Tactical manipulation of runoff voting

Like virtually all electoral systems, in runoff voting there is potential for both tactical voting and strategic nomination. [The Gibbard-Satterthwaite theorem shows that any voting method which does not allow tactical voting must be either dictatorial or non-deterministic (incorporating random elements). A non-deterministic system may not select the same outcome every time it is applied to the same set of ballots, so non-deterministic systems are rarely suggested for public elections.] Tactical voting is where voters do not vote in accordance with their true preferences, but instead vote insincerely in an attempt to influence the result. 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. In particular voters are strongly encouraged to 'compromise' by voting for one of the three leading candidates in the first round of an election.

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. Runoff is intended to reduce the 'spoiler effect', but is not immune to it. A famous example of the importance of both strategic nomination and tactical voting in runoff voting was the 2002 French presidential election.

ample election

For illustrative purposes, the following is a sample election that does not involve any tactical manipulation. Imagine an election to choose which food to eat for dessert. There are 100 people having dessert and three candidates: Ice Cream, Apple Pie and Fruit. Runoff voting is used 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: 43 votes
*Apple Pie: 16 votes
*Fruit: 41 votes

Round 2: No candidate has an absolute majority of votes (in this election that would be 51) so the two candidates with the most votes, Ice Cream and Fruit, proceed to a second round, while Apple Pie is eliminated. Because their favourite candidate has been eliminated Apple Pie supporters must now vote for one of the two remaining candidates. The Apple Pie supporters split into two even groups: 8 vote for Ice Cream and 8 for Fruit. Of those who supported Ice Cream and Fruit in the first round no-one decides to change their vote. The results of the second round the are therefore:

*Icecream: 51
*Fruit: 49

Result: Ice Cream now has an absolute majority so is declared the winner.

Tactical voting

Runoff voting attempts to reduce the potential for tactical voting by eliminating 'wasted' votes. Under the 'first past the post' (plurality) system voters are indirectly 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 runoff voting this tactic, known as 'compromising', is sometimes unnecessary because, even if a voter's favourite candidate is eliminated in the first round, she will still have an opportunity to influence the result of the election by voting for a more popular candidate in the second round. However the tactic of compromising can still be used in runoff voting because it is sometimes necessary to compromise as a way of influencing which two candidates will survive to the second round.

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 runoff voting eliminates many candidates in the first round, and these often include a candidate who might have received an absolute majority of votes had he been permitted to participate in the second round. This creates strong incentives for voters to vote tactically in the first round as a way of ensuring that at least one of the two candidates who survives to the second round is acceptable to them. In order to do this it is necessary to vote for one of the "three" leading candidates in the first round, just as in an election held under the plurality system it is necessary to vote for one of the "two" leading candidates. Whether or not compromising will be an effective tactic depends on the precise candidates and voting patterns present in each election. For example, if there are two very popular centrist candidates standing in the election, so that the outcome of the first round is inevitable, then compromise will be unnecessary.

Examples

In Example I above, if Fruit supporters had voted tactically for Apple Pie in the first round then Apple Pie (their second choice) would have been elected instead of Icecream (their last choice). By voting tactically they ensure that Apple Pie has the opportunity to advance to the second round, Apple Pie is then able to achieve an absolute majority. However in the following election compromising is unnecessary; in the first round 100 voters vote as follows:

*Far-Left candidate: 10
*Centre-Left candidate: 41
*Centre-Right candidate: 40
*Far-Right candidate: 9

Provided we assume that the second preference of Far-Left voters is the Centre-Left candidate, and the second preference of Far-Right voters is the Centre-Right candidate, then the result of the second round will be:

*Centre-Left candidate: 51
*Centre-Right candidate: 49

In this election 'compromise' will be an unnecessary and ineffective tactic. This is because once the Far-left Candidate is eliminated his supporters have the opportunity to vote for the Centre-Left candidate in the second round, so it is unnecessary for Far-Left supporters to vote tactically for the Centre-Left candidate as a way of ensuring she survives to the second round. For the same reason the outcome will not be altered if Far-Right supporters vote tactically in the first round for Centre-Right.

