A joint Politics and Economics series
Social choice and electoral systems
Social choice Mechanism design Comparative politics Comparison List (By country)
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) 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 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
Politics portal Economics portal Mathematics portal

The contingent vote is an electoral system used to elect a single representative in which a candidate requires a majority of votes to win. It is a form of preferential voting. The voter ranks the candidates in order of preference, and when the votes are counted, the first preference votes only are counted. If no candidate has a majority (more than half) of the votes cast, then all but the two leading candidates are eliminated and the votes received by the eliminated candidates are distributed among the two remaining candidates according to voters' preferences.

The contingent vote can be considered a compressed or "instant" form of the two-round system (runoff system), in which both "rounds" occur without the need for voters to go to the polls twice. For this reason, the term instant-runoff voting has also been used for this method,^{[citation needed]} though this conflicts with the more common meaning.

It also has similarities to other ranked-choice systems. Unlike the contingent vote, systems like instant-runoff voting (IRV), Coombs' method, and Baldwin's method allow for many rounds of counting, eliminating only one weakest candidate each round. IRV allows a candidate other than the top two in the first count to win.

A variant of the contingent vote has been used to elect the president of Sri Lanka since 1978.^[1]

The supplementary vote was used to pick directly elected mayors and police and crime commissioners in England prior to 2022.^[1]

In the past, the ordinary form of the contingent vote was used to elect the Legislative Assembly of Queensland from 1892 to 1942. To date, this has been the longest continuous use of the system anywhere in the world.^[1]

Contingent voting was used for Democratic party primaries in the US state of Alabama from 1915 to 1931.^[1]

In an election held using the contingent vote, the voters rank the list of candidates in order of preference. Under the most common ballot layout, they place a '1' beside their most preferred candidate, a '2' beside their second most preferred, and so on. In this respect the contingent vote is the same as other ranked ballot methods.

There are then a maximum of two rounds of counting. In the first round only first preferences are counted. Candidates receiving an absolute majority of first preferences (i.e. more than half) are immediately declared the winner. However, if no candidate has an absolute majority, then all but the two candidates with the most first preferences are eliminated, and there is a second round. In the second round, the votes of the voters whose first preference had been eliminated are transferred to whichever of the two remaining candidates they ranked the highest. The votes are then counted, and whichever candidate has an absolute majority is declared elected.

The supplementary vote and the Sri Lankan contingent vote are two implementation variations, in which voters cannot rank all of the candidates but rather are only permitted to express two or three preferences, respectively.

This means that if a voter's marked preferences do not include either of the candidates who survive to the second round, then it will be impossible to transfer the vote, which is therefore declared "wasted" or "exhausted".

In Sri Lanka, since the 1982 presidential election, a variant of the contingent vote electoral system is used to elect the country's president. As under the conventional contingent vote, in an election held using the Sri Lankan form of the contingent vote each voter ranks the candidates in order of preference, and if no candidate receives an overall majority of first preference votes on the first count then all but the two leading candidates are eliminated and their votes redistributed to help determine a winner in a second and final round. However, whereas under the ordinary form of the contingent vote voters can rank all of the candidates in order of preference, under Sri Lankan contingent voting the voter can only express their top three preferences (which can lead to exhausted ballots). Each direct presidential election going back to the first in 1981 had seen a candidate from one of the two major parties or alliances at the time winning in the first count so the second round of vote counting had never been conducted.^[2] However, in the 2024 presidential election, the strong third-party candidacy of Anura Kumara Dissanayake, who won 42% of the first preference vote, forced a second round of counting for the first time in the nation's history. Dissanayake went on to win the election in the second round.^[3][4]

Example ballot designs

Two column	Single column
Each voter ranks at least one and no more than two candidates by placing an 'X' in one column to indicate their first choice of candidate and another 'X' in a second column to indicate their second choice of candidate.	A less common form is to print a single column on the ballot paper and require voters to write '1' next to their first preference and '2' next to their second.[a]

The supplementary vote (SV) is a variation of the contingent vote in which the voter ranks only two of the candidates in order of preference. If a voter's first-choice candidate is eliminated but their second choice is one of the two remaining candidates, their vote is transferred to the second-choice candidate. This means that the winning candidate has the support of a majority of voters who expressed a preference among the top two, although not necessarily a majority of votes cast in the first count.

The supplementary vote was used in all elections for directly elected mayors in England, including the Mayor of London, and in elections for police and crime commissioners, until 2022, when it was replaced by first-past-the-post voting (FPTP).

