Beat Path

Violation of Participation

Profile type: ProfileWithTies
Config: 4 c, 4 v
Parameters: set_preference=pessimist

Violation of Participation for Beat Path under the pessimist set preference.
A voter with the ranking 1 3 ( 0  2 )  can benefit by abstaining.

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

Beat Path winners are {0, 1, 3}

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

Beat Path winner is {3}