Tactical manipulation of instant-runoff voting
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Like virtually all voting systems, in instant-runoff voting (also known as the Alternative Vote) there is potential for both tactical voting and strategic nomination. Tactical voting is where voters do not vote in accordance with their true preferences, but instead vote insincerely in the hope that this will give their candidate a better chance of winning. Instant-runoff voting is intended as a method that reduces tactical voting, but two tactics called 'compromising' and 'push-over' are still possible in many circumstances. The tactic of 'burying', which can be used in some other preferential systems, does not work in IRV.
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. IRV is intended to reduce the 'spoiler effect', but is not immune to it.
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[edit] Sample election
For illustrative purposes, the following is a sample election that does not involve any tactical manipulation. Imagine an election in which there are three candidates: Andrew, Brian and Catherine. There are 100 voters and they vote as follows:
| # | 43 voters | 16 voters | 41 voters |
|---|---|---|---|
| 1st | Andrew | Brian | Catherine |
| 2nd | Brian | Andrew | Brian |
| 3rd | Catherine | Catherine | Andrew |
1. First the first preferences are counted, so the tallies stand at:
- Andrew: 43
- Brian: 16
- Catherine: 41
2. No candidate has an absolute majority of votes so Brian, who has the fewest votes, is eliminated. All of Brian's supporters have given Andrew as their second preference, so his votes all transfer to Andrew. The tallies then become:
- Andrew: 59
- Catherine: 41
3. Andrew now has an absolute majority so is declared the winner.
[edit] Tactical voting
Instant-runoff voting is intended to reduce the potential for tactical voting by eliminating 'wasted' votes. Under the 'first past the post' (plurality) system 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 affect the result. Under IRV this tactic, known as 'compromising', is sometimes unnecessary because, even if the voter's first choice is unlikely to be elected, her vote has the opportunity of being transferred to her second or subsequent choices, who may be more successful. However the tactic of compromising can still be used in IRV elections, as can another tactic called 'push over'.
[edit] Compromise
Compromising is where a voter gives a first or other 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 compromising tactic is sometimes effective because IRV eliminates candidates with few higher preferences, preventing them from ever receiving any lower preferences expressed for them. This can create strong incentives for voters to allow the order of their preferences to be dictated by tactics.
In the sample election above, 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. Whether or not compromising will be an effective tactic depends on the precise candidates and voting patterns present in each election. In the following election compromising will not be effective; there are 100 voters who vote as follows (only preferences that effect the result are shown):
| # | 10 voters | 41 voters | 40 voters | 9 voters |
|---|---|---|---|---|
| 1st | Andrea | Brad | Carter | Delilah |
| 2nd | Brad | Carter |
It is not necessary for Andrea supporters to compromise, by giving their first preference to Brad, because once Andrea is eliminated their votes will be transferred to Brad anyway. The number of votes ultimately received by Carter is also unaffected by whether or not Delilah supporters compromise. Were this election conducted using the plurality system compromising would be an effective strategy. For example if Delilah supporters voted tactically for Carter then he would be elected instead of Brad. In this example, therefore, IRV removes the potential for tactical voting that would be there under the plurality system.
[edit] Push-over
'Push-over' is a tactic by which voters insincerely rank an unpopular 'push-over' candidate higher than their 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, that remains to challenge their preferred candidate in later rounds of the count. 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. It also requires voters to understand the tactic and be aware that it exists. For all of these reasons some doubt that push-over is likely to be a factor in real elections; indeed there is no record of it being a factor in the thousands of IRV elections that have taken place for public office.
The push over tactic is possible because, unusually, IRV is a system that lacks monotonicity. This means that, paradoxically, it is sometimes possible to aid a candidate by ranking them lower and to harm a candidate by ranking them higher. Like compromise, the push-over tactic arises from IRV's method of sequential eliminations. It works by manipulating the order in which candidates are excluded from the count.
