Pareto criterion

The Pareto criterion or unanimity criterion is a basic criterion for evaluating voting systems. It can be defined in this way:

This criterion is important in the context of Arrow's impossibility theorem.

Virtually every devised election method satisfies this criterion. An example of a method which would fail it would be Random Candidate, where some candidate is elected at random, regardless of the submitted votes.

A second, stronger variation of the criterion (meaning it implies the first variation of the criterion as well) is "if at least one voter prefers X over Y, and no voters prefer Y over X, then the system prefers X over Y."

Independence of Pareto-dominated alternatives (IPDA) says that if one option (X) wins an election, and a new alternative (Y) is added, X will win the election if Y is Pareto-dominated (using the second version of the criterion).

The Pareto criterion is Hare-PSC in the single-winner case.