Later-no-harm criterion

Statement of Criterion

A voter giving an additional ranking or positive rating to a less-preferred candidate cannot cause a more-preferred candidate to lose.

Complying Methods

Later-no-harm (usually LNH, but sometimes LNHa or LNHarm to avoid confusion with Later-no-help) is satisfied by Instant Runoff Voting, Minmax(pairwise opposition), and Douglas Woodall's Descending Solid Coalitions method. 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.

Later-no-harm is incompatible with the Condorcet criterion.

Example:

46 A>B

10 B

44 C>B

B is the Condorcet winner, and would win in any Condorcet method, and if using a rated method, would win if given a high enough rating by all voters. But if the A-top voters bullet vote, then they can make A the winner in several voting methods, such as most Condorcet-IRV hybrid methods and likely in the rated methods. However, notice that to pass LNH in this situation, the majority of voters who prefer B over A have to have their preferences ignored; in a method like IRV, that means that the C-top voters may have to choose between supporting C or using Favorite Betrayal to help B win. Essentially, passing LNH ensures voters never have to worry about their later preferences hurting them, but it can at times force them to lie about their higher preferences.

Commentary

Later-no-harm guarantees that the method will not use a voter's lower preferences to elect a candidate who that voter likes less than the candidate that would have been elected if this voter had kept his lower preferences a secret.

As a result, voters may feel free to vote their complete ranking of the candidates, which in turn may give the election method more complete information to use to find a winner. There is a tradeoff however, in that this criterion simultaneously minimizes the amount of information that the voting method can use to find a winner.

This criteria is equivalent to the criteria that the system is non-compromising in that it will never elect a compromise (i.e. a Utilitarian winner or Condorcet winner.) This is not universally desired so it cannot be claimed that this criteria is always one which would be desirable to pass. If one wants a system which can elect a compromise winner then it would be desirable to fail this criteria.

It is believed that some methods fail LNH at higher rates than others. For example, Condorcet methods are expected to fail less often than something like Score voting.