Neutrality criterion

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.