Later-no-harm criterion

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.

Voting system
NameComply?
Two-round systemYes
Single transferable voteYes
Instant-runoff votingYes
Contingent voteYes
Minimax CondorcetYes
Anti-pluralityNo
Approval votingNo
Borda countNo
Dodgson's methodNo
Copeland's methodNo
Kemeny–Young methodNo
Ranked PairsNo
Schulze methodNo
Range votingNo

Complying methods

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 methods

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 Compliance

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.

Examples

Anti-plurality

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 voting

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 count

Coombs' method

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.

Copeland

Dodgson's method

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 method

Majority judgment

Minimax

Ranked pairs

Range voting

Schulze method

Criticism

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]

See also

References

  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
  • D R Woodall, "Properties of Preferential Election Rules", Voting matters, Issue 3, December 1994
  • Tony Anderson Solgard and Paul Landskroener, Bench and Bar of Minnesota, Vol 59, No 9, October 2002.
  • Brown v. Smallwood, 1915
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