Later-no-help criterion: Difference between revisions
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{{Wikipedia}}<h4 class=left>Statement of Criterion</h4>
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[[Approval voting]] and [[Score voting]], when tweaking the definition to involve rating rather than ranking, pass the criterion.
<p>'''Later-no-help''' (LNHe or LNHelp; not to be confused with [[later-no-harm]], which is often LNH) is satisfied by [[IRV|Instant Runoff Voting]] and Douglas Woodall's [[Descending Acquiescing Coalitions]] method. Some forms of [[Majority Choice Approval]] satisfy this criterion. It is trivially satisfied by [[Plurality voting|First-Preference Plurality]] and [[Random Ballot]], since those methods do not usually regard lower preferences. Virtually every other method fails this criterion. </p>
[[Symmetrical ICT]] doesn't pass LNHe, but complies with Strong [[0-info LNHe]], which, some claim for practical purposes is just as good.
Example for [[Smith//Score]] (using [[Rated ballot|rated ballots]]):
30 A:5 B:4
21 B:5 A:4
4 B:5
49 C:5
The [[pairwise comparison matrix]] (indicates in each cell how many voters prefer the candidate on the left to the candidate on the top):
{| class="wikitable"
|+
!
!A
!B
!C
|-
|A
|''234 points''
|'''30 (+4 Win)'''
|'''51 (+2 Win)'''
|-
|B
|26 (-4 Loss)
|''250 points''
|'''55 (+6 Win)'''
|-
|C
|49 (-2 Loss)
|49 (-6 Loss)
|''245 points''
|}
A is the [[Condorcet winner]], and there is a [[Condorcet ranking]] of A>B>C. But now if the 4 B [[Bullet voting|bullet voters]] instead vote B:5 C:1, then:
{| class="wikitable"
|+
!
!B
!C
!A
|-
|B
|'''''<u><big>250 points</big></u>'''''
|'''51 (+2 Win)'''
|26 (-4 Loss)
|-
|C
|49 (-2 Loss)
|''249 points''
|'''54 (+3 Win)'''
|-
|A
|'''30 (+4 Win)'''
|51 (-3 Loss)
|''234 points''
|}
Now there is a [[Condorcet cycle]] between all 3 candidates, because the 4 strategic B-top voters have helped C [[pairwise beat]] A. Since all 3 candidates are in the Smith set, and B has the most points (250 points to A's 234 and C's 249), B is the Smith//Score winner, and the overall Smith//Score ranking is just the [[Score voting]] ranking: B>C>A (ordered by points). This is an example of the [[chicken dilemma]] and voters in a [[mutual majority]] being able to sometimes alter who wins within the majority.<h4 class=left>Commentary</h4>
'''Later-no-help''' guarantees that the method will not use a voter's indicated lower preferences to elect a higher-ranked candidate who would not have been elected if this voter had not expressed any lower preferences; it is about the absence of need for bottom-end strategy. For instance, many methods that fail LNHe have a strategy-need to rank unacceptable candidates in reverse order of winnability.
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LNHe-complying methods' freedom from bottom-end strategy is reminiscent of and analogous to [[FBC]] complying methods' freedom from need for the top-end strategy of favorite-burial.
'''Later-no-help''' is incompatible with the [[Condorcet Criterion|Condorcet criterion]]. Thus, all Condorcet methods are at least somewhat vulnerable to [[burial]] strategy.
== Alternative Definitions ==
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