[edit] Example
Imagine an election in which there are 100 voters who vote as follows:
| # | 25 voters | 30 voters | 45 voters |
|---|---|---|---|
| 1st | Andrea | Brad | Carter |
| 2nd | Brad | Carter | Brad |
Under IRV Brad will win, because Andrea will be eliminated in the first round and transfer her votes to Brad. However if six Carter supporters had voted for Andrea as a push-over candidate they would have ensured the election of Carter. If this tactic was used the votes cast would have looked like this (the second preferences of Andrea supporters are not illustrated because they will not effect the result):
| # | 31 voters | 30 voters | 39 voters |
|---|---|---|---|
| 1st | Andrea | Brad | Carter |
| 2nd | Carter | Brad |
This time Brad is eliminated first and Andrea and Carters proceed to the next round. This outcome is deliberate. The tactical voters know that Andrea will be an easier candidate for Carter to beat in the last round than Brad–in other words, that she will be a 'push-over'. Because Andrea is an unpopular candidate she receives no transfers from Brad. Instead his transfers go to Carter and Carter is elected. The success of this tactic relied on Carter supporters being able to predict that Andrea would be unpopular among Brad supporters. If a large majority of Brad supporters had given their second preferences to Andrea then the push over tactic would have backfired, leading to the election of Andrea, who Carter supporters like even less than Brad.
[edit] Invulerability to burying
Instant-runoff voting is immune to 'burying'. Burying is a tactic used in preferential systems in which a voter, without changing the ranking of a more preferred candidate, helps that candidate win by altering the rankings of lower ranked candidates, so that a less preferred candidate is insincerely ranked even lower than he should be. It differs from 'push over' because 'push over' involves lowering the ranking of the actual candidate one seeks to help win. Burying can be an effective tactic under both the Borda count and Condorcet's method.
[edit] Example
Imagine an election in which 100 voters vote as follows:
| # | 48 voters | 27 voters | 25 voters |
|---|---|---|---|
| 1st | Andrea | Brad | Carter |
| 2nd | Brad | Andrea | Brad |
| 3rd | Carter | Carter | Andrea |
The winner of this election will be Brad whether instant-runoff, Condorcet or the Borda count is used. However, under the Borda count, and some variants of Condorcet, Andrea supporters can change the outcome of this election by 'burying'. They can do this by insincerely ranking Brad, their true second choice, lower than Carter, their true last choice. If Andrea supporters had 'buried' Brad beneath Carter in this way the votes cast in the election would have been as follows:
| # | 48 voters | 27 voters | 25 voters |
|---|---|---|---|
| 1st | Andrea | Brad | Carter |
| 2nd | Carter | Andrea | Brad |
| 3rd | Brad | Carter | Andrea |
This tactic will not work if instant-runoff is used. This is because, whether or not burying occurs, Andrea is not eliminated from the count until the very end, and therefore his votes are never transferred to any other candidate. This means that under IRV the second and third preferences of Andrea supporters are never counted and are irrelevant to the result. However if the Borda count is used then the tactic will result in the election of Andrea instead of Brad. The results of the Borda count before and after Andrea supporters use the burying tactic are as follows:
| Candidate | Points without burying | Points with burying |
|---|---|---|
| Andrea | 123 | 123 |
| Brad | 127 | 79 |
| Carter | 50 | 98 |
Under Condorcet's method the winner is the candidate who, when paired against each other candidate one at a time, is preferred to every other individual candidate by a majority of voters. Before the tactic of burying occurs the results of these pairings are as follows:
| Pair | Winner |
|---|---|
| Brad (52) vs. Andrea (48) | Brad |
| Brad (75) vs. Carter (25) | Brad |
| Andrea (75) vs. Carter (25) | Andrea |
Brad is the winner because he beats both other candidates by a majority of votes. However the ploy of the Andrea supporters may be effective under Condorcet because it will change the results to the following
| Pair | Winner |
|---|---|
| Brad (52) vs. Andrea (48) | Brad |
| Brad (23) vs. Carter (73) | Carter |
| Andrea (75) vs. Carter (25) | Andrea |
It can be seen above that the election no longer produces any clear winner, because there is no one candidate who beats both other candidates. Instead each candidate loses one pairing and wins one pairing. In a Condorcet election this outcome is known as a 'majority rule cycle'. Each variant of Condorcet's method resolves such a cycle in a different manner, so under some Condorcet methods the tactic of Andrea supporters may be successful and lead to the election of Andrea, while under others it will fail, either not altering the outcome or backfiring by resulting in the election of Carter. However even if it will not work in this particular election, under all Condorcet methods burying is a theoretical possibility, and will be effective in at least some elections.
It should be noted that the above example of burying resulted from Andrea supporters ranking Brad lower, which caused Brad not to be elected. Some would say that this is the intended result and should indicate that the voting system is working as intended.
[edit] Strategic nomination
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. For the same reasons that IRV is vulnerable to the voting tactic of 'compromising' it is also open to strategic nomination. 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 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.
