False name manipulations in weighted voting games: splitting, merging and annexation

TL;DR

This paper investigates the computational complexity of false-name manipulations such as splitting, merging, and annexation in weighted voting games, revealing limits and paradoxes that impact coalition formation strategies.

Contribution

It analyzes the complexity of manipulation via splitting, merging, and annexation in weighted voting games for Banzhaf and Shapley-Shubik indices, providing algorithms and characterizations.

Findings

Optimal split algorithm for Banzhaf index

Complexity bounds for merging and annexation manipulations

Discovery of annexation non-monotonicity paradox

Abstract

An important aspect of mechanism design in social choice protocols and multiagent systems is to discourage insincere and manipulative behaviour. We examine the computational complexity of false-name manipulation in weighted voting games which are an important class of coalitional voting games. Weighted voting games have received increased interest in the multiagent community due to their compact representation and ability to model coalitional formation scenarios. Bachrach and Elkind in their AAMAS 2008 paper examined divide and conquer false-name manipulation in weighted voting games from the point of view of Shapley-Shubik index. We analyse the corresponding case of the Banzhaf index and check how much the Banzhaf index of a player increases or decreases if it splits up into sub-players. A pseudo-polynomial algorithm to find the optimal split is also provided. Bachrach and Elkind also mentioned manipulation via merging as an open problem. In the paper, we examine the cases where a player annexes other players or merges with them to increase their Banzhaf index or Shapley-Shubik index payoff. We characterize the computational complexity of such manipulations and provide limits to the manipulation. The annexation non-monotonicity paradox is also discovered in the case of the Banzhaf index. The results give insight into coalition formation and manipulation.