Weak Nanson

Violation of Participation

Profile type: Profile
Config: 4 c, 5 v
Parameters: set_preference=optimist

Violation of Participation for Weak Nanson under the optimist set preference.
A voter with the ranking (1, 3, 2, 0) can benefit by abstaining.

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

Weak Nanson winner is {2}

Profile if the voter abstains:
+---+---+
| 2 | 2 |
+---+---+
| 2 | 3 |
| 1 | 2 |
| 3 | 1 |
| 0 | 0 |
+---+---+
Profile([[2, 1, 3, 0], [3, 2, 1, 0]], rcounts=[2, 2], cmap={0: '0', 1: '1', 2: '2', 3: '3'})

Weak Nanson winners are {2, 3}