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The contingent vote is an electoral system used to elect a single winner, in which the voter ranks the candidates in order of preference. In an election, if no candidate receives an absolute majority of first preference votes, then all but the two leading candidates are eliminated and there is a second count. In the second count the votes of those who supported eliminated candidates are distributed among the two remaining candidates, so that one candidate achieves an absolute majority. The contingent vote is similar to instant-runoff voting (also known as the 'Alternative Vote') but differs from it in that IRV allows for many rounds of counting, whereas under the contingent vote there are never more than two. It can also be considered a compressed form of the two round system, in which both 'rounds' occur without the need for voters to go to the polls twice.

Today a special variant of the contingent vote is used to elect the President of Sri Lanka. Another variant, called the supplementary vote, is used to elect mayors in England. In the past the ordinary form of the contingent vote was used to elect the Queensland Legislative Assembly from 1892 to 1942. To date, this has been the longest continuous use of the system anywhere in the world. It was also used in the U.S. state of Alabama in the 1920s.

Contents 1 Voting and counting 2 Examples 2.1 Example I 2.2 Example II 3 Variants 4 Similar systems 4.1 Two round system 4.2 Instant run-off voting 4.2.1 Example 5 Tactical voting 6 Strategic nomination 7 Impact on factions and candidates 8 See also 9 External links

In an election held using the contingent vote the voter ranks the list of candidates in order of preference. Under the most common ballot layout, she places a '1' beside her most preferred candidate, a '2' beside her second most preferred, and so on. In this respect the contingent vote is the same as instant-runoff voting.

There are then a maximum of two rounds of counting. In the first round only first preferences are counted. If a candidate has received an absolute majority of first preferences (i.e. more than half) then he is 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 any voter whose first preference has been eliminated has her vote transferred to whichever of the two remaining candidates she has ranked the highest. The votes are then counted and whichever candidate has an absolute majority is declared elected.

Imagine an election in which there are three candidates: Andrew, Brian and Catherine. There are 100 voters and they vote as follows (third preferences are omitted):

#	36 voters	16 voters	48 voters
1st	Andrew	Brian	Catherine
2nd	Brian	Andrew	Brian

1. To begin the count first preferences are counted, and the tallies stand at:

• Andrew: 36
• Brian: 16
• Catherine: 48

2. No candidate has an absolute majority of votes (this would be 51), so the two candidates with most votes proceed to a second round and Brian, who has the fewest votes, is excluded. All of Brian's supporters have given Andrew as their second preference, so his votes all transfer to Andrew. The tallies then become:

• Andrew: 52
• Catherine: 48

Result: Andrew has the most votes so is declared the winner.

Imagine another election in which there are four candidates: Andrea, Brad, Carter and Delilah. There are 120 voters and they vote as follows (fourth preferences are omitted):

#	34 voters		17 voters		22 voters	10 voters		37 voters
1st	Andrea		Brad		Carter	Carter		Delilah
2nd	Brad		Carter		Brad	Delilah		Carter
3rd	Carter		Andrea		Andrea	Brad		Brad

The count would proceed as follows:

• Round 1: First preferences are tallied and no candidate has a majority (in this election an absolute majority would be 61).
• Round 2: Andrea and Delilah have the most votes so they proceed to a second round while Brad and Carter are excluded. The votes of Brad and Carter supporters are now distributed among the two survivors. To do this the ballot papers of Brad and Carter supporters are examined to see which of the two remaining candidates each voter has ranked higher. The preferences expressed on the ballot papers of Brad and Carter supporters were as follows:

#	17 voters	22 voters	10 voters
1st	Brad	Carter	Carter
2nd	Carter	Brad	Delilah
3rd	Andrea	Andrea	Brad
4th	Delilah	Delilah	Andrea

On the basis of these ballot papers 39 votes are transferred to Andrea and 10 to Delilah.

• Winner: Once Brad and Carter's votes have been transferred Andrea has a majority of votes and so is the winner.

• Supplementary vote: The supplementary vote is a variant of the contingent vote in which voters cannot rank all of the candidates, but rather are only permitted to express a first and a second preference. This means that if a voter does not use either of his preferences to support one of the candidates who survives to the second round then it will be impossible to transfer his vote, which is therefore 'wasted' or 'exhausted'. This possibility means that the supplementary vote often produces a different winner to the conventional form of the contingent vote.
• Sri Lankan contingent vote: The system used to elect the Sri Lankan president is a variant of the contingent vote in which the voter is only permitted to express her top three preferences.

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 then 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 his mind from one round to another, even if his favourite candidate in the first round has not been eliminated.

As noted above, instant-runoff voting (IRV) differs from the contingent vote in that it permits several rounds rather than just two. Under IRV only one candidate is 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 IRV 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 he been allowed to receive transfers in later rounds.

