Editing Strategic voting (section)

== By method ==

=== Plurality voting ===
{{See also|Plurality voting#Tactical voting}}
Lesser-evil voting is exceedingly common in [[Plurality voting method|plurality]] elections, where the first preference is all that counts (and thus lesser-evil voting is the only effective kind of strategic voting). The most typical tactic is to assess which two candidates are frontrunners (most likely to win) and to vote for the preferred one of those two, even if a third candidate is preferred over both. [[Duverger's law]] is the observation that this kind of strategic voting and [[strategic nomination]] is sufficiently common for any method based on first preferences to produce two-party domination.

=== Plurality-runoff family (RCV, two-round, and partisan primaries) ===
{{See also|Instant-runoff voting#Resistance to tactical voting}}
Theoretical results indicate that, under two-round runoff voting with three candidates, strategic equilibria exist in which only two candidates receive votes.<ref>{{Cite journal |last=Bouton |first=Laurent |date=2013 |title=A Theory of Strategic Voting in Runoff Elections |url=https://www.jstor.org/stable/23469618 |journal=The American Economic Review |volume=103 |issue=4 |pages=1248–1288 |doi=10.1257/aer.103.4.1248 |issn=0002-8282 |jstor=23469618}}</ref> It has been shown experimentally that voters are influenced by a candidate's perceived likelihood of winning the election.<ref>{{Cite journal |last1=Blais |first1=André |last2=Labbé-St-Vincent |first2=Simon |last3=Laslier |first3=Jean-François |last4=Sauger |first4=Nicolas |last5=Van der Straeten |first5=Karine |date=2011 |title=Strategic Vote Choice in One-round and Two-round Elections: An Experimental Study |url=https://www.jstor.org/stable/23056381 |journal=Political Research Quarterly |volume=64 |issue=3 |pages=637–645 |doi=10.1177/1065912909358583 |issn=1065-9129 |jstor=23056381 |s2cid=14130949}}</ref>

[[Instant-runoff voting|Instant runoff voting]] is vulnerable to three of the four kinds of strategy discussed above. It is vulnerable to lesser-evil voting; to turkey-raising; and to strategic truncation.

There is a common misconception that instant-runoff is not affected by a kind of strategic voting called [[Truncation (voting)|truncation]] or [[bullet voting]].<ref>{{cite web |last1=The Non-majority Rule Desk |date=July 29, 2011 |title=Why Approval Voting is Unworkable in Contested Elections - FairVote |url=http://www.fairvote.org/why-approval-voting-is-unworkable-in-contested-elections |accessdate=11 October 2016 |website=FairVote Blog}}</ref> However, satisfying later-no-harm does not (by itself) provide resistance to such strategies, unless paired with the [[participation criterion]]. Systems like [[Instant runoff voting|instant runoff]] that pass later-no-harm but fail [[Participation criterion|participation]] still incentivize truncation or bullet voting in some situations.<ref name=":12" /><ref>{{Cite journal |last1=Graham-Squire |first1=Adam |last2=McCune |first2=David |date=2023-06-12 |title=An Examination of Ranked-Choice Voting in the United States, 2004–2022 |url=https://www.tandfonline.com/doi/full/10.1080/00344893.2023.2221689 |journal=Representation |language=en |pages=1–19 |arxiv=2301.12075 |doi=10.1080/00344893.2023.2221689 |issn=0034-4893}}</ref>

=== Cardinal single-winner voting ===
{{See also|Score voting#Strategy|Approval voting#Strategy}}
Most cardinal, single-winner voting systems in large elections encourage similar strategies:

# Calculate the expected (average) utility of the election result (the average [[utility]] if the election was repeated many times).
# Top-rate all candidates with above-average utility, and bottom-rate all candidates with below-average utility.

