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.

Allocation rules map preference profiles into allocations, whereas trading rules map preference profiles and allocations into allocations. It is shown that no allocation rule can derive from a trading rule based on voluntary trade and satisfying a weak efficiency condition. If the trading rule...