Later-no-harm criterion
The later-no-harm 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 lose. Voting systems that fail the later-no-harm criterion are vulnerable to the tactical voting strategies called bullet voting and burying, which can deny victory to a sincere Condorcet winner. Complying methods. Two-round system, Single transferable vote, Instant Runoff Voting, Contingent vote, Minimax Condorcet (a pairwise opposition variant which does  not satisfy the Condorcet Criterion), and Descending Solid Coalitions, a variant of Woodall's Descending Acquiescing Coalitions rule, satisfy the later-no-harm criterion. When a voter is allowed to choose only one preferred candidate, as in plurality voting, later-no-harm can be either considered satisfied (as the voter's later preferences can not harm their chosen candidate) or not applicable. Noncomplying methods. Approval voting, Borda count, Range voting, Majority Judgment, Bucklin voting, Ranked Pairs, Schulze method, Kemeny-Young method, Copeland's method, and Nanson's method do not satisfy later-no-harm. The Condorcet criterion is incompatible with  later-no-harm (assuming the discrimination axiom, according to which any tie can be removed by some single voter changing her rating). Plurality-at-large voting, which allows the voter to select up to a certain number of candidates, doesn't satisfy later-no-harm when used to fill two or more seats in a single district. Checking Compliance. Checking for satisfaction of the Later-no-harm 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 decrease in probability. Later-no-harm presumes  that later preferences are added to the ballot sequentially, so that candidates already listed are preferred to a candidate added later. Examples. Anti-plurality. Anti-plurality elects the candidate the fewest voters rank last when submitting a complete ranking of the candidates. Later-No-Harm 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-Harm 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. Approval voting. Since Approval voting does not allow voters to differentiate their views about candidates for whom they choose to vote and the later-no-harm criterion explicitly requires the voter's ability to express later preferences on the ballot, the criterion using this definition is not applicable for Approval voting. However, if the later-no-harm criterion is expanded to consider the preferences within the mind of the voter to determine whether a preference is "later" instead of actually expressing it as a later preference as demanded in the definition, Approval would not satisfy the criterion. Under Approval  voting, this may in some cases encourage the tactical voting strategy called bullet voting. Coombs' method. Coombs' method repeatedly eliminates the candidate listed last on most ballots, until a winner is reached. If at any time a candidate wins an absolute majority of first place votes among candidates not eliminated, that candidate is elected. Later-No-Harm can be considered not applicable to Coombs if the method is assumed to not accept truncated preference listings from the voter. On the other hand, Later-No-Harm can be applied to Coombs if the method is assumed to apportion the last place  vote among unlisted candidates equally, as shown in the example below. Dodgson's method. Dodgson's' method elects a Condorcet winner if there is one, and otherwise elects the candidate who can become the Condorcet winner after the fewest ordinal preference swaps on voters' ballots. Later-No-Harm can be considered not applicable to Dodgson if the method is assumed to not accept truncated preference listings from the voter. On the other hand, Later-No-Harm can be applied to Dodgson if the method is assumed to apportion possible rankings among unlisted candidates equally, as shown in the example below . Criticism. Woodall, author of the Later-no-harm writes: