The difference between manipulability indices in the IC and IANC models

We consider the calculation of Nitzan–Kelly’s manipulability index in the impartial anonymous and neutral culture (IANC) model. We provide a new theoretical study of this model and an estimation for the maximal difference between manipulability indices in the IANC model and a basic model, the impartial culture (IC). The asymptotic behavior of this difference is studied with the help of the impartial anonymous culture (IAC) model. It is shown that the difference between the IAC and IANC models tends to zero as the number of alternatives or the number of voters grows. These results hold for any other probabilistic measure that is anonymous and neutral. Finally, we calculate Nitzan–Kelly’s index in the IANC model for four social choice rules and compare it with the IC model.