row caption to the candidate listed in the column caption
Result: A has the closest biggest defeat. Thus, A is elected Minimax winner.
Read more about this topic: Local Independence Of Irrelevant Alternatives, Voting Theory, Examples