Dynamic programming algorithms for computing power indices in weighted multi-tier games

In weighted games each voter has a weight assigned and "yes"-voters win if the sum of each weight is greater than or equal to the quota. In weighted multi-tier games, we have several weighted games (tiers) over the same set of voters. In this article, algorithms for calculating Banzhaf and Shapley-Shubik indices for three different type of games are proposed: weighted AND-games, weighted OR-games and games where the tiers have conjunctive normal form. The presented algorithms are generalizations of known computational methods using dynamic programming technique. Finally, some applications and experiments are carried out and these algorithms are compared to a fairly new method based on binary decision diagrams. (C) 2020 Elsevier B.V. All rights reserved.