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.

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...