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. The numbers of variables and constraints in our formulation are both bounded by O(nW+), 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. •We discuss the least core of a weighted voting game.•We address a problem for finding a payoff vector in the least core.•We propose a pseudo polynomial size LP formulation for the problem.•A polynomial time algorithm for LP solves the problem in pseudo polynomial time.•One can adopt his/her favored software (LP solver) for calculating a payoff vector.•A commercial LP solver calculates a payoff vector in a few seconds.