# Non-dictatorship

In voting theory, non-dictatorship is a property of social choice functions which requires that the results of voting cannot simply mirror that of any single person's preferences without consideration of the other voters.

There is no single voter i with the individual preference order P, such that P is the societal ("winning") preference order, unless all voters have the same P. Thus, as long as there are voters in the society that have different preference orderings, the preferences of individual i should not always prevail.

Blind voting systems (with at least two voters) automatically satisfy the non-dictatorship property.

## Arrow's impossibility theorem

Non-dictatorship is one of the necessary conditions in Arrow's impossibility theorem.[1] 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 $P_i$ y implies x P y.

## References

1. Game Theory Second Edition Guillermo Owen Ch 6 pp124-5 Axiom 5 Academic Press, 1982 ISBN 0-12-531150-8