Dodgson

Violation of Participation

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

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

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

Dodgson winner is {1}

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

Dodgson winners are {1, 3}