On efficient schemes of estimating the degree of manipulability of aggregation procedures

We study the algorithms for evaluation of manipulatility of aggregation procedures. We consider 27 known aggregation procedures and generalized scoring rules, when the weights of second or second and third alternatives are different. Both Impartial Culture and Impartial Anonymous Culture are studied. We calculate 6 manipulability indices including well-known Nitzan-Kelly index. We provide asymptotic estimations of the computational complexity. It is shown that optimization allows to calculate manipulability indices for aggregation procedures for the number of agents between 3 and 100 and for 3, 4 and 5 alternatives. The algorithms and their structures are discussed.