Tactical voting

In voting systems, tactical voting (or strategic voting) occurs when a voter misrepresents his or her sincere preferences in order to gain a more favorable outcome. Any minimally useful voting system has some form of tactical voting. However, the type of tactical voting and the extent to which it affects the timbre of the campaign and the results of the election vary dramatically from one voting system to another.

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Tactical voting

Types of tactical voting

There are different types of tactical voting:

Compromising

Compromising (sometimes favorite-burying or useful vote) is a type of tactical voting in which a voter insincerely ranks or rates an alternative higher (more generally, increases their support for that alternative) in the hope of getting it elected. For example, in the first-past-the-post election, a voter may vote for an option they perceive as having a greater chance of winning over an option they prefer (e.g., a left-wing voter voting for a popular moderate candidate over an unpopular leftist candidate). Duverger's law suggests that, for this reason, first-past-the-post election systems will lead to two party systems in most cases.

Compromising-compression is a compromising strategy that involves insincerely giving two candidates an equal ranking (or equal rating). Compromising-reversal is a compromising strategy that involves insincerely reversing the order of two candidates on the ballot.

A simple example with Approval voting using approval thresholds:

30 A| >B>C
20 B| >A>C
31 C| >A=B

C has the most approvals (31), but if A-top voters decide to also approve B (vote A>B| >C), then they can make B win instead with 50 approvals, a result that they prefer.

1 A>B>C
1 B>C>A
1 C>A>B

This is an example of a Condorcet cycle where each candidate pairwise beats another. If any voter here decides to swap their 1st choice and 2nd choice, then they can make their 2nd choice win in any Condorcet method i.e. if the A-top voter instead votes B>A>C, then B becomes a majority's 1st choice.

Burying

Burying is a type of tactical voting in which a voter insincerely ranks (or rates) an alternative lower in the hopes of defeating it. For example, in the Borda count, a voter may insincerely rank a perceived strong alternative last in order to help their preferred alternative beat it. A real-world analogy would be voters of one party crossing over to vote in the other party's primary against the candidate they think might beat the candidate of their party.

Burying-compression is a burying strategy that involves insincerely giving two candidates an equal ranking or rating (or truncating, which generally amounts to the same thing).

Burying-reversal is a burying strategy that involves insincerely reversing the order of two candidates on the ballot.

30 A>B
25 B>A
40 C

A is the Condorcet winner here (pairwise beats B 30 to 25 and C 55 to 40). But if A-top voters vote A>C instead, then they can make A win in several Condorcet methods, such as Schulze, Minimax, etc. This is because they start a Condorcet cycle where A has the weakest pairwise defeat of the three (A loses 30 to 40 to C, while B loses 25 to 70 to C and C loses 40 to 55 to A). This is an example of the chicken dilemma.

Also see later-no-help for some examples of burying.

Pushover

Push-over is a type of tactical voting that is only useful in methods that violate monotonicity. It may involve a voter ranking or rating an alternative lower in the hope of getting it elected, or ranking or rating an alternative higher in the hope of defeating it. Also known as a paradoxical strategy. Note that it is usually very difficult to successfully pull off, and often backfires (i.e. elects the pushed over candidate).

Pushover is mainly discussed in the context of IRV or voting methods that operate with runoffs or otherwise have multiple rounds of voting where fewer and fewer candidates advance to the next round, because who advances can depend on who they're facing in a given round i.e. if the majority prefer a Democrat to a Republican, many Dems prefer a Green>Democrat, but the majority prefer Republican>Green, then it can benefit Republicans to vote Green in the first round of runoff voting and then vote Republican in the runoff, even though they may have actually preferred the Democrat to the Green.

Free Riding

Free riding is a form of tactical voting which affects any Multi-Member System that has a mechanisms to increase the level of Proportional representation. The strategy is to lower your endorsement for candidates which you expect to be elected without your support. This allows more of your vote power to go into electing other candidates, because the voting method takes less of your voting power.

