Profile type: ProfileWithTies
Config: 4 c, 4 v
Parameters: ∅
Semi-Positive Involvement violation found:
Original profile:
+-----+-----+-----+-----+
| 1 | 1 | 1 | 1 |
+-----+-----+-----+-----+
| 3 | 0 1 | 1 2 | 2 3 |
| 2 | 3 | 0 | 0 |
| 0 1 | 2 | 3 | 1 |
| | | | |
+-----+-----+-----+-----+
ProfileWithTies([{0: 2, 1: 2, 2: 1, 3: 0}, {2: 2, 3: 1, 0: 0, 1: 0}, {3: 2, 0: 1, 1: 0, 2: 0}, {1: 2, 0: 1, 2: 0, 3: 0}], rcounts=[1, 1, 1, 1], cmap={0: 0, 1: 1, 2: 2, 3: 3})
Split Cycle winner is {3}
Profile with ballot removed:
+-----+-----+-----+
| 1 | 1 | 1 |
+-----+-----+-----+
| 3 | 0 1 | 1 2 |
| 2 | 3 | 0 |
| 0 1 | 2 | 3 |
| | | |
+-----+-----+-----+
ProfileWithTies([{0: 2, 1: 2, 2: 1, 3: 0}, {2: 2, 3: 1, 0: 0, 1: 0}, {3: 2, 0: 1, 1: 0, 2: 0}], rcounts=[1, 1, 1], cmap={0: '0', 1: '1', 2: '2', 3: '3'})
Split Cycle winners are {1, 2}
Margin graph of profile with ballot removed:
Winners: [1, 2]
Truncated ballot: {2: 0, 3: 0, 0: 1}
Top-ranked candidates: [2, 3]
Ranked candidates: [2, 3, 0]
Unranked candidates: [1]
Profile with truncated ballot:
+-----+-----+-----+-----+
| 1 | 1 | 1 | 1 |
+-----+-----+-----+-----+
| 3 | 0 1 | 1 2 | 2 3 |
| 2 | 3 | 0 | 0 |
| 0 1 | 2 | 3 | |
| | | | |
+-----+-----+-----+-----+
ProfileWithTies([{0: 2, 1: 2, 2: 1, 3: 0}, {2: 2, 3: 1, 0: 0, 1: 0}, {3: 2, 0: 1, 1: 0, 2: 0}, {2: 0, 3: 0, 0: 1}], rcounts=[1, 1, 1, 1], cmap={0: '0', 1: '1', 2: '2', 3: '3'})
Split Cycle winner is {1}
Margin graph of profile with truncated ballot:
Winners: [1]
Winners shifted from including top-ranked candidate(s) [2] to unranked candidates [1]