Were the election conducted using the plurality system compromising would be an effective strategy. For example if Far-Right supporters voted tactically for Centre-Right then he would be elected instead of Centre-Left. To counteract this tactic Far-Left supporters would also have to vote tactically. In this example, therefore, runoff voting removes the potential for tactical voting that would be there under the plurality system.

Push over

'Push over' is a tactic by which voters vote tactically for an unpopular 'push over' candidate in the first round as a way of helping their true favourite candidate win in the second 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 round two. By supporting a 'push over' candidate it is hoped to eliminate a stronger candidate who might have won the second round. 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 in round two.

Example

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 will mean that Apple Pie is eliminated in the first round instead of Icecream. 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.

trategic nomination

Runoff voting can 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. Runoff voting 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.

Runoff votings system of two rounds 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 not take away sufficient support from any candidate likely to win in the second round to prevent them surviving to that point. In runoff voting voters can counteract the effect of vote splitting in the first round by using the compromise tactic. The spoiler effect is impossible in the second round because there are only two candidates.

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 runoff voting.

2002 French presidential election

The 2002 French presidential election is a famous example of the importance of both tactical voting and strategic nomination in runoff voting. The three main candidates were Jacque Chirac of the centre-right, Lionel Jospin of the centre-left, and the far-right Jean-Marie Le Pen. However there were sixteen candidates in total.

In French presidential elections the common outcome is for one candidate of the centre-right and one of the centre-left to proceed to the second round. However in 2002 the two candidates to advance to the second round were Chirac and Le Pen. Chircac then won the election but the inclusion of Le Pen in the second round was highly controversial, because of what many considered his 'extreme' political views. Le Pen was an unpopular candidate, as testified by the fact that he won only 18% of the vote in the second round. Had Jospin proceeded to the second round, as expect, it would have been a closer contest. In the first round the results were as follows:

The right

*Jacques Chirac (Rally for the Republic): 19.88%
*Jean-Marie Le Pen (National Front): 16.86%
*François Bayrou (Union for French Democracy): 6.84%
*Alain Madelin (Liberal Democracy): 3.91%
*Bruno Mégret (National Republican Movement): 2.34%
*Christine Boutin (Forum of Social Republicans): 1.19%
*Total: 51.02%

The left

*Lionel Jospin (Socialist Party): 16.18%
*Arlette Laguiller (Workers' Struggle) 5.72%
*Noël Mamère (The Greens) 5.25%
*Olivier Besancenot (Revolutionary Communist League) 4.25%
*Robert Hue (French Communist Party) 3.37%
*Christiane Taubira (Left Radical Party) 2.32%
*Daniel Gluckstein (Party of the Workers) 0.47%
*Total: 37.56%

The reason that the left had no candidate in the second round was not a shortage of voters. As can be seen above, more than 37% of voters supported left-wing candidates. The problem was that the left-wing vote was split between seven different candidates. The left could have improved its performance using strategic nomination. If even a small left wing party had withdrawn its candidate then Jospin might have had enough votes to avoid elimination. On the other hand, even with seven different candidates, left-wing voters could have altered the first round by voting tactically. If only about 2% more left-wing voters had practiced the tactic of 'compromise', and voted for Jospin rather than their true favourite, then he would have survived elimination. One reason Jospin was eliminated was that many voters assumed that he would survive to the second round, and therefore felt free to cast a protest vote for a minor candidate, rather than vote tactically. Had Jospin survived, whether by reason of tactical voting or strategic nomination, it is possible he could have won the second round and beaten Chirac.

A similar situation occurred in Louisiana. In the 1991 gubnertorial election the white supremacist David Duke secured enough votes to be admitted to the second round, in place of the incumbent governor, who would have been expected to survive. In the second round Duke lost to the more moderate Edwin Edwards. Louisiana uses a form of runoff voting called the run-off primary election.

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