If the election in Example II had been conducted using IRV instead of the contingent vote then the winner would have been Carter rather than Andrea. This is because the election would have proceeded as follows:

• Round 1: First preferences are tallied and no candidate has a majority.
• Round 2: Under IRV only one candidate is now eliminated. This is Brad as he has the fewest votes. His votes all transfer to Carter.
• Round 3: There is still no candidate with an absolute majority. Now Andrea has the fewest votes so she is eliminated. Her votes all transfer to Carter, who then has an absolute majority..
• Winner: After three rounds Carter is elected.

Like virtually all electoral systems, the contingent vote is open to tactical voting. In particular, like both the two round system and instant-runoff voting, it is vulnerable to the tactics of 'push over' and 'compromise'. Under the contingent vote compromising occurs where a voter gives a first or other high preference to a candidate not because they necessarily support them, but as a way of avoiding the election of a candidate who they dislike even more. The contingent vote is more vulnerable to compromising than IRV. In the first example given in this article if a large number of Catherine supporters had 'compromised', and given a first preference to Brian, then Brian would have been elected instead of Andrew, a candidate who Catherine supporters dislike even more. This tactic would have been effective under IRV as well as the contingent vote. In Example II Brad supporters, had they predicted that Carter would not make it to the second round, could have compromised by giving their first preferences to Carter, and thereby have ensured his election. This would not have been a necessary tactic under IRV because the votes of Brad supporters would have ended up with Carter anyway–when Bad was eliminated they would have transferred to him.

However the contingent vote is less vulnerable to the tactic of compromise than the 'first-past-the-post' (plurality) system. This is because the contingent vote's system of transferring votes means that even if a voter's first choice is unlikely to be elected, her vote may still have a chance to be transferred to one of her subsequent preferences. In Example I above Catherine would have won under the plurality system because she has more votes than any other candidate. However Brian voters would have been able to ensure the election of their second choice, Andrew, by voting tactically for Andrew instead of Brian. This tactic is not necessary under the contingent vote because the votes of Brian supporters will transfer to Andrew in the second round anyway.

'Push-over' is a tactic by which a voter insincerely ranks an unpopular 'push-over' candidate higher than her real first choice. The purpose of voting for the 'push-over' is to ensure that it is this weak candidate, rather than a more popular rival, who remains to challenge her preferred candidate in the second round. By supporting a push-over candidate it is hoped to eliminate a stronger candidate who might have gone on to win the election. Under the contingent vote a voter uses the tactic by giving her first preference to a 'push over' and her lower preferences to the candidates she really supports.

The push-over tactic requires voters to be able to reliably predict how others will vote. It runs the risk of backfiring, because if the tactical voter miscalculates then the candidate intended as a push-over might end up actually beating the voter's preferred candidate. It also requires voters to understand the tactic and be aware that it exists. For these reasons some doubt that push-over is likely to be a factor in real elections. Because under the contingent vote, as under IRV, it is paradoxically possible to harm the chances of a candidate by giving them a first preference, or to aid the chances of a candidate by ranking them lower than first, the system is said to fail the monotonicity criterion.

The contingent vote can be influenced by the same forms of strategic nomination as IRV and the two round system. Strategic nomination is where candidates and political factions influence the result of an election by either nominating extra candidates or withdrawing a candidate who would otherwise have stood. The contingent vote is vulnerable to strategic nomination for the same reasons that it is open to the voting tactic of 'compromising'. This is because it is sometimes necessary for a candidate who knows they are unlikely to win to ensure that another candidate he supports makes it to the second round by withdrawing from the race before the first round occurs, or by never choosing to stand in the first place. By withdrawing candidates a political faction can avoid the 'spoiler effect', whereby a candidate 'splits the vote' of her supporters and prevents any candidate acceptable to them from surviving to the last round. For instance, in Example I above, if Catherine had chosen not to stand then Brian would have been elected instead of Andrew, a more desirable result for Catherine's supporters. However the contingent vote's system of transfers makes it less vulnerable to the spoiler effect than the plurality system.

Like IRV and the two round system, the contingent vote is said to encourage candidates to seek support beyond their core base of supporters in order to secure the lower preferences of the supporters of other candidates. This is said to create a more conciliatory campaigning style among candidates with similar policy platforms. However this effect will be diminished by the fact that lower preferences are less important under the contingent vote than under IRV; under the contingent vote it is especially important for candidates to receive many first preferences so that they are not eliminated straight away.

The contingent vote is not a form of proportional representation, and therefore, if used to elect a council or legislature, it overrepresents larger parties at the expense of smaller ones, and encourages a two party system, in the same manner as other systems based on single seat constituencies (districts), such as 'first past the post', instant run-off and the two round system. However the contingent vote does aid the chances of 'third party' candidates to some extent, by encouraging voters who wish to do so to vote sincerely for such candidates where under 'first past the post' they would be discouraged from doing so for tactical reasons.

• Preferential voting
• History and use of instant-runoff voting
• Tactical manipulation of runoff voting
• Tactical manipulation of instant-runoff voting

• Democratic and Electoral Shifts in Queensland (PDF)