Fishburn (1970) showed that in an infinite society Arrow's axioms for a preference aggregation rule do not necessarily imply a dictator. Kirman and Sondermann (1972) showed that, in this case, nondictatorial rules imply an invisible dictator that, whenever the agent set is an atomless finite...

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...

Arrow’s and the Gibbard-Satterthwaite theorems are proved using a common proof strategy based on a dictatorship result for choice functions. One of the instrumental results obtained shows the inconsistency between the basic assumption in each of these theorems and a mild majority principle.

A procedure to construct a social welfare function from a social choice function is suggested and it is shown that the dictatorial are the only unanimous social welfare functions that can be reconstructed from a social choice function that does not change the social choice when a defeated...