An Experimental View on Committees Providing Justified Representation
R. Bredereck, P. Faliszewski, A. Kaczmarczyk, R. Niedermeier
IJCAI 2019
Abstract
We provide an experimental study of committees that achieve (proportional/extended) justified representation (JR/PJR/EJR). In particular, we ask how many such committees exist and how varied they are in terms of voter satisfaction and coverage. We find that under many natural distributions of preferences a large fraction of randomly selected JR committees also provide PJR and EJR. Further, we find that the sets of JR committees for our elections are very varied and include both high-quality ones and not-so-appealing ones.
Experiments:
| Election type |
Culture |
Candidates |
Voters |
Instances |
Parameters |
| Approval |
Impartial Culture |
{100, 200} |
{200, 100} |
500 |
None |
| Approval |
Euclidean 1D |
{100} |
{100} |
500 |
1D: Uniform Interval (r-UI) [0,1]; 2D: Uniform Square (r-US) [0,1]x[0,1]; For r-UI, r between 0.01 and 0.25 with step 0.01; For r-US, r between 0.02 and 0.5 with step 0.02 |
| Approval |
Euclidean 2D |
{100, 200} |
{200, 100} |
500 |
1D: Uniform Interval (r-UI) [0,1]; 2D: Uniform Square (r-US) [0,1]x[0,1]; For r-UI, r between 0.01 and 0.25 with step 0.01; For r-US, r between 0.02 and 0.5 with step 0.02 |
| Approval |
Impartial Culture |
{100} |
{100} |
500 |
None |
| Approval |
Euclidean 2D |
{100} |
{100} |
500 |
1D: Uniform Interval (r-UI) [0,1]; 2D: Uniform Square (r-US) [0,1]x[0,1]; For r-UI, r between 0.01 and 0.25 with step 0.01; For r-US, r between 0.02 and 0.5 with step 0.02 |
| Approval |
Euclidean 1D |
{100, 200} |
{200, 100} |
500 |
1D: Uniform Interval (r-UI) [0,1]; 2D: Uniform Square (r-US) [0,1]x[0,1]; For r-UI, r between 0.01 and 0.25 with step 0.01; For r-US, r between 0.02 and 0.5 with step 0.02 |