Strategic voting
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Strategic or tactical voting is a situation where a voter casts a ballot in a way other than to obtain a more desirable outcome.
Gibbard's theorem shows that all voting systems for choosing between more than three candidates can sometimes encourage dishonest voting. With two candidates, only majority rule is an exception, although score voting guarantees weak sincerity (an honestly-ordered ballot) for up to three candidates.
For multi-winner elections strategic voting applies as well as shown by
Common types of strategic voting
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Four common types of strategic voting are compromising, burying, pushover, and bullet voting or truncation.[3]
- Lesser evil voting (includes compromising, sometimes called decapitation)
- A voter supports the "lesser of two evils" by raising a candidate they dislike, in hopes of getting them elected. For example, under first-past-the-post or instant-runoff voting, voters may choose to support an option they believe has a better chance of winning. Duverger's law says that systems vulnerable to this strategy will typically devolve into two party-rule.
- Most affects: instant-runoff and plurality.
- Immune: Most favorite betrayal criterion), Anti-plurality voting.
- Burial
- A voter ranks an alternative lower in the hope of defeating it. For example, a voter may insincerely rank a perceived strong alternative last in order to help their preferred alternative win.
- Most affects: Borda count and some Condorcet methods.
- Immune: Instant-runoff voting and plurality voting.
- Turkey-raising (includes raiding, sometimes called pushover or pied-piper)
- A voter gives a high rank to a weak (bad) candidate they dislike, but not with the intent of getting them elected. Instead the voter intends the weak candidate to eliminate a strong candidate that would otherwise keep the voter's preferred candidate from winning.Party raidingis a well-known example of such a strategy.
- Most affects: Instant-runoff, two-round, partisan primaries, and Borda[citation needed].
- Immune: Methods passing the Condorcet methods, as well as score voting and most other rated votingsystems.
- Compression (includes bullet-voting, exaggeration, and truncation)
- Compression is a strategy where a voter refuses to disclose which of two candidates they honestly prefer (i.e. both candidates are equally-ranked). Compression is unique in that it involves casting a sincere vote, i.e. one that does not lie about which candidate a voter prefers (only "how much" they are preferred).
- In its most common form, the strategy involves exaggerating the differences between candidates: all above-average candidates are given perfect scores, while all below-average candidates are given the lowest possible score.
- Most affects: Rated voting and some Condorcet methods.
- Immune: Random ballot. No deterministic system. (Removing the option of equal-ratings removes the possibility of compression, but replaces it with an opportunity for compromising and/or burial.)
Coordination
Tactical voting may occur in isolation or as part of an organized campaign. In the former situation, electors make their own judgement as to the most effective way to (typically) prevent the election of a specific candidate or party. In the latter, one or more parties or groups encourage their supporters to vote tactically in an effort to influence the outcome.
In an example of individuals voting tactically, Labour voters in the 2022 Tiverton and Honiton by-election in the UK tactically supported the Liberal Democrat candidate in order to ensure the defeat of the Conservatives.[5] This resulted in the Liberal Democrats winning what had previously been a Conservative safe seat thanks to a divided anti-Conservative vote.
Organized tactical voting in which a political party mounts a campaign calling on its supporters not to vote for their own favoured candidates, but for those of a party which it perceives as more likely to defeat a common opponent, is less common. An example is the
An intermediate case also exists, where a non-party campaign attempts to coordinate tactical voting, typically with the goal of defeating a certain party. Cases of this include the Canadian Anything But Conservative campaign, which opposed the Conservative Party of Canada in the 2008 and 2015 federal elections, or the Smart Voting campaign organized by Russia's Anti-Corruption Foundation with the goal of opposing and weakening the United Russia party in the 2021 Russian legislative election.
Examples in real elections
Canada
The observed effect of
In the 2004 federal election, and to a lesser extent in the 2006 election, strategic voting was a concern for the federal New Democratic Party (NDP). In the 2004 election, the governing Liberal Party was able to convince many New Democratic voters to vote Liberal to avoid a Conservative government[citation needed]. In the 2006 elections, the Liberal Party attempted the same strategy, with Prime Minister Paul Martin asking New Democrats and Greens to vote for the Liberal Party to prevent a Conservative win. The New Democratic Party leader Jack Layton responded by asking voters to "lend" their votes to his party, suggesting that the Liberal Party was bound to lose the election regardless of strategic voting. This failed to prevent the Conservatives from winning the election, although they did not win a majority of seats.
