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The "'''later-no-harm criterion'''" criterion (sometimes referred to as "'''LNHarm'''"<ref>{{Cite web |title=[EM] Favorite Betrayal and Condorcet, and LNHarm |url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2022-April/003796.html |access-date=2022-04-22 |website=lists.electorama.com}}</ref>) posits that a voter giving an additional ranking or positive rating to a less-preferred candidate should not cause a higher ranked (or rated) candidate on that volter's ballot to lose.  It was published in "[[Voting Matters]]" in 1994.<ref>Woodall, Douglas, Properties of Preferential Election Rules, [http://www.votingmatters.org.uk/ISSUE3/P5.HTM Voting matters - Issue 3, December 1994]</ref>  It was called "Theorem 2" in [[Douglas Woodall]]'s 1997 paper on the subject.<ref>Douglas Woodall (1997): [http://scorevoting.net/Woodall97.pdf Monotonicity of Single-Seat Election Rules], Theorem 2 (b)</ref>

== Definition ==
Here's a definition of the later-no-harm criterion (if [[electowiki]] editors are to be believed):
{{definition|A voter giving an additional ranking or positive rating to a less-preferred candidate cannot cause a more-preferred candidate to lose.}}

== Complying Methods ==

<p>'''Later-no-harm''' (usually LNH, but sometimes LNHa or LNHarm to avoid confusion with [[Later-no-help]]) is satisfied by [[IRV|Instant Runoff Voting]], [[Minmax|Minmax(pairwise opposition)]], and Douglas Woodall's [[Descending Solid Coalitions]] method. It is trivially satisfied by  [[Plurality voting|First-Preference Plurality]] and [[Random Ballot]], since those methods do not usually regard lower preferences. Virtually every other method fails this criterion.</p>

<p>'''Later-no-harm''' is incompatible with the [[Condorcet Criterion|Condorcet criterion]].</p>

== Example ==
<p>46 A>B</p>

<p>10 B</p>

<p>44 C>B</p>

<p>B is the [[Condorcet winner]], and would win in any [[Condorcet method]], and if using a [[rated method]], would win if given a high enough rating by all voters. But if the A-top voters [[Bullet voting|bullet vote]], then they can make A the winner in several voting methods, such as most [[:Category:Condorcet-IRV hybrid methods|Condorcet-IRV hybrid methods]] and likely in the rated methods. However, notice that to pass LNH in this situation, the majority of voters who [[Pairwise beat|prefer]] B over A have to have their preferences ignored; in a method like [[IRV]], that means that the C-top voters may have to choose between supporting C or using [[Favorite Betrayal]] to help B win. Essentially, passing LNH ensures voters never have to worry about their later preferences hurting them, but it can at times force them to lie about their higher preferences.</p>

== Commentary ==

'''Later-no-harm''' guarantees that the method will not use a voter's lower preferences to elect a candidate who that voter likes less than the candidate that would have been elected if this voter had kept his lower preferences a secret.

=== Benefits ===
As a result, voters may feel free to vote their complete ranking of the candidates, which in turn may give the election method more complete information to use to find a winner. There is a tradeoff however, in that this criterion simultaneously minimizes the amount of information that the voting method can use to find a winner. 

==== Bullet voting ====
A common criticism of LNH-failing voting reforms is that they will incentivize [[bullet voting]] to such a large degree that they will end up becoming just like [[FPTP]]. However, note that bullet voting is not always the strategically best move; if it was, FPTP would be [[strategyproof]]. In particular, any voter who would do [[Favorite Betrayal]] in FPTP likely has an incentive to support multiple candidates in LNH-failing methods.  

===== Chicken dilemma =====
One consequence of too many voters bullet voting is that there will be a [[chicken dilemma]].   

=== Criterion failure rate ===
It is believed that some methods fail LNH at higher rates than others, and this is used as an argument for or against them. For example, [[Condorcet methods]] are expected to fail less often than something like [[Score voting]].    

== Criticism ==

=== Preventing compromise ===
This criterion is equivalent to the criterion that the system is non-compromising in that it will never elect a compromise (i.e. a [[Utilitarian winner]] or [[Condorcet winner]].) This is not universally desired so it cannot be claimed that this criteria is always one which would be desirable to pass. If one wants a system which can elect a compromise winner then it would be desirable to fail this criteria.

=== Not reflecting voter preferences ===
One argument against LNH is that it can result in arbitrary changes in election outcomes based on voter preferences.<ref>{{Cite web|url=https://medium.com/@ClayShentrup/later-no-harm-72c44e145510|title=Later-no-harm|last=Shentrup|first=Clay|date=2020-01-02|website=Medium|language=en|access-date=2020-04-30}}</ref> A counterargument would be that the example given involves two major candidates, L and R, and because the voters' [[pairwise preference]]<nowiki/>s between the two didn't change (rather, their preference between L/R and C changed), no change should occur in who was the better of the two. This argument is an example of how those against LNH are often in favor of [[rated method]]<nowiki/>s, where the strength of each of the voter's pairwise preferences are connected (i.e. the fact that some voters increased their support for a major candidate in relation to an irrelevant candidate is argued to mean that their strength of preference between the two major candidates ought to be weakened), rather than [[ranked method]]<nowiki/>s, which are often based on the idea that a voter's pairwise preferences are independent and maximal (i.e. [[:Category:Pairwise counting-based voting methods]]).

== Notes ==

=== Misleading name ===
Though LNH is often touted as preventing voters from being hurt by indicating later preferences, in truth it only prevents voters from hurting a candidate they ranked higher when they do this.<ref>{{Cite web|url=https://www.electionscience.org/library/later-no-harm-criterion/|title=Later-No-Harm Criterion|last=|first=|date=|website=The Center for Election Science|language=en-US|url-status=live|archive-url=|archive-date=|access-date=2020-05-14|quote=So those two voters get a better result by limiting the number of candidates they rank. That is, sincerely ranking candidates after W hurt them. It’s almost as though we need to have two different criteria: voter later-no-harm, and candidate later-no-harm. The “later-no-harm” criterion is actually the latter. IRV ensures that a voter can’t harm a candidate by ranking additional less preferred candidates further down the list. But voters can still hurt themselves by doing so.}}</ref> It is not known which voting methods, if any, pass the generalized form of LNH.

== References ==
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[[Category:Voting system criteria]]