Voting criteria

There are a number of different criteria which can be used for voting systems in an election, including the following A Condorcet (French: [kɔ̃dɔʁsɛ], English: /kɒndɔːrˈseɪ/) winner is a candidate who would receive the support of more than half of the electorate in a one-on-one race against any one of their opponents.

[8][9] Previous research has found cycles to be somewhat rare in real elections, with estimates of their prevalence ranging from 1-10% of races.

Systems that fail the consistency criterion (such as Instant-runoff voting or Condorcet methods) are susceptible to the multiple-district paradox, a pathological behavior where a candidate can win an election without carrying even a single precinct.

[14] Conversely, it can be seen as allowing for a particularly egregious kind of gerrymander: it is possible to draw boundaries in such a way that a candidate who wins the overall election fails to carry even a single electoral district.

[22] It can be considered a weak form of the independence of irrelevant alternatives (IIA) criterion that nevertheless is failed by a number of voting rules.

If they are allowed, its clone independence depends on specific details of how the criterion is defined and how tied ranks are handled.

The Borda count, minimax, Kemeny–Young, Copeland's method, plurality, and the two-round system all fail the independence of clones criterion.

Voting methods that limit the number of allowed ranks also fail the criterion, because the addition of clones can leave voters with insufficient space to express their preferences about other candidates.

Independence of Smith-dominated alternatives (ISDA, also known as Smith-IIA) is a voting system criterion which says that the winner of an election should not be affected by candidates who are not in the Smith set.

In the next election, Bob focuses on expanding his appeal with this group of voters, but does not manage to defeat Alice—Bob's rating increases from 6th-place to 3rd.

[46] Perversity is often described by social choice theorists as an exceptionally severe kind of electoral pathology,[47] as such rules can have "backwards" responses to voters' opinions, where popularity causes defeat while unpopularity leads to a win.

It is an adaptation of the quota rule to voting systems in which there are no official party lists, and voters can directly support candidates.

[55][56] In social choice, a no-show paradox is a surprising behavior in some voting rules, where a candidate loses an election as a result of having too many supporters.

[65] Ranked-choice voting (RCV) and the two-round system both fail the participation criterion with high frequency in competitive elections, typically as a result of a center squeeze.

It is stated as follows:[68] [69] Woodall has called the plurality criterion "a rather weak property that surely must hold in any real election" opining that "every reasonable electoral system seems to satisfy it."

Among Condorcet methods which permit truncation, whether the plurality criterion is satisfied depends often on the measure of defeat strength.

A voting system is called decisive, resolvable, or resolute if it ensures a low probability of tied elections.

[70] In social choice theory, the best-is-worst paradox occurs when a voting rule declares the same candidate to be both the best and worst possible winner.

Intuitively, unrestricted domain is a common requirement for social choice functions, and is a condition for Arrow's impossibility theorem.