During the 2015 federal election, strategic voting was primarily against the Conservative government of Stephen Harper, which had benefited from vote splitting among centrist and left-leaning parties in the 2011 election.[7][8] Following the landslide victory of the Liberals led by Justin Trudeau over Harper's Conservatives, observers noted that the increase in support for the Liberals at the expense of the NDP and Green Party was partially due to strategic voting for Liberal candidates.[9]
France
The two-round system in France shows strategic voting in the first round, due to considerations which candidate will reach the second round.[10]
Germany
The mixed-member proportional representation allows to estimate the share of strategic voters in first-past-the-post voting due to the separate votes for party-lists and local single-winner electoral district candidates. The vote for party-lists is considered sincere if the party vote share is significantly above the 5% electoral threshold in Germany. In Germany the share of strategic voters was found around 30%, which decreased to 9% if only non-allied party candidates were contenders for the electoral district winner.[11] In a contentious election year the share of strategic voters increased to around 45%.
Due to electoral threshold in party-list proportional representation one party asked in several elections their voters to vote for another allied party to help this party cross the electoral threshold.[12]
Hong Kong
In
Hungary
In Hungary, during the 2018 Hungarian parliamentary election, several websites, such as taktikaiszavazas.hu[14] (meaning "strategic voting"), promoted the idea to vote for opposition candidates with the highest probability of winning a given seat. About a quarter of opposition voters adopted this behavior, resulting in a total of 498,000 extra votes gained by opposition parties. A total of 14 extra single seats were taken by several parties and independent candidates.
Lithuania
In
New Zealand
Since New Zealand moved to mixed-member proportional representation voting in 1996, the electoral system of New Zealand has seen strategic voting[20] regularly occur in several elections, including one party explicitly or implicitly encouraging voters to vote for a candidate other than theirs. This happened first in 1996 in the Wellington Central, and then in 1999 in the Coromandel. From 1996 until 2005, it was a regular feature in the Ohariu-Belmont electorate,[21] which was won by Peter Dunne throughout its existence and from 2005 in the Epsom electorate which has been won solely by the ACT party since 2005.[22]
Poland
In the
Slovenia
According to some media, in the 2011 Slovenian parliamentary election, 30% of voters voted tactically. Public polls predicted an easy win for Janez Janša, the candidate of the Slovenian Democratic Party; however, his opponent Zoran Janković, the candidate of Positive Slovenia, won. Prominent Slovenian public opinion researchers claimed that such proportions of strategic voting had not been recorded anywhere else before.[26]
Spain
In the 2016 General Election in Spain, the incentives for voting tactically were much larger than usual, following the rise of the Podemos and Ciudadanos and following the economic crisis and election in 2015.
Taiwan
In the 1995 Legislative Yuan election, strategic voting was implemented by the opposition parties, such as the Democratic Progressive Party[29] and the New Party.[30] As the members were elected in multi-member districts, the parties urged their supporters to vote for a party-nominated candidate according to criteria, such as the last digit of the voter's National Identification Card Number or the voter's birth month. This maximized the opposition's seat gains and resulted in the ruling Kuomintang losing 10 seats, receiving the lowest share of seats in history at the time.
United Kingdom
In the
In the 2006 local elections in London, strategic voting was promoted by sites such as London Strategic Voter in a response to national and international issues.
In Northern Ireland, it is believed that (predominantly Protestant) Unionist voters in Nationalist strongholds have voted for the Social Democratic and Labour Party (SDLP) to prevent Sinn Féin from capturing such seats. This conclusion was reached by comparing results to the demographics of constituencies and polling districts.
