Exhaustive ballot
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The exhaustive ballot is a voting system used to elect a single winner. Under the exhaustive ballot the voter simply casts a single vote for his favourite candidate. However if no candidate receives an absolute majority of votes then the candidate with the fewest votes is eliminated and a further round of voting occurs. This process is repeated for as many rounds as necessary until one candidate has a majority.
The exhaustive ballot is similar to the two round system, but differs from it in that the two round system involves only two rounds of voting, whereas in the exhaustive ballot there are often several. Because voters may have to cast votes several times, the exhaustive ballot is not used in large-scale public elections. Instead it is usually used in elections involving, at most, a few hundred voters, such as the election of the presiding officer of an assembly. The exhaustive ballot is currently used, in different forms, to elect the President of the European Parliament, the speakers of the Canadian and British Houses of Commons, and the host city of the Olympic Games.
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[edit] Voting and counting
In each round of an exhaustive ballot the voter simply marks an 'x' beside his favourite candidate. If no candidate has an absolute majority of votes (i.e. more than half) in the first round, then the candidate with the fewest votes is eliminated while all other candidates advance to a second round. If there is still no candidate with a majority then the candidate with fewest votes is again eliminated there is a third round. The process repeats itself for as many rounds as are necessary for one candidate achieve a majority. If necessary the election will continue until only two candidates remain. When this occurs one of the two must achieve an absolute majority. From one round to another, the voter is entirely free to change the candidate he votes for, even if his preferred candidate has not yet been eliminated but he has merely changed his mind.
Under some variants of the exhaustive ballot there is no formal rule for eliminating candidates from one round to another; rather, candidates are expected to withdraw voluntarily. There are also variants which exclude more than one candidate at a time. For example in elections for the speakers of the Canadian and British Houses of Commons any candidate with fewer than 5% of all votes in the first round is immediately eliminated.
[edit] Examples
[edit] Example I
Imagine an election to choose which food to eat for dessert. There are 25 people having dessert and four candidates: Ice Cream, Apple Pie, Fruit and Celery. An exhaustive ballot is held to find the winner.
Round 1: In the first round of voting each diner votes for the one candidate they most prefer. The results are as follows:
- Ice Cream: 10 votes
- Apple Pie: 6 votes
- Fruit: 8 votes
- Celery: 1 vote
Round 2: No candidate has an absolute majority of votes (in this election that would be 13), so Celery, which has the fewest votes, is eliminated. The three remaining candidates proceed to the second round. The Celery supporter is health conscious, so now gives his vote to Fruit rather than either of the other two candidates. None of the other diners choose to change their votes. So in the second round the votes cast are:
- Ice Cream: 10
- Apple Pie: 6
- Fruit: 9
Round 3: There is still no candidate with a majority so Apple Pie, who is now the candidate with least votes, is eliminated. Apple Pie supporters now split into two groups. 2 prefer Icecream but 4 vote for Fruit. So the final result is:
- Ice Cream: 12
- Fruit: 13
Result: Fruit now has an absolute majority so is declared the winner.
[edit] Example II
Imagine that the population of Tennessee, a state in the United States, is voting on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate live in one of these four cities, and that they would like the capital to be established as close to their city as possible.
The candidates for the capital are:
- Memphis, the state's largest city, with 42% of the voters, but located far from the other cities
- Nashville, with 26% of the voters
- Knoxville, with 17% of the voters
- Chattanooga, with 15% of the voters
Round 1: In the first round of voting the results will be as follows:
- Memphis: 42%
- Nashville: 26%
- Knoxville: 17%
- Chattanooga: 15%
Round 2: No candidate has an absolute majority in the first round (this would be greater than 50%), so Chattanooga, who has the fewest votes, is eliminated and the remaining three candidates proceed to Round 2. In this round the Chattanooga supporters vote instead for Knoxville, the next nearest city to their own. None of the other voters need change their votes. The results are therefore:
- Memphis: 42%
- Nashville: 26%
- Knoxville: 32%
Round 3: Nashville is now eliminated, so that only two candidates remain for the final round. The Nashville supporters change their vote to Knoxville, the next nearest city to their own. The result of the third round is therefore:
- Memphis: 42%
- Knoxville: 58%
Result: After round three Knoxville has an absolute majority so is the winner.
