Computation and Bribery of Voting Power in Delegative Simple Games

TL;DR

This paper analyzes a variant of weighted voting games based on transitive support structures, proposing algorithms for computing voting power indices and exploring the computational complexity of bribery problems within this framework.

Contribution

It introduces a pseudo-polynomial algorithm for voting power indices and studies the complexity of bribery problems in this game class.

Findings

Efficient algorithm for Banzhaf and Shapley-Shubik indices

Bribery problems are computationally hard

Parameterized complexity results for bribery scenarios

Abstract

Following Zhang and Grossi~(AAAI 2021), we study in more depth a variant of weighted voting games in which agents' weights are induced by a transitive support structure. This class of simple games is notably well suited to study the relative importance of agents in the liquid democracy framework. We first propose a pseudo-polynomial time algorithm to compute the Banzhaf and Shapley-Shubik indices for this class of game. Then, we study a bribery problem, in which one tries to maximize/minimize the voting power/weight of a given agent by changing the support structure under a budget constraint. We show that these problems are computationally hard and provide several parameterized complexity results.