Copeland

Violation of Participation

Profile type: ProfileWithTies
Config: 4 c, 4 v
Parameters: set_preference=weak-dominance

Violation of Participation for Copeland under the weak-dominance set preference.
A voter with the ranking ( 0  1 ) 3 2  can benefit by abstaining.

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

Copeland winners are {2, 3}

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

Copeland winner is {3}