| Comply? | ||
| Plurality | Yes | |
| Two-round system | Yes | |
| Partisan primary | Yes | |
| Instant-runoff voting | Yes | |
| Minimax Opposition | Yes | |
| DSC | Yes | |
| Anti-plurality | Yes | |
| Approval | N/A | |
| Borda | No | |
| Dodgson | No | |
| Copeland | No | |
| Kemeny–Young | No | |
| Ranked Pairs | No | |
| Schulze | No | |
| Score | No | |
| Majority judgment | No |
Later-no-harm is a property of some ranked-choice voting systems, first described by Douglas Woodall. In later-no-harm systems, increasing the rating or rank of a candidate ranked below the winner of an election cannot cause a higher-ranked candidate to lose.
For example, say a group of voters ranks Alice 2nd and Bob 6th, and Alice wins the election. In the next election, Bob focuses on expanding his appeal with this group of voters, but does not manage to defeat Alice—Bob's rating increases from 6th-place to 3rd. Later-no-harm says that this increased support from Alice's voters should not allow Bob to win.
Later-no-harm is a defining characteristic of first-preference plurality (FPP), instant-runoff voting (IRV), and descending solid coalitions (DSC); all three systems have similar mechanics, in that they are based only on counting the number of first-place votes for uneliminated candidates. In later-no-harm systems, the results either do not depend on lower preferences at all (as in plurality) or only depend on them if all higher preferences have been eliminated (as in IRV and DSC).[1] [2] This tends to favor candidates with strong (but narrow) support over candidates closer to the center of public opinion, which can lead to a phenomenon known as center-squeeze.[3] [4] [5] Rated and Condorcet methods, by contrast, tend to select candidates whose ideology is a closer match to that of the median voter. This has led many social choice theorists to question whether the property is desirable in the first place or should instead be seen as a negative property.[6] [7]
Later-no-harm is often confused with resistance to a kind of strategic voting called strategic truncation or bullet voting.[8] However, satisfying later-no-harm does not provide resistance to such strategies. Systems like instant runoff that pass later-no-harm but fail monotonicity still incentivize truncation or bullet voting in some situations.[9] [10] [11]
The plurality vote, two-round system, instant-runoff voting, and descending solid coalitions satisfy the later-no-harm criterion. First-preference plurality satisfies later-no-harm trivially, by ignoring every preference after the first.
Nearly all voting methods other than first-past-the-post do not pass LNH, including score voting, highest medians, Borda count, and all Condorcet methods. The Condorcet criterion is incompatible with later-no-harm (assuming the resolvability criterion, i.e. any tie can be removed by a single voter changing their rating).[12]
Bloc voting, which allows a voter to select multiple candidates, does not satisfy later-no-harm when used to fill two or more seats in a single district, although the single non-transferable vote does.
See main article: Anti-plurality voting.
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.
See main article: Borda count.
See main article: Copeland's method.
See main article: Schulze method.
Douglas Woodall writes: