Ranked voting

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Names

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Various types of ranked voting ballot

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Single-winner methods Single vote - plurality methods First preference plurality (FPP) Two-round (US: Jungle primary) Partisan primary Instant-runoff UK: Alternative vote (AV) US: Ranked-choice (RCV) Condorcet methods Condorcet-IRV Round-robin voting Minimax Schulze Ranked pairs Maximal lottery Positional voting Plurality (el. IRV) Borda count (el. Baldwin, Mdn. Bucklin) Antiplurality (el. Coombs) Cardinal voting Score voting Approval voting Majority judgment STAR voting
Proportional representation Party-list Apportionment Highest averages Largest remainders National remnant Biproportional List type Closed list Open list Panachage List-free PR Localized list Quota-remainder methods Hare STV Schulze STV CPO-STV Quota Borda Approval-based committees Thiele's method Phragmen's method Expanding approvals rule Method of equal shares Fractional social choice Direct representation Interactive representation Liquid democracy Fractional approval voting Maximal lottery Random ballot Semi-proportional representation Cumulative SNTV Limited voting
Mixed systems By results of combination Mixed-member majoritarian Mixed-member proportional By mechanism of combination Non-compensatory Parallel (superposition) Coexistence Conditional Fusion (majority bonus) Compensatory Seat linkage system UK: 'AMS' NZ: 'MMP' Vote linkage system Negative vote transfer Mixed ballot Supermixed systems Dual-member proportional Rural–urban proportional Majority jackpot By ballot type Single vote Double simultaneous vote Dual-vote
Paradoxes and pathologies Spoiler effects Spoiler effect Cloning paradox Frustrated majorities paradox Center squeeze Pathological response Perverse response Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting Exaggeration Truncation Turkey-raising Wasted vote Paradoxes of majority rule Tyranny of the majority Discursive dilemma Conflicting majorities paradox
Social and collective choice Impossibility theorems Arrow's theorem Majority impossibility Moulin's impossibility theorem McKelvey–Schofield chaos theorem Gibbard's theorem Positive results Median voter theorem Condorcet's jury theorem May's theorem Condorcet dominance theorems Harsanyi's utilitarian theorem VCG mechanism Quadratic voting
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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, which gives them very different properties. In instant-runoff voting (IRV) and the single transferable vote system (STV), lower preferences are used as contingencies (back-up preferences) and are only applied when all 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 use ranks as weights; these systems are called positional voting. In the Borda method, the 1st, 2nd, 3rd... candidates on each ballot receive 1, 2, 3... points, and the candidate with the fewest points is elected. Thus intensity of preference is assumed to be at ratios of 1 to 2, 2 to 3, etc.

Although not typically described as such, the well-known first-past-the-post voting election system can be seen as a ranked voting system where a voter gives a single point to the candidate marked as their choice and zero points to all others, and the candidate with the most points (although not necessarily a majority) is elected. Taking the ranked ballots of instant-runoff voting and the single transferable vote system as indicating one choice at a time (that is, giving one point to the preference in use and zero points to all others), instant-runoff voting can be seen as a non-degenerate ranked voting system. It operates as a staged variant of the plurality system that repeatedly eliminates last-place candidates if necessary to transfer votes and determine a majority winner.^[1]

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 it could cause confusion.

Ranked votes as such do not incorporate any information about intensity of preferences. It records only that the voter prefers a candidate marked as a 1 to some degree over the candidate marked as number 2.

Ranked voting systems of the instant-runoff voting type and the Borda count type are contrasted with rated voting methods, which allow voters to indicate how strongly they support different candidates (e.g. on a scale from 0 to 10).^[2] Ranked vote systems produce more information than X voting systems such as first-past-the-post voting. Rated voting systems produce more information than ordinal ballots; as a result, some common results like Arrow's theorem do not directly apply to them.^[3]

Some ranked voting systems require the voter to rank a set number of candidates. Others allow the voter full liberty as to how many candidates they rank. Under STV or IRV, not all rankings are used in any case.^[4]