Such a strategy involves "semi-honest exaggeration". Unlike in most voting systems, voters rarely (if ever) have an incentive to lie about which of two candidates they prefer, which makes such far milder than under other voting systems. Voters exaggerate the difference between a certain pair of candidates but do not rank any less-preferred candidate over any more-preferred one. This form of exaggeration has an effect whenever the voter's honest rating for the intended winner is below that candidate's median rating; or when their honest rating for the intended loser is above it. In other words, half of voters will have an incentive to strategize, while half will not.

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.

[[Michel Balinski|Balinski]] and Laraki noted that under majority judgment, many voters have no opportunity or incentive to use strategy. They argued based on a simulation that the highest median methods minimized the number of voters with an incentive to misrepresent their opinions, among the methods they studied.<ref name=mjrank>{{cite book | last1=Balinski | first1=M. L. | last2=Laraki | first2=Rida | title=Majority judgment: measuring, ranking, and electing  | publisher=MIT Press | publication-place=Cambridge, Mass. | date=2010 | isbn=978-0-262-01513-4}}{{page?|date=February 2025}}</ref>

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 [[approval voting]], because the only option is to approve of a candidate or not, optimal strategic voting rarely includes ranking a less-preferred candidate over a more-preferred candidate. However, strategy is in fact inevitable when a voter decides their "approval cutoff". [[Steven Brams]] and [[Dudley R. Herschbach]] argued in a paper in ''[[Science (journal)|Science]]'' magazine in 2001 that [[approval voting]] was the method least amenable to tactical perturbations.<ref name="Heschbach2">{{cite journal |last1=Hershbach |first1=Dudley |last2=Brams |first2=Steven |date=2001-05-25 |title=The Science of Elections |url=https://www.science.org/doi/full/10.1126/science.292.5521.1449 |journal=Science |volume=292 |issue=5521 |page=1449 |doi=10.1126/science.292.5521.1449 |pmid=11379606 |access-date=2024-05-10}}</ref>

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, after majority judgment itself.<ref name="mjrank" />

=== Ranked single-winner voting ===
{{See also|Borda count#Potential for tactical manipulation}}
The [[Borda count]] has both a strong incentive and a large vulnerability to burial. 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.{{Cn|date=May 2024}}

=== Condorcet ===
{{See also|Condorcet method#Potential for tactical voting}}
[[Condorcet method|Condorcet methods]] are vulnerable to 3 of the 4 kinds of strategy listed above, because the [[Condorcet winner criterion]] is incompatible with the [[sincere favorite criterion]], [[participation criterion]], [[later-no-harm]], and [[later-no-help]]. Strategy in Condorcet methods can become highly complex, but almost always involves burial or truncation.

=== Multi-winner voting ===
==== Single transferable vote ====
{{See also|Single transferable vote#Tactics}}
The [[single transferable vote]] may incentivize free-riding: if a voter expects their favorite candidate will almost-certainly be elected, insincerely ranking the second candidate first does not hurt the favored candidate.<ref>{{cite web |last=Schulze |first=Markus |title=Free Riding and Vote Management under Proportional Representation by the Single Transferable Vote |url=http://m-schulze.9mail.de/schulze2.pdf |access-date=2016-03-14}}</ref>

Some forms of STV allow strategic voters to gain an advantage by listing a candidate who is very likely to lose in first place.<ref>{{cite web |last=Woodall |first=Douglas R. |date=March 1994 |title=Computer counting in STV elections |url=http://www.votingmatters.org.uk/ISSUE1/P3.HTM |access-date=6 March 2011 |publisher=McDougall Trust}}</ref> This strategy, called ''Woodall free riding'', is essentially eliminated by [[Counting single transferable votes#Meek|Meek's method]]; however, Meek's method is rarely used because of its substantial complexity, having been adopted only for some local elections in New Zealand.<ref>{{cite journal |author=Markus Schulze |date=June 2004 |title=Free Riding |url=http://www.votingmatters.org.uk/ISSUE18/I18P2.PDF |journal=Voting Matters |issue=18 |pages=2–8}}</ref>

In Malta's STV, the two-party system can cause strategic voting away from third parties.{{Cn|date=May 2024}}