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

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. Both the number of variables and number of constraints in our formulation are bounded by $\mbox{O}(Wn)$ where $W$ is the total sum of (integer) voting weights and $n$ is the number of players. 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.