Later-no-help criterion

The later-no-help criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less-preferred candidate can not cause a more-preferred candidate to win. Voting systems that fail the later-no-help criterion are vulnerable to the tactical voting strategy called mischief voting, which can deny victory to a sincere Condorcet winner. Two-round system, Single transferable vote (including traditional forms of Instant Runoff Voting and Contingent vote), Approval voting, Borda count, Range voting, Bucklin voting, and Majority Judgment satisfy the later-no-help criterion. When a voter is allowed to choose only one preferred candidate, as in plurality voting, later-no-help can either be considered satisfied (as the voter's later preferences can not help their chosen candidate) or not applicable. All Minimax Condorcet methods (including the pairwise opposition variant), Ranked Pairs, Schulze method, Kemeny-Young method, Copeland's method, Nanson's method, and Descending Solid Coalitions, a variant of Woodall's Descending Acquiescing Coalitions, do not satisfy later-no-help. The Condorcet criterion is incompatible with later-no-help. Checking for failures of the Later-no-help criterion requires ascertaining the probability of a voter's preferred candidate being elected before and after adding a later preference to the ballot, to determine any increase in probability. Later-no-help presumes that later preferences are added to the ballot sequentially, so that candidates already listed are preferred to a candidate added later. Anti-plurality voting Anti-plurality elects the candidate the fewest voters rank last when submitting a complete ranking of the candidates. Later-No-Help can be considered not applicable to Anti-Plurality if the method is assumed to not accept truncated preference listings from the voter. On the other hand, Later-No-Help can be applied to Anti-Plurality if the method is assumed to apportion the last place vote among unlisted candidates equally, as shown in the example below.