Dictatorship versus manipulability

Abstract

The Gibbard-Satterthwaite (1973/75) theorem roughly states that we have to accept dictatorship or manipulability in case of at least three alternatives. A large strand of the literature estimates the degree of manipulability of social choice functions (e.g. Aleskerov and Kurbanov, 1999, Favardin et al., 2002, and Aleskerov et al., 2012), most of them employing the Nitzan-Kelly index of manipulability. We take a different approach and introduce a non-dictatorship index based on our recent work (Bednay et al., 2017), where we have analysed social choice functions based on their distances to the dictatorial rules. By employing computer simulations, we investigate the relationship between the manipulability and nondictatorship indices of some prominent social choice functions, putting them into a common framework.