Later-no-harm criterion
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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.
Name | Comply? |
---|---|
Plurality | Yes[note 1] |
Two-round system | Yes |
Nonpartisan primary | Yes |
Partisan primary | Yes |
Instant-runoff voting | Yes |
Minimax Condorcet | Yes[note 2] |
Descending solid coalitions | Yes |
Anti-plurality | Yes |
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 |
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 tend to be more resistant to these strategies in practice.[2] The fact that all cardinal and Condorcet methods can sometimes 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. This has led many social choice theorists to question whether the criterion is even desirable in the first place, or should instead be seen as a negative (anti-criterion).[2]