# Neutrality criterion

(Redirected from Symmetry)

The neutrality criterion requires that a voting method must not prefer a particular candidate or alternative regardless of voters' opinions. It checks for this by seeing if any candidate can benefit in a voting method by swapping names with another candidate.

One example of a failure is the use of majority rule in legislatures. When there is a tie on a bill, it is customary to not pass the bill; this is biased towards the status quo. In order for neutrality to be met, there would have to be a 50% chance for either the bill or the status quo to happen.

In the case of a symmetrical Condorcet cycle, neutrality requires that voting methods with only ranked information give all of the candidates in the cycle an equal chance of winning. Example:

1 A>B>C

1 B>C>A

1 C>A>B

Because all the candidates have matchups or either a 2 to 1 pairwise victory or a 1 to 2 pairwise loss against someone, they are all in a symmetrical situation. So this is often called a pairwise tie.

## Anonymity criterion

The voting method shouldn't give priority to some voters over others. This is checked by seeing if any voters can swap ballots and change the result.

Some decision-making bodies allow the chairman to break ties. This is a failure of anonymity.