Later-no-help criterion

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Statement of Criterion

Adding a preference to a ballot must not increase the probability of election of any candidate ranked above the new preference.

Complying Methods

Approval voting and Score voting, when tweaking the definition to involve rating rather than ranking, pass the criterion.

Later-no-help (LNHe or LNHelp; not to be confused with later-no-harm, which is often LNH) is satisfied by 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 First-Preference Plurality and Random Ballot, since those methods do not usually regard lower preferences. Virtually every other method fails this criterion.

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 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):

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 voters instead vote B:5 C:1, then:

B 250 points 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.


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.

As a result, voters may feel free to rank candidates between whom they have no clear preference equally, rather than expressing insincere preferences between those candidates which could effect the outcome of the election.

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. Thus, all Condorcet methods are at least somewhat vulnerable to burial strategy.

Alternative Definitions

1. While making out your ballot, when you have voted for some candidates, you don't need to vote for additional candidates in order to fully help the candidates for whom you've already voted.

To vote for a candidate means to vote him/her over at least one other candidate.

To fully help a candidate means to vote in a way that does as much as possible toward making him/her win.