Phragmén Rules for Degressive and Regressive Proportionality
M. Jaworski, P. Skowron
IJCAI 2022
Abstract
We study two concepts of proportionality in the model of approval-based committee elections. In degressive proportionality small minorities of voters are favored in comparison with the standard linear proportionality. Regressive proportionality, on the other hand, requires that larger subdivisions of voters are privileged. We introduce a new family of rules that broadly generalize Phragmén's Sequential Rule spanning the spectrum between degressive and regressive proportionality. We analyze and compare the two principles of proportionality assuming the voters and the candidates can be represented as points in an Euclidean issue space.
Experiments:
| Election type |
Culture |
Candidates |
Voters |
Instances |
Parameters |
| Approval |
Euclidean 1D |
{150} |
{200} |
1000 |
We draw the individuals independently at random from beta distributions, scaled into [-1, 1]. We consider: Beta(1/2,1/2), Beta(1/2, 2), Beta(2, 2), Beta(2, 4). The voters’ preferences are constructed from their positions as follows. We fix the approval radius $\xi \in \{0.1, 0.2, 0.3, 0.4, 0.5\}$, and assume that a voter $v$ approves a candidate $c$ if and only if $|v - c| \leq \xi$. We set a threshold of 0.5 for the approval radius. Acceptance radius $\tau = 0.2$ and the parameters of the probability function $p\mu$ to: $\tau = 30$, $\delta = 120$. |