In the early 1990s, the Plant Commission was established by the Labour Party to recommend a new voting system for the Parliament of the United Kingdom. When the Commission reported in 1993, instead of suggesting an already existing system, it recommended the supplementary vote system, which it said had never been used anywhere. In actuality, contingent voting had been in use in Australia as early as 1892.^[1]

Although some commentators credit the head of the commission, Raymond Plant, with the invention of SV, according to others, it was the brainchild of a Labour member of Parliament (MP) at the time, Dale Campbell-Savours and academic Patrick Dunleavy, who outlined and advocated for it in an article for the New Statesman magazine that was published September 29, 1989.^[5]

In 2000, several districts in England introduced directly elected mayors. It was decided to use the supplementary vote for the election of these new mayors, including the Mayor of London, and for the election of police and crime commissioners across much of England and Wales.^[6] The supplementary vote was used for these offices from 2000 to 2022.

In the 2021 London election, a record 5 percent of ballots were wholly rejected, and no candidate achieved a majority of the vote.^[7] The government responded by ending the use of the supplementary vote in 2022,^[8] citing voter confusion with a complex system. However, critics, including the Labour and Green parties, argued that the wasted votes were due to ballot layout and that the change was aimed at benefitting Conservative Party candidates.^[9][10][11] They also claimed that the supplementary vote was effective in increasing multi-party participation and was popular among voters.^[12]

The histories of two-round voting and other forms of instant run-off voting may be seen as part of the history of SV due to their similarities.

The supplementary vote is said to encourage candidates to seek support beyond their core base of supporters in order to secure the second preferences of the supporters of other candidates, and so to create a more conciliatory campaigning style among candidates with similar policy platforms. SV is also likely to improve the chances of "third party" candidates by encouraging voters, who wish to do so, to vote sincerely for such candidates for whom, under systems such as first-past-the-post, they would be discouraged from doing so for tactical reasons.

These positive effects are moderated by the incentives SV creates for voting, in some circumstances, for only candidates from among the leading three.

Political scientists Colin Rallings and Michael Thrasher noted two flaws of SV:^[13]

• First, since the automatic dual-ballot nature of SV dispenses with any need for a runoff two weeks later – as often happens for, say, the election of the president of France – voters cast their second preferences without being certain of which candidates will make the runoff. Consequently, some second preferences will be declared invalid because they bear only preferences marked for eliminated candidates.
• Second, it is possible for the victor to fail to achieve an absolute majority overall, for it is not an obligation for a voter to cast a second preference, and even when a second preference is marked, the vote will be ineffective if it is cast for a candidate who does not make it into the top two, when the first preference is marked also for a candidate who does not make it into the second round.

Under the two-round system (also known as runoff voting and the second ballot) voters vote for only a single candidate, rather than ranking candidates in order of preference. As under the contingent vote, if no candidate has an absolute majority in the first round, all but the top two are eliminated and there is a second round. However, in the two round system, voters are asked to return and vote a second time. Because of the similarities between them, the contingent vote and the two-round system can usually be expected to elect the same winner. However, in the two-round system, the voter is permitted to change one's mind from one round to another, even if their favourite candidate in the first round has not been eliminated. It also guarantees that every voter has a chance to express a preference between the top two, unlike the limited forms of contingent vote. Voter turnout may also be higher in the second vote.

The nonpartisan blanket primary is a variation of the two-round system except the first round does not pick a winner, but instead picks the two highest candidates who will compete in the general election. Because the first round does not pick a winner, there will tend to be higher voter turnout in the second election.

The contingent vote will generally pick the same winner as a blanket primary, except fewer voters in the primary round may lead to a different top-two candidates than if the whole electorate voted in both rounds.

The top-four primary is a variant of the nonpartisan blanket primary which advances the top four candidates from a single primary, regardless of party, and uses instant-runoff voting in the general election to pick a majority winner.

As noted above, the instant-runoff voting (or alternative vote) differs from the contingent vote in that it permits several rounds rather than just two. Under the alternative vote only candidate(s) for whom it is mathematically impossible to win are eliminated after each round, and as many rounds occur as are necessary to give one candidate an absolute majority. These differences mean that the contingent vote and alternative vote can produce different results. Because, under the contingent vote, all but two candidates are eliminated in the first round, it is possible for a candidate to be eliminated who would have gone on to win had they been allowed to receive transfers in later rounds.

• Ranked voting systems
• History and use of instant-runoff voting
• Elected mayors in the United Kingdom
• List of democracy and elections-related topics
• Alternative vote
• Alternative Vote Plus
• Single transferable vote

1. ^ See Electoral Reform Society press release on Torbay election

• Democratic and Electoral Shifts in Queensland (PDF)
• London Elects: How the Mayor of London is Elected
• Electoral Systems Index: Sri Lanka