Voting system
Name Comply?
Plurality Yes[note 1]
Two-round system Yes
Partisan primary Yes
Instant-runoff voting Yes
Minimax Opposition Yes
Anti-plurality Yes
Approval No
Borda No
Dodgson No
Copeland No
Kemeny–Young No
Ranked Pairs No
Schulze No
Score No
Majority judgment No

Later-no-harm is a property of some ranked-choice voting systems, first described by Douglas Woodall. In later-no-harm systems, increasing the rating or rank of a candidate ranked below the winner of an election cannot cause this higher-ranked candidate to lose.[1]

For example, say a group of voters ranks Alice 2nd and Bob 6th, and Alice wins the election. In the next election, Bob focuses on expanding his appeal with this group of voters, but does not manage to defeat Alice—Bob's rating increases from 6th-place to 3rd. Later-no-harm says that this increased support from Alice's voters should not allow Bob to win.[1]

Later-no-harm is a defining characteristic of first-preference plurality (FPP), instant-runoff voting (IRV), and descending solid coalitions (DSC), three similar systems for comparing candidates based on how many eligible voters consider each uneliminated candidate their favorite. In later-no-harm systems, the results either do not depend on lower preferences at all (as in plurality) or only depend on them if all higher preferences have been eliminated (as in IRV and DSC).[2][3] This tends to favor candidates with strong (but narrow) support over candidates closer to the center of public opinion, which can lead to a phenomenon known as center-squeeze.[4][5][6] Cardinal and Condorcet methods, by contrast, tend to select candidates whose ideology is a closer match to that of the median voter.[4][5][6] This has led many social choice theorists to question whether the property is desirable in the first place or should instead be seen as a negative property.[6][7][8]

Later-no-harm is sometimes confused with resistance to a kind of strategic voting called truncation or bullet voting.[9] However, satisfying later-no-harm does not (by itself) provide resistance to such strategies, unless paired with the participation criterion; systems like instant runoff that pass later-no-harm but fail participation still incentivize truncation or bullet voting in some situations.[7][10]

Later-no-harm methods

The plurality vote, two-round system, instant-runoff voting, and descending solid coalitions satisfy the later-no-harm criterion. First-preference plurality satisfies later-no-harm trivially, by ignoring every preference after the first.[1]

Non-LNH methods

Nearly all voting methods other than first-past-the-post do not pass LNH, including score voting, highest medians, Borda count, and all Condorcet methods. The Condorcet criterion is incompatible with later-no-harm (assuming the resolvability criterion, i.e. any tie can be removed by a single voter changing their rating).[1]

Bloc voting, which allows a voter to select multiple candidates, does not satisfy later-no-harm when used to fill two or more seats in a single district, although the single non-transferable vote does.



Main article: Anti-plurality voting

Anti-plurality elects the candidate the fewest voters rank last when submitting a complete ranking of the candidates.

Later-No-Harm can be considered not applicable to Anti-Plurality if the method is assumed to not accept truncated preference listings from the voter. On the other hand, Later-No-Harm can be applied to Anti-Plurality if the method is assumed to apportion the last place vote among unlisted candidates equally, as shown in the example below.

Borda count

Main article: Borda count


Main article: Copeland's method

Schulze method

Main article: Schulze method


Douglas Woodall writes:

[U]nder STV the later preferences on a ballot are not even considered until the fates of all candidates of earlier preference have been decided. Thus a voter can be certain that adding extra preferences to his or her preference listing can neither help nor harm any candidate already listed. Supporters of STV usually regard this as a very important property, although it has to be said that not everyone agrees; the property has been described (by Michael Dummett, in a letter to Robert Newland) as "quite unreasonable", and (by an anonymous referee) as "unpalatable".[11]

See also


  1. ^ Plurality voting can be thought of as a ranked voting system that disregards preferences after the first; because all preferences other than the first are unimportant, plurality passes later-no-harm as traditionally defined.


  1. ^ a b c d Douglas Woodall (1997): Monotonicity of Single-Seat Election Rules, Theorem 2 (b)
  2. ^ Lewyn, Michael (2012). "Two Cheers for Instant Runoff Voting". 6 Phoenix L. Rev. 117. Rochester, NY. third place Candidate C is a centrist who is in fact the second choice of Candidate A's left-wing supporters and Candidate B's right-wing supporters. ... In such a situation, Candidate C would prevail over both Candidates A ... and B ... in a one-on-one runoff election. Yet, Candidate C would not prevail under IRV because he or she finished third and thus would be the first candidate eliminated
  3. ^ Stensholt, Eivind (2015-10-07). "What Happened in Burlington?". Discussion Papers: 13. There is a Condorcet ranking according to distance from the center, but Condorcet winner M, the most central candidate, was squeezed between the two others, got the smallest primary support, and was eliminated.
  4. ^ a b Hillinger, Claude (2005). "The Case for Utilitarian Voting". SSRN Electronic Journal. doi:10.2139/ssrn.732285. ISSN 1556-5068. S2CID 12873115. Retrieved 2022-05-27.
  5. ^ a b Merrill, Samuel (1984). "A Comparison of Efficiency of Multicandidate Electoral Systems". American Journal of Political Science. 28 (1): 23. doi:10.2307/2110786. ISSN 0092-5853. However, squeezed by surrounding opponents, a centrist candidate may receive few first-place votes and be eliminated under Hare.
  6. ^ a b c Merrill, Samuel (1985). "A statistical model for Condorcet efficiency based on simulation under spatial model assumptions". Public Choice. 47 (2): 389–403. doi:10.1007/bf00127534. ISSN 0048-5829. the 'squeeze effect' that tends to reduce Condorcet efficiency if the relative dispersion (RD) of candidates is low. This effect is particularly strong for the plurality, runoff, and Hare systems, for which the garnering of first-place votes in a large field is essential to winning
  7. ^ a b "Later-No-Harm Criterion". The Center for Election Science. Retrieved 2024-02-02.
  8. ^ Woodall, Douglas, Properties of Preferential Election Rules, Voting matters - Issue 3, December 1994
  9. ^ The Non-majority Rule Desk (July 29, 2011). "Why Approval Voting is Unworkable in Contested Elections - FairVote". FairVote Blog. Retrieved 11 October 2016.
  10. ^ Graham-Squire, Adam; McCune, David (2023-06-12). "An Examination of Ranked-Choice Voting in the United States, 2004–2022". Representation: 1–19. arXiv:2301.12075. doi:10.1080/00344893.2023.2221689. ISSN 0034-4893.
  11. ^ Woodall, Douglas, Properties of Preferential Election Rules, Voting matters - Issue 3, December 1994