When choosing a voting method, there are many properties that one would like the method to have. However, there are theorem(s) that say that no voting method can have certain subsets of these at once. Here are some of these VotingMethodCriterion**s; does anyone know of more?
- Universality. The voting method should provide a complete ranking of all alternatives from any set of individual preference ballots.
- MonotonicityCriterion. If one set of preference ballots would lead to an an overall ranking of alternative X above alternative Y and if some preference ballots are changed in such a way that the only alternative that has a higher ranking on any preference ballots is X, then the method should still rank X above Y.
- Criterion of independence of irrelevant alternatives. If one set of preference ballots would lead to an an overall ranking of alternative X above alternative Y and if some preference ballots are changed without changing the relative rank of X and Y, then the method should still rank X above Y.
- Citizen Sovereignty. Every possible ranking of alternatives can be achieved from some set of individual preference ballots.
- Non-dictatorship. There should not be one specific voter whose preference ballot is always adopted.
- DeCondorcet: Any candidate who is preferred by a majority of voters to each other candidate should win.
- Later No Harm: Expressing lower preferences cannot affect the fate of higher preferences.
See also ArrowsTheorem (a theorem that you can't have the first five on this list all at once)