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

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