Social Choice and Voting Theory

The assumptions of the theorem are that a group wishes to reach a decision by majority vote.

Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow.

The Gibbard-Satterthwaite theorem is a theorem in social choice theory.

In social choice theory, May's theorem, also called the general possibility theorem, says that majority vote is the unique ranked social choice function between two candidates that satisfies the following criteria: Anonymity: the decision rule treats each voter identically (one vote, one value).

The McKelvey-Schofield chaos theorem is a result in social choice theory.

The Duggan-Schwartz theorem (named after John Duggan and Thomas Schwartz) is a result about voting systems designed to choose a nonempty set of winners from the preferences of certain individuals, where each individual ranks all candidates in order of preference.

The liberal paradox, also Sen paradox or Sen's paradox, is a logical paradox proposed by Amartya Sen which shows that no means of aggregating individual preferences into a single, social choice, can simultaneously fulfill the following, seemingly mild conditions: The unrestrictedness condition, or U: every possible ranking of each individual's preferences and all outcomes of every possible voting rule will be considered equally, The Pareto condition, or P: if everybody individually likes some choice better at the same time, the society in its voting rule as a whole likes it better as well, and Liberalism, or L (from which the theorem derives its gist): all individuals in a society must have at least one possibility of choosing differently, so that the social choice under a given voting rule changes as well.