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Many criteria relate to sets of candidates; see the [[set theory]] article for more information.
Many criteria relate to sets of candidates; see the [[set theory]] article for more information.

Some criteria are very widely agreed to be important. Examples:

[[Cloneproofness]]

[[Pareto]]


Other criteria are also widely regarded as good, but there is disagreement over how important it is for a voting method to pass these:

[[Independence of irrelevant alternatives]]

[[Monotonicity]], [[Participation criterion]]

[[Summability criterion]]

There is disagreement over how important the various other criteria are. Some criteria are even considered bad by some.


Examples for such criteria are:
Examples for such criteria are:


* [[Condorcet Criterion|Condorcet criterion]], [[Consensus Criteria]], [[Consistency|Consistency criterion]], [[Favorite Betrayal criterion]], [[Generalized Strategy-Free criterion]], [[Greatest Possible Consensus Criterion]], [[Independence of irrelevant alternatives|independence from irrelevant alternatives]], [[Independence of irrelevant alternatives|local independence from irrelevant alternatives]], [[Tactical voting|invulnerability to burying]], [[Tactical voting|invulnerability to compromising]], [[Later-no-harm criterion]], [[Monotonicity criterion]], [[Pareto criterion]], [[Participation criterion]], [[Plurality criterion]], [[Schwartz set|Schwartz criterion]], [[Smith set|Smith criterion]] (also known as [[Generalized Condorcet criterion]]), [[Strategic nomination|Independence of clones]], [[Strategy-Free criterion]], [[Strong Defensive Strategy criterion]], [[Summability criterion]], [[Unanimous Consensus Criterion]], [[Weak Defensive Strategy criterion]]
* [[Condorcet Criterion|Condorcet criterion]], [[Consensus Criteria]], [[Consistency|Consistency criterion]], [[Favorite Betrayal criterion]], [[Generalized Strategy-Free criterion]], [[Greatest Possible Consensus Criterion]], [[Independence of irrelevant alternatives|independence from irrelevant alternatives]], [[Independence of irrelevant alternatives|local independence from irrelevant alternatives]], [[Tactical voting|invulnerability to burying]], [[Tactical voting|invulnerability to compromising]], [[Later-no-harm criterion]], [[Monotonicity criterion]], [[Pareto criterion]], [[Participation criterion]], [[Plurality criterion]], [[Schwartz set|Schwartz criterion]], [[Smith set|Smith criterion]] (also known as [[Generalized Condorcet criterion]]), [[Strategic nomination|Independence of clones]], [[Strategy-Free criterion]], [[Strong Defensive Strategy criterion]], [[Summability criterion]], [[Unanimous Consensus Criterion]], [[Weak Defensive Strategy criterion]]

Here are some criteria often touted by advocates of [[majority rule]], split into categories of "widely agreed on" and criteria which are more polarizing:

[[Majority criterion]], [[Mutual majority criterion]], [[Droop proportionality criterion]]


[[Condorcet criterion]], [[Smith criterion]]


=== Absolute criterion ===
=== Absolute criterion ===