In the 2017 general election, it is estimated that 6.5 million people (more than 20% of voters) voted tactically[31] either as a way of preventing a "hard Brexit" or preventing another Conservative government led by the Tactical2017 campaign.[31] Many Green Party candidates withdrew from the race in order to help the Labour Party[32] secure closely fought seats against the Conservatives. This ultimately led to the Conservatives losing seats in the election even though they increased their overall vote share.[33]
In the 2019 Conservative Party leadership election to determine the final two candidates for the party vote, it was suggested that front-runner Boris Johnson's campaign encouraged some of its MPs to back Jeremy Hunt instead of Johnson, so that Hunt—seen as "a lower-energy challenger"—would finish in second place, allowing an easier defeat in the party vote.[34] Strategic voting was expected to play a major role in the 2019 General Election, with a YouGov poll suggesting that 19% of voters would be doing so tactically. 49% of strategic voters said they would do so in the hope of stopping a party whose views they opposed.[35]
According to a 2020 study, older voters in the UK vote strategically more than younger voters, and richer voters vote more strategically than poorer voters.[36]
United States
Strategic voting in the US's
Similarly, in 2012, Claire McCaskill boosted Todd Akin in the 2012 US Senate election in Missouri. In addition to running ads highlighting Akin's conservative stances, McCaskill also directed messages to surrogates to tell Akin to run ads which would increase his primary polling.[37]
Puerto Rico
Rational voter model
Academic analysis of strategic 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 strategic voting to their advantage. The extent to which this model resembles real-life elections is the subject of considerable academic debate.
Myerson–Weber strategy
An example of a rational voter strategy is described by
This rational voter model assumes that the voter's utility of the election result is dependent only on which candidate wins and not on any other aspect of the election, for example showing support for a losing candidate in the vote tallies. The model also assumes the voter chooses how to vote individually and not in collaboration with other voters.
Given a set of k candidates and a voter let:
- vi = the number of points to be voted for candidate i
- ui = the voter's gain in utility if candidate i wins the election
- pij = the (voter's perceived) pivot probability that candidates i and j will be tied for the most total points to win the election.
Then the voter's prospective rating for a candidate i is defined as:
The gain in expected utility for a given vote is given by:
The gain in expected utility can be maximized by choosing a vote with suitable values of vi, depending on the voting method and the voter's prospective ratings for each candidate. For specific voting methods, the gain can be maximized using the following rules:
- Plurality: Vote for the candidate with the highest prospective rating. This is different from choosing the best of the frontrunners, which is a common heuristic approach to voting. In rare cases, the highest prospective rating can belong to a weak candidate (one with a low probability of winning).
- Borda: Rank the candidates in decreasing order of prospective rating.
- Approval: Vote for all candidates that have a positive prospective rating.
- Range: Vote the maximum (minimum) for all candidates with a positive (negative) prospective rating.
Pivot probabilities are rarely estimated in political forecasting, but can be estimated from predicted winning probabilities. An important special case occurs when the voter has no information about how other voters will vote. This is sometimes referred to as the zero information strategy. In this special case, the pij pivot probabilities are all equal and the rules for the specific voting methods become:
- Plurality: Vote for the most preferred (highest utility) candidate. This is the sincere plurality vote.
- Borda: Rank the candidates in decreasing order preference (decreasing order of utility). This is the sincere ranking of the candidates.
- Approval: Calculate the average utility of all candidates. Vote for all candidates that have a higher-than-average utility; do not vote for any candidates that have a lower-than-average utility.
- Range: Calculate the average utility of all candidates. Vote the maximum points for all candidates that have a higher-than-average utility; vote the minimum points for all candidates that have a lower-than-average utility; vote any value for a candidate with a utility equal to the average.
Myerson and Weber also describe voting equilibria that require all voters use the optimal strategy and all voters share a common set of pij pivot probabilities. Because of these additional requirements, such equilibria may in practice be less widely applicable than the strategies.
Pre-election influence
Because strategic voting relies heavily on voters' perception of how other voters intend to vote, campaigns in electoral methods 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 time.