[edit] Use in practice
- Host city of the Olympic Games: The host city of Olympic Games is chosen by an exhaustive ballot of members of the International Olympic Committee. Members from a country which has a city competing in the election are forbidden from voting unless the city has been eliminated.
- President of the European Parliament: The President of the European Parliament is elected by all members of the body to be its 'speaker' or chairperson. In the election if no candidate receives an absolute majority in the first round then there are up to three more rounds. In the second and third rounds anyone who wants to is free to stand, but candidates who perform poorly sometimes withdraw to help others be elected. If no-one achieves an absolute majority in the third round then only the two candidates with most votes are allowed to proceed to the fourth and final round of voting.
- Speaker of the British House of Commons: The Speaker of the British House of Commons is elected by secret ballot by members of the house. If no candidate achieves an absolute majority in the first round then the candidate with fewest votes and any other candidate who has received less than 5% of all votes is immediately eliminated. Subsequent rounds proceed according to the ordinary rules of the exhaustive ballot.
- Speaker of the Canadian House of Commons: The Speaker of the Canadian House of Commons is elected under essentially the same variant of the exhaustive ballot used for her British counterpart, with candidates on less than 5% in the first round immediately excluded.
[edit] Other 'runoff' systems
[edit] The two round system
As noted above the exhaustive ballot is similar to the two round system. However under the two round system if no candidate achieves an absolute majority in the first round then, rather than just a single candidate being eliminated, all candidates are immediately excluded except the two with the most votes. There is then a second and final round. Because, at most, it only requires voters to return to the polls once, the two-round system is considered more practical for large public elections than the exhaustive ballot, and is used in many countries for the election of presidents and legislative bodies. However the two systems often produce different winners. This is because, under the two-round system, a candidate may be eliminated in the first round who would have gone on to win the contest if they had been permitted to survive to the second round. In Example I above the winner would not have changed if the two rounds system had been used instead of the exhaustive ballot. However in Example II the two round system would have elected Nashville instead of Knoxville.
[edit] Instant-runoff voting
In some respects the exhaustive ballot closely ressembles instant-runoff voting (also known as the 'Alternative Vote'). Under both systems if no candidate has an absolute majority in the first round then there are further rounds, with the candidate with the fewest votes being eliminated after each round. However while under the exhaustive ballot each round involves voters returning to cast a new vote, under instant-runoff (IRV) voters vote only once. This is possible because, rather than voting only for a single candidate, the voter ranks all of the candidates in order of preference. These preferences are then used to 'transfer' the votes of those whose first preference has been eliminated during the course of the count.
Because the exhaustive ballot involves separate rounds of voting, voters can use the results of one round to inform how they will vote in the next, whereas this is not possible under IRV. Furthermore, because it is only necessary to vote once, IRV has been used for large-scale elections in many places.
[edit] Tactical voting
Like instant-runoff voting, the exhaustive ballot is intended to improve upon the simpler 'first past the post' (plurality) system by reducing the potential for tactical voting by avoiding 'wasted' votes. Under the plurality system, which involves only one round, voters are encouraged to vote tactically by voting only for one of the two leading candidates, because a vote for any other candidate will not effect the result. Under the exhaustive ballot this tactic, known as 'compromising', is sometimes unnecessary because, even if the voter's first choice is unlikely to be elected, she will still have the opportunity to influence the outcome of the election by voting for more popular candidates once her favourite has been eliminated. However the exhaustive ballot is still vulnerable to tactical voting under some circumstance. Because of the similarity between the two systems it is open to the same forms of tactical voting as IRV.
Although the exhaustive ballot is designed to avoid 'compromising' the tactic is still effective in some elections. Compromising is where a voter votes for a certain candidate, not because they necessarily support them, but as a way of avoiding the election of a candidate who they dislike even more. The compromising tactic is sometimes effective because the exhaustive ballot eliminates candidates who are unpopular in early rounds, who might have had sufficient support to win the election had they survived a little longer. This can create strong incentives for voters to vote tactically.
