Weighted Majority Voting with a Heterogeneous System in the Game of Shogi

In this paper, we propose a weighted voting method for a heterogeneous game system, which assigns the strength of engines and win probabilities of their positions to the weights for voting. Assigning the strength as the weight solves the problem of weaker engines entering the majority voting. The win probabilities are transformed from the evaluation values by a sigmoid function generated for each engine. Through the sigmoid functions, we can compare the win probabilities between the different engines and resolve the problem of optimistic voting in heterogeneous systems. Optimistic voting, which simply selects the highest-scoring move, may select a suboptimal random move when random players are involved in the game. Finally, we competed the proposed system and other voting systems against a single engine in shogi tournaments and compared the strengths of the systems in shogi. The experimental results confirmed the effectiveness of the proposed method.