Later-no-harm criterion

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Voting system
Name Comply?
Plurality Yes[note 1]
Two-round system Yes
Nonpartisan primary Yes
Instant-runoff voting Yes
Minimax Condorcet Yes[note 2]
Descending solid coalitions 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
Score voting No
Usual judgment No

The later-no-harm criterion is a voting system criterion first formulated by Douglas Woodall. Woodall defined the criterion by saying that "[a]dding a later preference to a ballot should not harm any candidate already listed."[1] For example, a ranked voting method in which a voter adding a 3rd preference could reduce the likelihood of their 1st preference being selected, fails later-no-harm.

Voting systems that fail the later-no-harm criterion can sometimes be vulnerable to the tactical voting strategies called bullet voting and burying, which can deny victory to a sincere Condorcet winner. However, both strategies can also be successful in criteria that pass later-no-harm (including instant runoff voting),[2] and cardinal voting systems seem to be more resistant to these strategies in practice.[2] Moreover, the fact that all cardinal voting methods can fail the later-no-harm criterion in theory is essential to their favoring consensus options (broad, moderate support) over pluralitarian options (narrow, strong support);[3] voting systems that pass later-no-harm are unable to consider weak (secondary) preferences when evaluating candidates. As a result, many social choice theorists question whether the criterion is even desirable in the first place.[2]

Complying methods[edit]

The plurality vote, 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.

Plurality voting is typically considered to satisfy later-no-harm because it can be thought of as a ranked voting system where only the first preference matters.

Noncomplying methods[edit]

Approval voting, score voting, highest medians, Borda count, ranked pairs, the Schulze method, the 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 resolvability criterion, i.e. that any tie can be removed by some single voter changing their rating).[1]

Plurality-at-large voting, which allows the voter to select multiple candidates, does not satisfy later-no-harm when used to fill two or more seats in a single district.

Examples[edit]

Anti-plurality[edit]

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.

Approval voting[edit]

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[edit]

Coombs' method[edit]

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[edit]

Dodgson's method[edit]

Dodgson's method elects a Condorcet winner if there is one, and otherwise elects the candidate who can become the Condorcet winner after the fewest 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[edit]

Majority judgment[edit]

Minimax[edit]

Ranked pairs[edit]

Score voting[edit]

Schulze method[edit]

Criticism[edit]

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,[4] 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".[5]

See also[edit]

Notes[edit]

  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.
  2. ^ Minimax can occasionally violate later-no-harm if tied ranks are allowed.

References[edit]

  1. ^ a b Douglas Woodall (1997): Monotonicity of Single-Seat Election Rules, Theorem 2 (b)
  2. ^ a b c "Later-No-Harm Criterion". The Center for Election Science. Retrieved 2024-02-02.
  3. ^ 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.
  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. ^ Woodall, Douglas, Properties of Preferential Election Rules, Voting matters - Issue 3, December 1994
  • 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