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
Famous quotes containing the words compliance with, compliance, voting, system and/or criteria:
“This is the day when people reciprocally offer, and receive, the kindest and the warmest wishes, though, in general, without meaning them on one side, or believing them on the other. They are formed by the head, in compliance with custom, though disavowed by the heart, in consequence of nature.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Discipline isn’t just punishing, forcing compliance or stamping out bad behavior. Rather, discipline has to do with teaching proper deportment, caring about others, controlling oneself and putting someone else’s wishes before one’s own when the occasion calls for it.”
—Lawrence Balter (20th century)
“All voting is a sort of gaming, like checkers or backgammon, with a slight moral tinge to it, a playing with right and wrong, with moral questions; and betting naturally accompanies it. The character of the voters is not staked. I cast my vote, perchance, as I think right; but I am not vitally concerned that right should prevail. I am willing to leave it to the majority.”
—Henry David Thoreau (1817–1862)
“Loving feels lonely in a violent world,
irrelevant to people burning like last year’s weed
with bellies distended, with fish throats agape
and flesh melting down to glue.
We can no longer shut out the screaming
That leaks through the ventilation system ...”
—Marge Piercy (b. 1936)
“There are ... two minimum conditions necessary and sufficient for the existence of a legal system. On the one hand those rules of behavior which are valid according to the system’s ultimate criteria of validity must be generally obeyed, and on the other hand, its rules of recognition specifying the criteria of legal validity and its rules of change and adjudication must be effectively accepted as common public standards of official behavior by its officials.”
—H.L.A. (Herbert Lionel Adolphus)