Profile type: Profile
Config: 4 c, 10 v
Parameters: ∅
Semi-Positive Involvement violation found:
Original profile:
+---+---+---+---+---+
| 3 | 1 | 1 | 2 | 3 |
+---+---+---+---+---+
| 1 | 2 | 2 | 2 | 3 |
| 3 | 0 | 0 | 1 | 2 |
| 2 | 1 | 3 | 3 | 0 |
| 0 | 3 | 1 | 0 | 1 |
+---+---+---+---+---+
Profile([[1, 3, 2, 0], [2, 0, 1, 3], [2, 0, 3, 1], [2, 1, 3, 0], [3, 2, 0, 1]], rcounts=[3, 1, 1, 2, 3], cmap={0: '0', 1: '1', 2: '2', 3: '3'})
Copeland-Local-Minimax winner is {3}
Profile with ballot removed:
+---+---+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
+---+---+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 2 | 2 | 2 | 3 | 3 | 3 |
| 3 | 3 | 3 | 0 | 1 | 1 | 2 | 2 | 2 |
| 2 | 2 | 2 | 1 | 3 | 3 | 0 | 0 | 0 |
| 0 | 0 | 0 | 3 | 0 | 0 | 1 | 1 | 1 |
+---+---+---+---+---+---+---+---+---+
Profile([[1, 3, 2, 0], [1, 3, 2, 0], [1, 3, 2, 0], [2, 0, 1, 3], [2, 1, 3, 0], [2, 1, 3, 0], [3, 2, 0, 1], [3, 2, 0, 1], [3, 2, 0, 1]], rcounts=[1, 1, 1, 1, 1, 1, 1, 1, 1], cmap={0: '0', 1: '1', 2: '2', 3: '3'})
Copeland-Local-Minimax winners are {1, 2, 3}
Margin graph of profile with ballot removed:
Winners: [1, 2, 3]
Truncated ballot: {np.int64(2): 1, np.int64(0): 2}
Top-ranked candidate: 2
Ranked candidates: (np.int64(2), np.int64(0))
Unranked candidates: [1, 3]
Profile with truncated ballot:
+---+---+---+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
+---+---+---+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 2 | 2 | 2 | 3 | 3 | 3 | 2 |
| 3 | 3 | 3 | 0 | 1 | 1 | 2 | 2 | 2 | 0 |
| 2 | 2 | 2 | 1 | 3 | 3 | 0 | 0 | 0 | |
| 0 | 0 | 0 | 3 | 0 | 0 | 1 | 1 | 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(1): 2, np.int64(3): 3, np.int64(0): 4}, {np.int64(2): 1, np.int64(1): 2, np.int64(3): 3, np.int64(0): 4}, {np.int64(3): 1, np.int64(2): 2, np.int64(0): 3, np.int64(1): 4}, {np.int64(3): 1, np.int64(2): 2, np.int64(0): 3, np.int64(1): 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}], rcounts=[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], cmap={0: '0', 1: '1', 2: '2', 3: '3'})
Copeland-Local-Minimax winner is {3}
Margin graph of profile with truncated ballot:
Winners: [3]
Winners shifted from including top-ranked candidate 2 to unranked candidates [3]