Dictatorship mechanism

In social choice theory, a dictatorship mechanism is a rule by which, among all possible alternatives, the results of voting mirror a single pre-determined person's preferences, without consideration of the other voters. Dictatorship by itself is not considered a good mechanism in practice, but it is theoretically important: by Arrow's impossibility theorem, when there are at least three alternatives, dictatorship is the only ranked voting electoral system that satisfies unrestricted domain, Pareto efficiency, and independence of irrelevant alternatives. Similarly, by Gibbard's theorem, when there are at least three alternatives, dictatorship is the only strategyproof rule. Non-dictatorship is a property of more common voting rules, in which the results are influenced by the preferences of all individuals. This property is satisfied if there is no single voter i with the individual preference order P, such that P is always the societal ("winning") preference order. In other words, the preferences of individual i should not always prevail. Anonymous voting systems (with at least two voters) automatically satisfy the non-dictatorship property. The dictatorship rule has variants that are useful in practice: serial dictatorship, random dictatorship, and random serial dictatorship (see below). Non-dictatorship is one of the necessary conditions in Arrow's impossibility theorem. In Social Choice and Individual Values, Kenneth Arrow defines non-dictatorship as: There is no voter i in {1, ..., n} such that, for every set of orderings in the domain of the constitution, and every pair of social states x and y, x y implies x P y. Naturally, dictatorship is a rule that does not satisfy non-dictatorship. A dictatorship mechanism is well-defined only when the dictator has a single best-preferred option. When the dictator is indifferent between two or more best-preferred options, it is possible to choose one of them arbitrarily/randomly, but this will not be Pareto efficient.