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Later-no-harm criterion: Difference between revisions
Linking to Douglas Woodall's papers from 1994 and 1997, one of which was published in Voting Matters
(Linking to Douglas Woodall's papers from 1994 and 1997, one of which was published in Voting Matters) |
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{{Wikipedia}}
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.}}
<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>
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<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>
'''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.
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