2-winner example:

30 A1>A2
14 B1
5 C1

In any PR method that spends a Droop quota or more of ballots when a candidate is elected, A1 is likely to win first, and then at least 16.333 A voters' ballots will be spent, leaving them with 13.666 ballots to support A2. This allows B1 to win the second seat in most methods. However, if the A1 voters had split into two groups of 15 voters each, with one bullet voting (only voting for) A1 and the other only for A2, then they guarantee that both A1 and A2 win in most methods, because the two candidates have more votes each (15) than the other candidates (B1 with 14 and C1 with only 5), and when the votes in favor of one are spent, only the 15 voters who chose that candidate lose their ballot weight.

Strategy-free voting methods

It has been shown by the Gibbard-Satterthwaite theorem that it is impossible for a voting method to be both strategy-free and deterministic (that is, select the same outcome every time it is applied to the same set of ballots). The Random Ballot voting method, which selects the ballot of a random voter and uses this to determine the outcome, is strategy-free, but may result in different choices being selected if applied multiple times to the same set of ballots.

However, the extent to which tactical voting affects the timbre and results of the campaign varies dramatically from system to system: see below.

Examples in real elections

In United Kingdom elections, there are three main parties represented in the Parliament: the Labour party, the Conservative party and the Liberal Democrats. Of these three, Labour and the Liberal Democrats are most similar. Many people who prefer the Liberal Democrats vote for the Labour candidate where Labour is stronger and vice-versa where the Liberal Democrats are stronger, in order to prevent the Conservative candidate from winning.

In 2010, Liberal and Conservative governments shared the vote of the UK voters creating a hung government, it was decided that Conservatives and Liberal Democrats will perform as a power-sharing government. However this was not the first time the country has been run in a similar fashion as Liberal and Conservative governments alternated in power until World War I and Labour formed two short-lived minority governments in 1923-24 and 1929-31.

In the 1997 UK General Election, the Democratic Left organised GROT - Get Rid Of Them - a tactical voter campaign. In 2001, the Democratic Left's successor organisation the New Politics Network organised a similar campaign tacticalvoter.net. Since then tactical voting has become a real consideration in British politics as is reflected in by-elections and by the growth in sites such as www.tacticalvoting.com who encourage tactical voting as a way of defusing the two party system and empowering the individual voter.

Rational voter model

Academic analysis of tactical voting is based on the rational voter model, derived from rational choice theory. In this model, voters are short-term instrumentally rational. That is, voters are only voting in order to make an impact on one election at a time (not, say, to build the political party for next election); voters have a set of sincere preferences, or utility rankings, by which to rate candidates; voters have some knowledge of each other's preferences; and voters understand how best to use tactical voting to their advantage. The extent to which this model resembles real-life elections is the subject of considerable academic debate.

Pre-election influence

Because tactical voting relies heavily on voters' perception of how other voters intend to vote, campaigns in electoral systems that promote compromise frequently focus on affecting voters' perception of campaign viability. Most campaigns craft refined media strategies to shape the way voters see their candidacy. During this phase, there can be an analogous effect where campaign donors and activists may decide whether or not to support candidates tactically with their money and labor.

In rolling elections, or runoff votes, where some voters have information about previous voters' preferences (e.g. presidential primaries in the United States, French presidential elections), candidates put disproportionate resources into competing strongly in the first few stages, because those stages affect the reaction of latter stages.

Views on tactical voting

Some people view tactical voting as providing misleading information. In this view, a ballot paper is asking the question "which of these candidates is the best?". This means that if one votes for a candidate who one does not believe is the best, then one is lying. Labour Party politician Anne Begg considers tactical voting dangerous: [1]

"Tactical voting is fine in theory and as an intellectual discussion in the drawing room or living rooms around the country, but when you actually get to polling day and you have to vote against your principles, then it is much harder to do".

While most agree that tactical voting is generally a problem, there are some cases when a strictly limited amount of it may bring about an more democratic result. Since Arrow's impossibility theorem proves that any voting system is arguably undemocratic in at least some case, tactical voting may be used to correct such flaws. For instance, under purely honest voting, Condorcet method-like systems tend to settle on compromise candidates, while Instant-Runoff Voting favors those candidates which have strong core support - who may often be more extremist. An electorate using one of these two systems but which (in the general or the specific case) preferred the characteristics of the other system could consciously use strategy to achieve a result more characteristic of the other system. Under Condorcet, they may be able to win by "burying" the compromise candidate (although this risks throwing the election to the opposing extreme); while under IRV, they could always "compromise".

