Later-no-harm criterion

Voting system
Name Comply?
Plurality Yes[note 1]
Two-round system Yes
Partisan primary Yes
Instant-runoff voting Yes
Minimax Opposition Yes
DSC Yes
Anti-plurality No[citation needed]
Approval N/A
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 a higher-ranked candidate to lose. It is a common property in the plurality-rule family of voting systems.

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); all three systems have similar mechanics, in that they are based only on counting the number of first-place votes for uneliminated candidates. In these 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]

Later-no-harm is often confused with resistance to a kind of strategic voting called strategic truncation or bullet voting.[4] However, satisfying later-no-harm does not provide resistance to such strategies. Systems like instant runoff that pass later-no-harm but fail monotonicity still incentivize truncation or bullet voting in some situations.[5][6][7][8]

Though later-no-harm may be confused with center squeeze due to instant-runoff voting passing both later-no-harm and being susceptible to center squeeze, these properties are distinct, as Minimax opposition also passes later-no-harm.


Cite error: There are <ref group=note> tags on this page, but the references will not show without a {{reflist|group=note}} template (see the help page).

  1. ^ Cite error: The named reference :0 was invoked but never defined (see the help page).
  2. ^ Lewyn, Michael (2012). "Two Cheers for Instant Runoff Voting". 6 Phoenix L. Rev. 117. Rochester, NY. SSRN 2276015. 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. ^ The Non-majority Rule Desk (July 29, 2011). "Why Approval Voting is Unworkable in Contested Elections - FairVote". FairVote Blog. Retrieved 11 October 2016.
  5. ^ "Later-No-Harm Criterion". The Center for Election Science. Retrieved 2024-02-02.
  6. ^ 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.
  7. ^ Brams, Steven. "The AMS nomination procedure is vulnerable to ‘truncation of preferences’." Notices of the American Mathematical Society 29 (1982): 136-138.
  8. ^ Fishburn, Peter C.; Brams, Steven J. (1984-01-01). "Manipulability of voting by sincere truncation of preferences". Public Choice. 44 (3): 397–410. doi:10.1007/BF00119689. ISSN 1573-7101.