Like IRV, the exhaustive ballot is also vulnerable to the tactic of 'push over'. 'Push over' is a tactic by which voters vote tactically for an unpopular 'push over' candidate in one round as a way of helping their true favourite candidate win in a later round. The purpose of voting for the 'push over' is to ensure that it is this weak candidate, rather than a stronger rival, who remains to challenge a voter's preferred candidate in later rounds. By supporting a 'push over' candidate it is hoped to eliminate a stronger candidate who might have gone on to win the election. 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.
[edit] Examples
[edit] Compromise
In Example I above, if Ice Cream supporters had voted tactically for Apple Pie in the first round then Apple Pie (their second choice) would have been elected instead of Fruit (their last choice). In Example II Knoxville wins, the last choice of both Nashville and Memphis supporters. If Memphis supporters had 'compromised' by voting for Nashville (their second choice) in the first round then Nashville would have been elected immediately, while if Nashville supporters had all 'compromised' by voting for their second choice of Chattanooga in the first round, then Chattanooga would have gone on to be elected in the second round
[edit] Push over
Imagine an election, like the one at the start of this article, in which there are 100 voters who vote as follows:
- Icecream: 25 votes
- Apple Pie: 30 votes
- Fruit: 45 votes
No candidate has an absolute majority of votes so Icecream is eliminated in the first round. Icecream supporters prefer Apple Pie to Fruit so in the second round they vote for Apple Pie and Apple Pie is the winner. However, if only six Fruit supporters had used the tactic of 'push over' then they could have changed this outcome and ensured the election of Fruit. These six voters can do this by voting for Icecream in the first round as a 'push over'. If they do this then the votes cast in the first round will look like this:
- Icecream: 31
- Apple Pie: 30
- Fruit: 39
This time Apple Pie is eliminated in the first round and Icecream and Fruit survive to the second round. This outcome is deliberate. The tactical voters know that Icecream will be an easier candidate for Fruit to beat in the second round than Apple Pie–in other words, that Icecream will be a 'push-over'. In the second round the tactical voters vote for their real first preference, Fruit. Therefore even if only 6 Apple Pie supporters prefer Fruit to Icecream, the result of the second round will be:
- Icecream: 49
- Fruit: 51
Fruit will therefore be elected. The success of this tactic relies on the Fruit supporters being able to predict that Icecream can be beaten by Fruit in the second round. If a large majority of Apple Pie supporters had voted for Icecream then the 'push over' tactic would have backfired, leading to the election of Icecream, which Fruit partisans like even less than Apple Pie.
[edit] Strategic nomination
The exhaustive ballot can also be influenced by strategic nomination; this 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 exhaustive ballot is vulnerable to strategic nomination for the same reasons that it is open to the voting tactic of 'compromising'. This is because a candidate who knows they are unlikely to win can bring about the election of a more desirable compromise candidate by withdrawing from the race, or by never standing in the first place. By the same token a candidate can bring about a less desirable result by unwisely choosing to stand in an election; this is because of the spoiler effect, by which a new candidate can 'split the vote' and cost another similar candidate the election.
The exhaustive vote's system of multiple rounds makes it less vulnerable to the spoiler effect than the plurality system or the two round system. This is because a potential spoiler candidate often has only minor support; therefore he will be eliminated early and his supporters will have the opportunity to influence the result of the election by voting for more popular candidates in later rounds. Voters can also counteract the effect of vote splitting by using the 'compromise' tactic.
The exhaustive vote is essentially vulnerable to the same forms of strategic nomination as instant-runoff voting, the difference being that under the exhaustive vote candidates can use the results of early rounds to inform whether or not they should strategically withdraw in later rounds. This is impossible under IRV. In IRV the electorate votes only once, so candidates must make the judgement of whether or not to participate in an election before the poll, and before even one round of counting has occurred.
[edit] Effect on candidates and factions
The exhaustive ballot encourages candidates to appeal to a broad cross-section of voters. This is because, in order to eventually receive an absolute majority of votes, it is necessary for a candidate to win the support of voters whose favourite candidate has been eliminated. Under the exhaustive ballot eliminated candidates, and the factions who previously supported them, often issue recommendations to their supporters as to who they should vote for the remaining rounds of the contest. This means that eliminated candidates are still able to influence the result of the election.
