Beat Path

Violation of Positive Involvement

Profile type: Profile
Config: 4 c, 10 v
Parameters:

3 loses in the full profile, but 3 is a winner after removing voter with the ranking (np.int64(3), np.int64(2), np.int64(1), np.int64(0)):

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

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