Compliance With Voting System Criteria
Most of the mathematical criteria by which voting systems are compared were formulated for voters with ordinal preferences. In this case, approval voting requires voters to make an additional decision of where to put their approval cutoff (see examples above). Depending on how this decision is made, approval voting satisfies different sets of criteria.
There is no ultimate authority on which criteria should be considered, but the following are some criteria that are accepted and considered to be desirable by many voting theorists:
- Majority criterion—If there exists a majority that ranks (or rates) a single candidate higher than all other candidates, does that candidate always win?
- Monotonicity criterion—Is it impossible to cause a winning candidate to lose by ranking him higher, or to cause a losing candidate to win by ranking him lower?
- Consistency criterion—If the electorate is divided in two and a choice wins in both parts, does it always win overall?
- Participation criterion—Is voting honestly always better than not voting at all? (This is grouped with the distinct but similar Consistency Criterion in the table below.)
- Condorcet criterion—If a candidate beats every other candidate in pairwise comparison, does that candidate always win? (This implies the majority criterion, above)
- Condorcet loser criterion—If a candidate loses to every other candidate in pairwise comparison, does that candidate always lose?
- Independence of irrelevant alternatives—Is the outcome the same after adding or removing non-winning candidates?
- Independence of clone candidates—Is the outcome the same if candidates identical to existing candidates are added?
- Reversal symmetry—If individual preferences of each voter are inverted, does the original winner never win?
| Majority | Monotone | Consistency & Participation | Condorcet | Condorcet loser | IIA | Clone independence | Reversal symmetry | |
|---|---|---|---|---|---|---|---|---|
| Inherently dichotomous preferences | Yes | Yes | Yes | Yes | Yes | Yes | Yes | Yes |
| Arbitrary cutoff | No | Yes | Yes | No | No | Yes | Yes | Yes |
| Strong Nash equilibrium (Perfect information, rational voters, and perfect strategy) | Yes | Yes | No | Yes | No | No | Yes | Yes |
Read more about this topic: Approval Voting
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