Statement of Criterion
Adding a preference to a ballot must not decrease the probability of election of any candidate ranked above the new preference.
Later-no-harm 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 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.
Later-no-harm is incompatible with the Condorcet criterion.