Most Wins, Smallest Loss

Violation of Truncated Involvement

Profile type: Profile
Config: 4 c, 8 v
Parameters: ∅

Truncated Involvement violation found:

Original profile:
+---+---+---+---+
| 3 | 3 | 1 | 1 |
+---+---+---+---+
| 1 | 2 | 3 | 3 |
| 3 | 0 | 0 | 2 |
| 2 | 1 | 1 | 0 |
| 0 | 3 | 2 | 1 |
+---+---+---+---+
Profile([[1, 3, 2, 0], [2, 0, 1, 3], [3, 0, 1, 2], [3, 2, 0, 1]], rcounts=[3, 3, 1, 1], cmap={0: '0', 1: '1', 2: '2', 3: '3'})
Most Wins, Smallest Loss winner is {3}

Profile with ballot removed:
+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 2 | 2 | 3 | 3 |
| 3 | 3 | 3 | 0 | 0 | 0 | 2 |
| 2 | 2 | 2 | 1 | 1 | 1 | 0 |
| 0 | 0 | 0 | 3 | 3 | 2 | 1 |
+---+---+---+---+---+---+---+
Profile([[1, 3, 2, 0], [1, 3, 2, 0], [1, 3, 2, 0], [2, 0, 1, 3], [2, 0, 1, 3], [3, 0, 1, 2], [3, 2, 0, 1]], rcounts=[1, 1, 1, 1, 1, 1, 1], cmap={0: '0', 1: '1', 2: '2', 3: '3'})
Most Wins, Smallest Loss winner is {1}

Margin graph of profile with ballot removed:

Profile with truncated ballot:
+---+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
+---+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 2 | 2 | 3 | 3 | 2 |
| 3 | 3 | 3 | 0 | 0 | 0 | 2 | 0 |
| 2 | 2 | 2 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 3 | 3 | 2 | 1 |   |
+---+---+---+---+---+---+---+---+
ProfileWithTies([{np.int64(1): 1, np.int64(3): 2, np.int64(2): 3, np.int64(0): 4}, {np.int64(1): 1, np.int64(3): 2, np.int64(2): 3, np.int64(0): 4}, {np.int64(1): 1, np.int64(3): 2, np.int64(2): 3, np.int64(0): 4}, {np.int64(2): 1, np.int64(0): 2, np.int64(1): 3, np.int64(3): 4}, {np.int64(2): 1, np.int64(0): 2, np.int64(1): 3, np.int64(3): 4}, {np.int64(3): 1, np.int64(0): 2, np.int64(1): 3, np.int64(2): 4}, {np.int64(3): 1, np.int64(2): 2, np.int64(0): 3, np.int64(1): 4}, {np.int64(2): 1, np.int64(0): 2, np.int64(1): 3}], rcounts=[1, 1, 1, 1, 1, 1, 1, 1], cmap={0: '0', 1: '1', 2: '2', 3: '3'})
Most Wins, Smallest Loss winner is {3}

Margin graph of profile with truncated ballot:

Truncated ballot: {np.int64(2): 1, np.int64(0): 2, np.int64(1): 3}
Ranked candidates: (np.int64(2), np.int64(0), np.int64(1))
Unranked candidates: [3]
Winners: [3]

Winners shifted from ranked candidates ['1'] to unranked candidates ['3']