Pareto efficiency
The Pareto criterion is a basic criterion for evaluating voting systems. It can be defined in this way:
If every voter prefers alternative X over alternative Y, then the system prefers X over Y
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.