In
Influence of voting method
Strategic voting is highly dependent on the voting method being used. A strategic vote which improves a voter's satisfaction under one method could make no change or lead to a less-satisfying result under another method. Arrow's impossibility theorem[39] and the Gibbard–Satterthwaite theorem prove that any useful single-winner voting method based on preference ranking is prone to some kind of manipulation. Game theory has been used to search for some kind of "minimally manipulable" (incentive compatibility) voting schemes. Game theory can also be used to analyze the pros and cons of different methods. For instance, when electors vote for their own preferences rather than tactically, Condorcet method-like methods tend to settle on compromise candidates, while instant-runoff voting favors those candidates with strong core support but otherwise narrower appeal due to holding more uncompromising positions.[citation needed]
Moreover, although by the Gibbard–Satterthwaite theorem no deterministic single-winner voting method is immune to strategic voting in all cases, some methods' results are more resistant to strategic voting than others'.
In particular methods
Plurality voting
Strategic voting by compromising is exceedingly common in
Due to the especially deep impact of strategic voting in such a method, some argue that systems with three or more strong or persistent parties become in effect forms of disapproval voting, where the expression of disapproval in order to keep an opponent out of office overwhelms the expression of approval to elect a desirable candidate.
Two-round voting
Theoretical results indicate that, under two-round runoff voting with three candidates, strategic equilibria exist in which only two candidates receive votes.[43] It has been shown experimentally that voters are influenced by a candidate's perceived likelihood of winning the election.[44]
Party-list proportional representation
The presence of an electoral threshold (typically at around 5% or 4%) can lead to voters voting tactically for a different party to their preferred political party (which may be more hardline or more moderate) in order to ensure that the party passes the threshold. An alliance of parties can fail to win a majority despite outpolling their rivals if one party in the alliance falls beneath the threshold. An example of this is the 2009 Norwegian election in which the right-wing opposition parties won more votes between them than the parties in the governing coalition, but the narrow failure of the Liberal Party to cross the 4% threshold led to the governing coalition winning a majority.
This effect has sometimes been nicknamed "Comrade 4%" in Sweden, where the electoral threshold is 4%, particularly when referring to supporters of the
In several recent elections in New Zealand the
Even in countries with a low threshold such as the Netherlands, strategic voting can still happen for other reasons. In the campaign for the 2012 Dutch election, the Socialist Party had enjoyed good poll ratings, but many voters who preferred the Socialists voted instead for the more centrist Labour Party out of fear that a strong showing from the Socialists would lead to political deadlock. It was also suggested that a symmetrical effect on the right caused the Party for Freedom to lose support to the more centrist VVD.[47]
In elections which there are many party lists competing with only a few seats, such as
Cardinal single-winner voting
All
Majority judgment
In majority judgment, strategy is typically "semi-honest exaggeration." Voters exaggerate the difference between a certain pair of candidates but do not rank any less-preferred candidate over any more-preferred one. Even this form of exaggeration can only have an effect if the voter's honest rating for the intended winner is below that candidate's median rating or their honest rating for the intended loser is above it.
Typically, this would not be the case unless there were two similar candidates favored by the same set of voters. A strategic vote against a similar rival could result in a favored candidate winning; although if voters for both similar rivals used this strategy, it could cause a candidate favored by neither of these voter groups to win.
Balinski and Laraki argue that since under Majority judgment, many voters have no opportunity to use strategy, in a test using simulated elections based on polling data, this method is the most strategy-resistant of the ones that the authors studied.[49]
Approval voting
Similarly, in approval voting, unlike many other methods, strategy almost never involves ranking a less-preferred candidate over a more-preferred candidate.[citation needed] However, strategy is in fact inevitable when a voter decides their "approval cutoff"; this is a variation of the compromising strategy. Overall, Steven Brams and Dudley R. Herschbach argued in a paper in Science magazine in 2001 that approval voting was the method least amenable to tactical perturbations. Meanwhile, Balinski and Laraki used rated ballots from a poll of the 2007 French presidential election to show that, if unstrategic voters only approved candidates whom they considered "very good" or better, strategic voters would be able to sway the result frequently, but that if unstrategic voters approved all candidates they considered "good" or better, approval was the second most strategy-resistant method of the ones they studied.[40]
Approval voting forces voters to face an initial voting tactical decision as to whether to vote for (or approve) of their second-choice candidate or not. The voter may want to express they prefer their first choice over their second, but doing so does not allow the same voter to express preference of their second choice over any other. This issue manifests in the
Score voting
In score voting, strategic voters who expect all other voters to be strategic will exaggerate their true preferences and use the same quasi-compromising strategy as in approval voting, above. That is, they will give all candidates either the highest possible or the lowest possible rating. This presents an additional problem as compared to the approval method if some voters give honest "weak" votes with middle rankings and other voters give strategic approval votes. A strategic minority could overpower an honest majority. This problem can be minimized through education or ballot design to encourage uninformed voters to give more-extreme rankings. A different path to minimize this problem is to use median scores instead of total scores, as median scores are less amenable to exaggeration, as in majority judgment.
