Pseudo Polynomial Size LP Formulation for Calculating the Least Core Value of Weighted Voting Games

TL;DR

This paper introduces a pseudo polynomial size linear programming formulation for efficiently computing the least core value in weighted voting games, enabling practical solutions for large instances.

Contribution

It presents a novel LP formulation with bounded size based on players and total weights, improving computational efficiency for weighted voting games.

Findings

LP solver computes least core payoff vectors in seconds

Formulation size is bounded by O(n W_+)

Applicable to vector weighted voting games

Abstract

In this paper, we propose a pseudo polynomial size LP formulation for finding a payoff vector in the least core of a weighted voting game. The numbers of variables and constraints in our formulation are both bounded by $\mbox{O}(n W_+)$, where $n$ is the number of players and $W_+$ is the total sum of (integer) voting weights. When we employ our formulation, a commercial LP solver calculates a payoff vector in the least core of practical weighted voting games in a few seconds. We also extend our approach to vector weighted voting games.