The problem is that such tactical voting would tend to overshoot and give undesired results. This greatly complicates the comparative analysis of voting systems. If tactical voting were to become significant, the perceived "advantages" of a given voting system could turn into disadvantages - and, more surprisingly, vice versa.

Tactical voting in particular systems

Steven Brams and Dudley R. Herschbach argued in a paper in Science magazine in 2000 that approval voting was the system least amenable to tactical perturbations. This may be related to the fact that approval voting does not permit preferences ('likes' or 'dislikes') to be stated at all, permitting only a statement of tolerances, that is, "which candidate could you stand to see win", as opposed to "which candidate would you like to see win".

Due to the especially deep impact of tactical voting in first past the post electoral systems, some argue that systems with three or more strong or persistent parties become in effect forms of disapproval voting, where the expression of disapproval, to keep an opponent out of office overwhelms the expression of approval, to approve a desirable candidate. Ralph Nader refers to this as the "least worst" choice, and argues that the similarity of parties and the candidates grows stronger due to the need to avoid this disapproval.

Some common terms:

Frontrunner/viable candidate: A candidate expected to have a significant chance of winning.

There are arguments about the best voting strategy to take in different systems, but the general consensus is:

Approval voting and Score voting: Give the highest score to your favorite frontrunner and all candidates you prefer equally or more than that frontrunner, and the lowest score to all other candidates (known as the threshold strategy or min-max-ing i.e. giving some candidates the minimum score and others the maximum score).

Definitions

Truncation: When a voter doesn't show support for some of their less-preferred candidates (i.e. an A>B>C voter truncates and only votes A>B or A).

Bullet voting: When a voter gives maximal support to one candidate, and no support to any other candidates. It is often a special case of truncation.

Min-maxing: When a voter gives maximal support to some candidates (usually defined here as ranking or rating them all equally) and no support to all other candidates.

Notes

It's important to differentiate between coordinated strategy, and uncoordinated strategy, as well as informed strategy vs. uninformed strategy. For example, Approval voting and Score voting guarantee that at least half of the voters can force their preferred candidates to tie or win, and force their dispreferred candidates to tie or lose. However, this crucially hinges on these half of the voters of voters knowing a) that they all prefer those candidates, and b) that they all plan to use the strategy. Otherwise, those who attempt the strategy may either fail to support all of the candidates supported by the group of voters, resulting in the strategy not always working, or they may do it while not everyone else in the group does, which potentially weakens their own vote's ability to influence who wins among the candidates not maximally preferred by that half of the voters. So strategy comes in difficulty levels of execution.

An important thing to consider with strategic voting is how difficult it is for voters to figure out how to strategically vote. Distinctions are made between zero-info strategy (strategy that can be applied to get a better result without any information of other voters' preferences) and strategies that revolve around having various amounts of (accurate) polling information. In addition, the likelihood of a strategy working, and the risk/amount of harm (see utility) coming from it backfiring is also studied. Another common measure of a voting method's resistance to strategic voting is manipulability, which measures how often a voter or group of voters can vote strategically to improve the election results from their point of view.

External links

tacticalvoter.net -- UK Tactical Voting
VotePair.org VotePair is a banding together of the people who started tactical voting online in the 2000 elections..
VoteRoll VoteRoll is a vote blog roll system developing statistics for people voting online.
tacticalvoting.org Info on tactical voting for the 2010 UK General Election

Sources

Making Votes Count, Gary Cox (1997)
The Proof of the Gibbard-Satterthwaite Theorem Revisited, Lars-Gunnar Svensson (1999)
Brams, Herschbach, "The Mathematics of Elections" (sic?), Science (2000)
Extending the Rational Voter Theory of Tactical Voting, Stephen Fisher (2001)
Strategy definitions by James Green-Armytage

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