IRV's system of transferring votes makes it less vulnerable to the spoiler effect than the plurality system. This is because a potential spoiler candidate often has only minor support; therefore he will be eliminated early and his votes will transfer to the candidate who would have received them anyway had he not stood. Alternatively a spoiler candidate may be sufficiently similar to an existing candidate (such as a candidate of the same party) that vote transfers between the two will ensure that at least one of them is ultimately elected. Voters can also counteract the effect of vote splitting by using the compromise tactic.
Because it is vulnerable to certain forms of strategic nomination IRV is said by electoral scientists to fail the 'independence of irrelevant alternatives' criterion. This criterion is so strict that it is failed by almost all voting systems, even those that are less susceptible to strategic nomination than IRV.
[edit] Examples
In the sample election at the beginning of this article Catherine could have changed the result by strategically withdrawing from the race. If Catherine had not stood in the election then Brian would have won. All of her supporters would have voted for Brian instead, immediately giving him a majority of votes. There would have been an incentive for Catherine to do this because Brian's victory would be a more desirable outcome for her supporters than the election of Andrew.
[edit] Resistance to spoilers
As an illustration of how IRV avoids the spoiler effect imagine if, in the sample election, an additional candidate had stood called Arthur. Arthur is similar to Andrew, perhaps because he is his twin or is a member of the same political party. For this reason, while some of those who originally voted for Andrew now prefer Arthur, the entire group of former Andrew supporters prefer both of these candidates to every other candidate. By the same token Brian supporters, who prefer Andrew to Catherine, also prefer Arthur to Catherine. The new breakdown of votes might be as follows:
| # | 29 voters | 14 voters | 16 voters | 41 voters |
|---|---|---|---|---|
| 1st | Arthur | Andrew | Brian | Catherine |
| 2nd | Andrew | Arthur | Andrew | |
| 3rd | Brian | Brian | Arthur |
The election would proceed as follows:
1. First of all Andrew would be eliminated. His votes would all transfer to Arthur so that the tallies became:
-
- Arthur: 43
- Brian: 16
- Catherine: 41
2. Brian would then be eliminated and his votes would transfer to Arthur. Arther would then be the winner.
Had this election been conducted under the plurality system the participation of Arthur would clearly have created a spoiler effect. Without Arthur, Andrew had a plurality of first preferences (i.e. more than anyone else) and so would win under 'first past the post'. When Arthur enters the race it is Catherine who has a plurality. Arthur's entrance would thus cost both himself and Andrew, his similar colleague, the election. Under IRV the use of vote transfers prevents Arthur from being a spoiler. The result is that he is elected, and the group of voters who favour both him and Andrew are not cost the election. Because introducing a candidate who is very similar to an existing candidate does not lead to a spoiler effect in IRV, IRV satisfies what scholars call the 'independence of clones' criterion. The plurality system is not 'clone independent'.
[edit] Vulnerability to spoilers
As an illustration of vote splitting in IRV, imagine that instead of Arthur joining the sample election a different candidate called Alice had. Unlike Arthur, Alice is similar to Andrew in some ways but also has important differences. It might be that she shares some views with Andrew but not others. For this reason, while some former Andrew supporters strongly favour Alice, and choose to switch to her, those who stick with Andrew in fact dislike Alice, and prefer Brian. With the addition of Alice the votes might breakdown as follows:
| # | 29 voters | 14 voters | 16 voters | 41 voters |
|---|---|---|---|---|
| 1st | Alice | Andrew | Brian | Catherine |
| 2nd | Andrew | Brian | ||
| 3rd | Brian |
In the first round Andrew will be eliminated instead of Brian, and once he receives the transfers from Andrew supporters Brian will be unstoppable. The inclusion of Alice in the race has therefore resulted in an outcome that her supporters do not want: the election of Brian instead of Andrew. Alice supporters could have avoided the spoiler effect by using the compromise tactic. If they had ignored Alice in sufficient numbers and given their first preferences to Andrew instead they would have ensured that Andrew was still elected.
[edit] Note
- ↑ –It has been proven by the Gibbard-Satterthwaite theorem that any voting method where ranking of candidates occurs, and which is completely free from tactical voting must be either dictatorial or non-deterministic (i.e. chaotic or random). A non-deterministic system will not select the same outcome every time it is applied to the same set of ballots, and so non-deterministic systems are very rarely suggested for public elections.
