Ranked voting

Ranked voting is any voting system that uses voters' rankings of candidates to choose a single winner or multiple winners. More formally, a ranked vote system depends only on voters' order of preference of the candidates.

Ranked voting systems vary dramatically in how preferences are tabulated and counted. This gives them different properties with respect to satisfying various voting groups and adherence to mathematical rules.

In instant-runoff voting (IRV) and the single transferable vote system (STV), lower preferences are used as contingencies and are only applied when all candidates marked as higher-ranked preferences on a ballot have been eliminated or when the vote has been cast for a candidate who has been elected and surplus votes need to be transferred. Ranked votes of this type do not suffer the problem that a marked lower preference may be used against a voter's higher marked preference.

Some ranked vote systems do not use ranking to transfer votes but instead use ranks as weights. These systems are called positional voting. In the Borda method, the least-favored candidates on each ballot receive fewer points; the most-favored receive more points. The points on each ballot for each candidate are added together, and the candidate with the most points is elected.

In the United States and Australia, the terms ranked-choice voting and preferential voting, respectively, almost always refer to instant-runoff voting; however, because these terms have also been used to mean ranked systems in general, many social choice theorists recommend the use of the term instant-runoff voting in contexts where confusion might arise.

Ranked votes do not incorporate any information about intensity of preferences. Furthermore, common implementations do not account for equality of preference among two or more candidates.

Ranked voting systems that use ordinal numbers (1, 2, 3, etc.) such as IRV, STV and the Borda method are contrasted with rated voting methods, which allow voters to indicate how strongly they support candidates (e.g. on a scale from 0 to 10). Ranked vote systems using ordinal numbers produce more information than X voting systems such as first-past-the-post voting. Rated voting systems produce more information than systems that use ordinal ballots; as a result, some common results, like Arrow's theorem, do not directly apply to them.

Some ranked voting systems require the voter rank a set number of candidates. Those that use optional preferential voting allow the voter full liberty as to how many candidates they rank. Under STV or IRV, not all rankings are used in any case.