Raynaud

Violation of Truncated Involvement

Profile type: Profile
Config: 3 c, 11 v
Parameters: ∅

Truncated Involvement violation found:

Original profile:
+---+---+---+
| 3 | 3 | 5 |
+---+---+---+
| 0 | 1 | 2 |
| 2 | 0 | 1 |
| 1 | 2 | 0 |
+---+---+---+
Profile([[0, 2, 1], [1, 0, 2], [2, 1, 0]], rcounts=[3, 3, 5], cmap={0: '0', 1: '1', 2: '2'})
Raynaud winner is {2}

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

Margin graph of profile with ballot removed:

Profile with truncated ballot:
+---+---+---+---+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
+---+---+---+---+---+---+---+---+---+---+---+
| 0 | 0 | 0 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 |
| 2 | 2 | 2 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |   |
| 1 | 1 | 1 | 2 | 2 | 2 | 0 | 0 | 0 | 0 |   |
+---+---+---+---+---+---+---+---+---+---+---+
ProfileWithTies([{0: 1, 2: 2, 1: 3}, {0: 1, 2: 2, 1: 3}, {0: 1, 2: 2, 1: 3}, {1: 1, 0: 2, 2: 3}, {1: 1, 0: 2, 2: 3}, {1: 1, 0: 2, 2: 3}, {2: 1, 1: 2, 0: 3}, {2: 1, 1: 2, 0: 3}, {2: 1, 1: 2, 0: 3}, {2: 1, 1: 2, 0: 3}, {2: 1}], rcounts=[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], cmap={0: '0', 1: '1', 2: '2'})
Raynaud winner is {0}

Margin graph of profile with truncated ballot:

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

Winners shifted from ranked candidates ['2'] to unranked candidates ['0']