Unrestricted domain

Intuitively, unrestricted domain is a common requirement for social choice functions, and is a condition for Arrow's impossibility theorem.

With unrestricted domain, the social welfare function accounts for all preferences among all voters to yield a unique and complete ranking of societal choices.

Under that theorem, it is impossible to have a social choice function that satisfies unrestricted domain, Pareto efficiency, independence of irrelevant alternatives, and non-dictatorship.

Duncan Black defined a restriction to domains of social choice functions called "single-peaked preferences".

Black proved that by replacing unrestricted domain with single-peaked preferences in Arrow's theorem removes the impossibility: there are Pareto-efficient non-dictatorships that satisfy the "independence of irrelevant alternatives" criterion.