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:
“I am not of the opinion generally entertained in this country [England], that man lives by Greek and Latin alone; that is, by knowing a great many words of two dead languages, which nobody living knows perfectly, and which are of no use in the common intercourse of life. Useful knowledge, in my opinion, consists of modern languages, history, and geography; some Latin may be thrown into the bargain, in compliance with custom, and for closet amusement.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“In this our talking America, we are ruined by our good nature and listening on all sides. This compliance takes away the power of being greatly useful.”
—Ralph Waldo Emerson (1803–1882)
“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)
“Social and scientific progress are assured, sir, once our great system of postpossession payments is in operation, not the installment plan, no sir, but a system of small postpossession payments that clinch the investment. No possible rational human wish unfulfilled. A man with a salary of fifty dollars a week can start payments on a Rolls-Royce, the Waldorf-Astoria, or a troupe of trained seals if he so desires.”
—John Dos Passos (1896–1970)
“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)