Loss-Trimmer Voting

Violation of Semi-Positive Involvement

Profile type: Profile
Config: 3 c, 9 v
Parameters: ∅

Semi-Positive Involvement violation found:
Original profile:
+---+---+---+---+
| 2 | 3 | 1 | 3 |
+---+---+---+---+
| 0 | 1 | 2 | 2 |
| 2 | 0 | 0 | 1 |
| 1 | 2 | 1 | 0 |
+---+---+---+---+
Profile([[0, 2, 1], [1, 0, 2], [2, 0, 1], [2, 1, 0]], rcounts=[2, 3, 1, 3], cmap={0: '0', 1: '1', 2: '2'})
Loss-Trimmer Voting winners are {0, 2}

Profile with ballot removed:
+---+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
+---+---+---+---+---+---+---+---+
| 0 | 0 | 1 | 1 | 1 | 2 | 2 | 2 |
| 2 | 2 | 0 | 0 | 0 | 0 | 1 | 1 |
| 1 | 1 | 2 | 2 | 2 | 1 | 0 | 0 |
+---+---+---+---+---+---+---+---+
Profile([[0, 2, 1], [0, 2, 1], [1, 0, 2], [1, 0, 2], [1, 0, 2], [2, 0, 1], [2, 1, 0], [2, 1, 0]], rcounts=[1, 1, 1, 1, 1, 1, 1, 1], cmap={0: '0', 1: '1', 2: '2'})
Loss-Trimmer Voting winners are {0, 1, 2}

Margin graph of profile with ballot removed:
Winners: [0, 1, 2]

Truncated ballot: {2: 1}
Top-ranked candidate: 2
Ranked candidates: (2,)
Unranked candidates: [0, 1]

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

Margin graph of profile with truncated ballot:
Winners: [0]

Winners shifted from including top-ranked candidate 2 to unranked candidates [0]