The liberal paradox arose from the attempt to introduce individual human rights into the theory of social choice. Being one of the major social institutions of a liberal democracy, such rights clearly belong in any complete social choice theory. Thus Sen in his pathbreaking study argued that a person's right consisted in a pair of social states (x, y) such that if the person preferred x to y or y to x so did society. Sen's condition L (liberalism) then required that for each person in society there exist such a pair of social states. Two other conditions proposed by Sen were condition U (universal domain: every profile of individual preference orderings is possible) and condition P (Pareto principle: if everyone in society prefers x to y, so does society). A social choice function f chooses from a set of social opportunities S according to the rule
Gardner, Roy, "The Liberal Paradox and Games of Incomplete Information" (1977). Economic Staff Paper Series. 116.