Voting system criterion

A "voting system criterion" (or "electoral system criterion") is formally defined pass/fail criterion by which a voting system may be assessed.

Criterion failure rates
Though a voting method may pass or fail a given criterion, that does not mean the voting method can't almost always pass or fail the criterion in practice, or that when it passes or fails the criterion, that this will be particularly bad. Advocates of various voting methods often make the argument that though their method may fail some criteria, that this should not be considered a major drawback of their methods; for example, advocates of Approval voting and IRV often argue that though those methods fail the Condorcet criterion, they almost always meet it in practice, and that when they fail it, it is for good reason, or at least not particularly bad.

Efficiency
For some criteria, it is common to use the term "efficient" or "efficiency" to indicate that the criterion is always met by some voting method, or to identify how often that is the case. For example, Smith efficiency measures how often a voting method passes the Smith criterion.

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

Terminology note
Further, a common terminology when comparing two criteria is to say one is stronger than the other when it applies to every situation the other applies to and more (a superset), with weaker meaning it applies to only a subset of the situations.

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

Clone independence

Pareto

Desirable criteria
Other criteria are also widely regarded as good, but there is disagreement over how important it is for a voting method to pass these (they are agreed to be desirable, but not necessarily essential):

Independence of irrelevant alternatives

Monotonicity, Participation criterion

Summability criterion

Sometimes desirable properties or criteria are called desiderata.

There is disagreement over how important the various other criteria are. Some criteria are even considered bad by some; for instance, Michael Dummett, in a letter to Robert Newland, regarded the combination of later-no-harm and later-no-help as "quite unreasonable".

Examples
Examples for such criteria are:


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

Majority-related criteria
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, Majority loser criterion, Droop proportionality criterion

Condorcet criterion, Smith criterion, Condorcet loser

Proportionality-related criteria
Proportionality for Solid Coalitions Justified representation Perfect representation Stable Winner Set Quota rule

Strategic voting-related criteria
Strategy-free criterion

Protecting voters' preferences
These can generally be split into two categories: criteria which protect a voter from hurting a candidate (which doesn't prevent the voter themselves from getting hurt, since they may end up hurting a candidate not covered by the criterion), and criteria that protect a voter from hurting themselves.

Protecting candidates
Later-no-harm, Monotonicity

Protecting voters
Favorite betrayal, Independence of irrelevant alternatives

Mathematical criteria
Consistency criterion, Summability

Axiomatic criteria
These generally are considered essential and basic features of any voting method

Discrimination axiom, Homogeneity criterion, Scale invariance

Miscellaneous criteria
Immunity from 2nd Place Complaints

Absolute criterion
An absolute criterion requires or prohibits some result due to some characteristic of a given a set of ballots. This is in contrast to the below-mentioned relative criterion, which requires (or prohibits) a change in the election's result given some modification to the ballots.

Examples of absolute criteria:


 * Condorcet criterion, Smith criterion, Plurality criterion, Minimal Defense criterion, Majority criterion, Pareto criterion

Relative criterion
A relative criterion requires that when the ballots are changed in some way, the result of the election must or must not change in some way. This is in contrast to the above-mentioned absolute criterion, which requires some result given some characteristic of a set of ballots.

Examples of relative criteria:


 * Monotonicity criterion, Participation criterion, Later-no-harm criterion, Later-no-help criterion, Sincere Favorite criterion, Independence of irrelevant alternatives, Independence of clones, Neutrality of Spoiled Ballots

Consensus criterion
Consensus criteria attempt to guarantee the election of consensus candidates. Examples of such criteria include greatest possible consensus criterion and unanimous consensus criterion.

Proportional Representation
Proportional representation is the general idea that groups of voters with shared preferences should be able to win an amount of representation in a multi-winner body (a legislature) proportional to how large they are. In partisan PR methods, proportionality can be measured using various measures of how well a party's seats matched up to its share of votes. For nonpartisan methods, there is disagreement on how to measure or quantify PR. Ranked PR advocates tend to tout Proportionality for Solid Coalitions, which is meant to account for coherent factions that can be identified from the rankings, while cardinal PR advocates gravitate towards the similar, but weaker, ￼￼Hare quota criterion and similar criteria.

Rated ballot adaptations
Several criteria have rated-ballot or other adaptations that may make more sense in certain contexts. For example, the majority criterion says that a candidate preferred by a majority over all other candidates must win. The Majority criterion for rated ballots further requires the majority to give this candidate the highest score. It can be argued that a voter who gives their favorite candidate less than full support (i.e. didn't do normalization) doesn't deserve full power, so this modification to the criterion ensures that only a strategic or strongly supportive majority gets their way. Similar adaptations can be made to any criterion involving voter preferences determining who should win, such as PSC, the plurality criterion, Mutual majority, etc.