Diversity, Agreement, and Polarization in Elections
P. Faliszewski, A. Kaczmarczyk, K. Sornat, S. Szufa, T. Was
IJCAI 2023
Abstract
We consider the notions of agreement, diversity, and polarization in ordinal elections (that is, in elections where voters rank the candidates). While (computational) social choice offers good measures of agreement between the voters, such measures for the other two notions are lacking. We attempt to rectify this issue by designing appropriate measures, providing means of their (approximate) computation, and arguing that they, indeed, capture diversity and polarization well. In particular, we present "maps of preference orders" that highlight relations between the votes in a given election and which help in making arguments about their nature.
Experiments:
| Election type |
Culture |
Candidates |
Voters |
Instances |
Parameters |
| Ordinal |
Euclidean 1D |
{8} |
{96} |
292 |
Uniform 1D {[0,1]} |
| Ordinal |
Euclidean 2D |
{8} |
{96} |
292 |
Uniform 2D ($[0,1]^2$); Uniform 2D Sphere |
| Ordinal |
Euclidean 3D-or-more |
{8} |
{96} |
292 |
Uniform 3D ($[0,1]^3$); Uniform 5D ($[0,1]^5$); Uniform 3D Sphere; Uniform 10D ($[0,1]^10$) |
| Ordinal |
Group-Separable |
{8} |
{96} |
292 |
None |
| Ordinal |
Impartial Culture |
{8} |
{96} |
292 |
None |
| Ordinal |
Mallows |
{8} |
{96} |
292 |
Normalized phi, chosen uniformly at random |
| Ordinal |
PrefLib |
None |
None |
292 |
https://www.preflib.org/dataset/00001 |
| Ordinal |
PrefLib |
None |
None |
None |
https://www.preflib.org/dataset/00014 |
| Ordinal |
PrefLib |
None |
None |
None |
None |
| Ordinal |
Single-Crossing |
{8} |
{96} |
292 |
None |
| Ordinal |
Single-Peaked (Conitzer/Random Peak) |
{8} |
{96} |
292 |
None |
| Ordinal |
Single-Peaked (Walsh/Uniform) |
{8} |
{96} |
292 |
None |
| Ordinal |
Urn Model |
{8} |
{96} |
292 |
$\alpha \in \{0.2,1\}$ |
| Ordinal |
Euclidean 1D |
[8] |
[1000] |
1 |
Uniform 1D {[0,1]} |
| Ordinal |
Euclidean 2D |
[8] |
[1000] |
1 |
Uniform 2D ($[0,1]^2$); Uniform 2D Sphere |
| Ordinal |
Euclidean 3D-or-more |
[8] |
[1000] |
1 |
Uniform 3D ($[0,1]^3$); Uniform 2D Sphere; Uniform 3D Sphere |
| Ordinal |
Identity |
[8] |
[1000] |
1 |
None |
| Ordinal |
Impartial Culture |
[8] |
[1000] |
1 |
None |
| Ordinal |
Mallows |
[8] |
[1000] |
1 |
norm-$\phi \in \{0.05, 0.2, 0.5\}$ |
| Ordinal |
PrefLib |
[8] |
[1000] |
1 |
https://www.preflib.org/dataset/00001 |
| Ordinal |
Single-Peaked (Conitzer/Random Peak) |
[8] |
[1000] |
1 |
None |
| Ordinal |
Single-Peaked (Walsh/Uniform) |
[8] |
[1000] |
1 |
None |
| Ordinal |
Urn Model |
[8] |
[1000] |
1 |
$\alpha \in \{0.2,1\}$ |