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Voting system
Name Comply?
Two-round system Yes
Single transferable vote Yes
Instant Runoff Voting Yes
Contingent vote Yes
Minimax Condorcet Yes
Anti-plurality No
Approval voting No
Borda count No
Dodgson's method No
Copeland's method No
Kemeny–Young method No
Ranked Pairs No
Schulze method No
Range voting No

The later-no-harm criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less-preferred candidate can not cause a more-preferred candidate to lose.

Contents

Complying methodsEdit

Two-round system, Single transferable vote, Instant Runoff Voting, Contingent vote, Minimax Condorcet (a pairwise opposition variant which does not satisfy the Condorcet Criterion), and Descending Solid Coalitions, a variant of Woodall's Descending Acquiescing Coalitions rule, satisfy the later-no-harm criterion.

When a voter is allowed to choose only one preferred candidate, as in plurality voting, later-no-harm can be either considered satisfied (as the voter's later preferences can not harm their chosen candidate) or not applicable.

Noncomplying methodsEdit

Approval voting, Borda count, Range voting, Majority Judgment, Bucklin voting, Ranked Pairs, Schulze method, Kemeny-Young method, Copeland's method, and Nanson's method do not satisfy later-no-harm. The Condorcet criterion is incompatible with later-no-harm (assuming the discrimination axiom, according to which any tie can be removed by some single voter changing her rating).[1]

Plurality-at-large voting, which allows the voter to select up to a certain number of candidates, doesn't satisfy later-no-harm when used to fill two or more seats in a single district.

Checking ComplianceEdit

Checking for satisfaction of the Later-no-harm criterion requires ascertaining the probability of a voter's preferred candidate being elected before and after adding a later preference to the ballot, to determine any decrease in probability. Later-no-harm presumes that later preferences are added to the ballot sequentially, so that candidates already listed are preferred to a candidate added later.

ExamplesEdit

Anti-pluralityEdit

Anti-plurality elects the candidate the least number of 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.

Approval votingEdit

Since Approval voting does not allow voters to differentiate their views about candidates for whom they choose to vote and the later-no-harm criterion explicitly requires the voter's ability to express later preferences on the ballot, the criterion using this definition is not applicable for Approval voting.

However, if the later-no-harm criterion is expanded to consider the preferences within the mind of the voter to determine whether a preference is "later" instead of actually expressing it as a later preference as demanded in the definition, Approval would not satisfy the criterion. Under Approval voting, this may in some cases encourage the tactical voting strategy called bullet voting.

Borda countEdit

Coombs' methodEdit

Coombs' method repeatedly eliminates the candidate listed last on most ballots, until a winner is reached. If at any time a candidate wins an absolute majority of first place votes among candidates not eliminated, that candidate is elected.

Later-No-Harm can be considered not applicable to Coombs 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 Coombs if the method is assumed to apportion the last place vote among unlisted candidates equally, as shown in the example below.

CopelandEdit

Dodgson's methodEdit

Dodgson's' method elects a Condorcet winner if there is one, and otherwise elects the candidate who can become the Condorcet winner after the least number of ordinal preference swaps on voters' ballots.

Later-No-Harm can be considered not applicable to Dodgson 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 Dodgson if the method is assumed to apportion possible rankings among unlisted candidates equally, as shown in the example below.

Kemeny–Young methodEdit

Majority judgmentEdit

MinimaxEdit

Ranked pairsEdit

Range votingEdit

Schulze methodEdit

CriticismEdit

Woodall, author of the Later-no-harm 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,[2] 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".[3]

Warren Smith writes that the Later-no-harm criterion is "a silly criterion" saying that "objectively, LNH is not even a desirable property with honest voters". He argues that rating a candidate higher should allow the possibility of that candidate winning if the candidates collective ratings are high enough. [4] The Center for Election Science, founded by Smith, also voices their opinion that the name itself is "misleading" and raises the concern that while "a voter can’t harm a candidate by ranking additional less preferred candidates, .. voters can still hurt themselves by doing so. This begs the question of whether the later-no-harm criterion actually has value."[5]

There is some evidence that failing this criterion may have some pro-social effects.[6]

See alsoEdit

ReferencesEdit

  1. ^ Douglas Woodall (1997): Monotonicity of Single-Seat Election Rules, Theorem 2 (b)
  2. ^ The Non-majority Rule Desk (July 29, 2011). "Why Approval Voting is Unworkable in Contested Elections - FairVote". FairVote Blog. Retrieved 11 October 2016.
  3. ^ Woodall, Douglas, Properties of Preferential Election Rules, Voting matters - Issue 3, December 1994
  4. ^ Warren D. Smith, "Later no harm" – an actually-silly (& massively overhyped by "FairVote") voting system criterion
  5. ^ Later-No-Harm Criterion
  6. ^ "Tyranny of Weak Preferences," The Least of All Evils Our Democracy is hampered by a voting system that poorly reflects the will of its electorate, one that often forces us to choose between the lesser of two evils. But there are alternative systems, approval voting and score voting, which can do the job better.
  • D R Woodall, "Properties of Preferential Election Rules", Voting matters, Issue 3, December 1994 [1]
  • Tony Anderson Solgard and Paul Landskroener, Bench and Bar of Minnesota, Vol 59, No 9, October 2002. [2]
  • Brown v. Smallwood, 1915