Strategic voters are faced with the initial tactic as to how highly to score their second-choice candidate. The voter may want to retain expression of a high preference of their favorite candidate over their second choice. But that does not allow the same voter to express a high preference of their second choice over any others.
In a simulation study using polling data collected under a majority judgment method, that method's designers found that score voting was more vulnerable to strategy than any other method they studied, including plurality.[40]
Cardinal multi-winner voting
Evaluative Proportional Representation (EPR) and sequential proportional approval voting reduces strategic voting compared to single-winner voting.[citation needed] Strategic voting is observed for cardinal multi-winner voting.[50]
Ranked single-winner voting
Instant runoff voting
Instant runoff voting is vulnerable to push-over and compromising strategies (although it is less vulnerable to compromising than the plurality method). Bullet voting is ineffective under Instant-runoff, since Instant-runoff satisfies the later-no-harm criterion.
Borda
The Borda count has both a strong compromising incentive and a large vulnerability to burying. Here is a hypothetical example of both factors at the same time: if there are two candidates the most likely to win, the voter can maximize the impact on the contest between these candidates by ranking the candidate the voter likes more in first place, ranking the candidate whom they like less in last place. If neither candidate is the sincere first or last choice, the voter is using both the compromising and burying strategies at once. If many different groups voters use this strategy, this gives a paradoxical advantage to the candidate generally thought least likely to win.
Condorcet
While IRV and STV generally do not satisfy the
do.Condorcet methods have a further-reduced incentive for the compromising strategy, but they have some vulnerability to the burying strategy. The extent of this vulnerability depends on the particular Condorcet method. Some Condorcet methods arguably reduce the vulnerability to burying to the point where it is no longer a significant problem. All guaranteed Condorcet methods are vulnerable to the bullet voting strategy, because they violate the later-no-harm criterion.
Ranked multi-winner voting
Single transferable vote
The single transferable vote has a strong incentive towards free riding, a kind of decapitation strategy. If a voter expects their favorite candidate will almost-certainly be elected, insincerely ranking the second candidate first does not hurt the favoured candidate.[51]
Some forms of STV allow strategic voters to gain an advantage by listing a candidate who is very likely to lose in first place, as a form of pushover.
In Malta's STV the two-party system can cause strategic voting away from third parties.
See also
- Electoral fusion
- Keynesian beauty contest
- Lesser of two evils
- Primary election
- Ranked voting
- Ranked-choice voting in the United States
- Skirt and Blouse voting
- Strategic nomination
- Vote allocation
- Vote swapping
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- ^ Stephenson, Laura B., et al., editors. The Many Faces of Strategic Voting: Tactical Behavior in Electoral Systems Around the World. University of Michigan Press, 2018. JSTOR, www.jstor.org/stable/j.ctvh4zhzr.
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- Cox, Gary (1997). Making Votes Count : Strategic Coordination in the World's Electoral Systems. ISBN 978-0-521-58527-9. Archived from the originalon 25 June 2015.
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- Fisher, Stephen (2001). [ Extending the Rational Voter Theory of Tactical Voting]
External links
- Tactical Voting Can Be a Weak Strategy—Article on strategic voting within larger strategic considerations [archived]
- "FAQs". VotePair: Uniting Progressives Through Strategic Voting. 20 October 2004. Archived from the original on 17 September 2008.
- VoteRoll.com VoteRoll is a blog roll voting system that offers tiered strategic voting to develop statistics for people voting online since 2010.