 The basic results of social choice theory are laid out in detail elsewhere in the encyclopedia (List 2013). Here we will simply articulate the basic result and an illustration. The question of Arrowian social choice theory is: how do we determine a social preference for a society overall on the basis of the set of the individual preferences of the members? Arrow shows that a social choice function that satisfies a number of plausible constraints cannot be defined when there are three or more alternatives to be chosen by the group. He lays out a number of conditions to be imposed on a social choice function. Unlimited domain: The social choice function must be able to give us a social preference no matter what the preferences of the individuals over alternatives are. Non dictatorship: the social choice function must not select the preference of one particular member regardless of others’ preferences. Transitivity and completeness: The individual preferences orderings must be transitive and complete orderings and the social preference derived from them must be transitive and complete. Independence of irrelevant alternatives: the social preference between two alternatives must be the result only of the individual orderings between those two alternatives. Pareto condition: if all the members prefer an alternative x over y, then x must be ranked above y in the social preference. The theorem says that no social choice function over more than two alternatives can satisfy all of these conditions.