Knockout Voting

Violation of Positive-Negative Involvement

Profile type: Profile
Config: 4 c, 7 v
Parameters: ∅

2 loses and 3 wins in the full profile, but 2 is a winner and 3 is a loser after removing a voter with the ranking (2, 0, 1, 3):

Full profile
+---+---+---+---+
| 2 | 2 | 1 | 2 |
+---+---+---+---+
| 1 | 2 | 2 | 3 |
| 3 | 0 | 1 | 2 |
| 2 | 1 | 3 | 0 |
| 0 | 3 | 0 | 1 |
+---+---+---+---+
Profile([[1, 3, 2, 0], [2, 0, 1, 3], [2, 1, 3, 0], [3, 2, 0, 1]], rcounts=[2, 2, 1, 2], cmap={0: '0', 1: '1', 2: '2', 3: '3'})
Knockout Voting winner is {3}

Profile with voter removed
+---+---+---+---+
| 2 | 1 | 1 | 2 |
+---+---+---+---+
| 1 | 2 | 2 | 3 |
| 3 | 0 | 1 | 2 |
| 2 | 1 | 3 | 0 |
| 0 | 3 | 0 | 1 |
+---+---+---+---+
Profile([[1, 3, 2, 0], [2, 0, 1, 3], [2, 1, 3, 0], [3, 2, 0, 1]], rcounts=[2, 1, 1, 2], cmap={0: '0', 1: '1', 2: '2', 3: '3'})
Knockout Voting winner is {2}