Robustness of Greedy Approval Rules

TL;DR

This paper investigates the robustness of greedy approval rules in multiwinner elections, demonstrating their vulnerability to small changes and the computational difficulty of predicting outcome shifts, supported by experimental analysis.

Contribution

It provides the first analysis of the robustness of GreedyCC, GreedyPAV, and Phargmen's sequential rule, including complexity results and empirical evaluation.

Findings

Adding or removing a single approval can drastically change the winning committee.

Deciding the minimal number of approvals to change the outcome is NP-complete.

Experimental results show varying robustness levels under random noise.

Abstract

We study the robustness of GreedyCC, GreedyPAV, and Phargmen's sequential rule, using the framework introduced by Bredereck et al. for the case of (multiwinner) ordinal elections and adopted to the approval setting by Gawron and Faliszewski. First, we show that for each of our rules and every committee size $k$, there are elections in which adding or removing a certain approval causes the winning committee to completely change (i.e., the winning committee after the operation is disjoint from the one before the operation). Second, we show that the problem of deciding how many approvals need to be added (or removed) from an election to change its outcome is NP-complete for each of our rules. Finally, we experimentally evaluate the robustness of our rules in the presence of random noise.