Smith IRV PUT

Violation of Positive-Negative Involvement

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

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

Full profile
+---+---+---+---+---+---+
| 1 | 1 | 1 | 2 | 1 | 1 |
+---+---+---+---+---+---+
| 0 | 1 | 1 | 2 | 3 | 3 |
| 3 | 0 | 3 | 0 | 1 | 1 |
| 2 | 3 | 0 | 3 | 0 | 2 |
| 1 | 2 | 2 | 1 | 2 | 0 |
+---+---+---+---+---+---+
Profile([[0, 3, 2, 1], [1, 0, 3, 2], [1, 3, 0, 2], [2, 0, 3, 1], [3, 1, 0, 2], [3, 1, 2, 0]], rcounts=[1, 1, 1, 2, 1, 1], cmap={0: '0', 1: '1', 2: '2', 3: '3'})
Smith IRV PUT winners are {0, 1}

Profile with voter removed
+---+---+---+---+---+
| 1 | 1 | 1 | 2 | 1 |
+---+---+---+---+---+
| 0 | 1 | 1 | 2 | 3 |
| 3 | 0 | 3 | 0 | 1 |
| 2 | 3 | 0 | 3 | 0 |
| 1 | 2 | 2 | 1 | 2 |
+---+---+---+---+---+
Profile([[0, 3, 2, 1], [1, 0, 3, 2], [1, 3, 0, 2], [2, 0, 3, 1], [3, 1, 0, 2]], rcounts=[1, 1, 1, 2, 1], cmap={0: '0', 1: '1', 2: '2', 3: '3'})
Smith IRV PUT winners are {1, 2, 3}