For the case of strict preferences, a measure of a voter’s average power in a dictatorial social welfare function is defined making the dictator never have more average power than three voters and, as the number of voters grows, making the dictator average power converge to the average power...

Voting operators map n-tuples of subsets of a given set X of candidates (the voters’ choices) into subsets of X (the social choice). This paper characterizes dictatorial voting operators by means of three conditions (the non-emptiness condition A1, the independence condition A2 and the...

Denicolò [2, Theorem 1] strengthens Arrow's [1, p. 97] theorem by replacing the independence of irrelevant alternatives (IIA) condition by a strictly weaker one, relational independent decisiveness (RID). It is shown here that RID can be still substantially weakened. Yet, the new condition is...

If, for strict preferences, a unique choice function (CF) is used to aggregate preferences position-wise then the resulting social welfare function (SWF) is dictatorial. This suggests that the task performed by non-dictatorial SWFs must be “more complex” than just selecting an alternative...