Later-no-harm criterion

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 this 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), three similar systems for comparing candidates based on how many eligible voters consider each uneliminated candidate their favorite. 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). 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. Cardinal 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.

Later-no-harm is sometimes confused with resistance to a kind of strategic voting called truncation or bullet voting. However, satisfying later-no-harm does not (by itself) provide resistance to such strategies, unless paired with the participation criterion; systems like instant runoff that pass later-no-harm but fail participation still incentivize truncation or bullet voting in some situations.

Later-no-harm methods
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.

Non-LNH methods
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).

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.

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.

Schulze method
{| class="wikitable collapsible collapsed" !Examples This example shows that the Schulze method doesn't satisfy the Later-no-harm criterion. Assume three candidates A, B and C and 16 voters with the following preferences:

Assume that all preferences are expressed on the ballots.
 * Express later preferences

The pairwise preferences would be tabulated as follows:

Result: B is Condorcet winner and thus, the Schulze method will elect B.

Hide later preferences
Assume now that the three voters supporting A (marked bold) would not express their later preferences on the ballots:

The pairwise preferences would be tabulated as follows:

Now, the strongest paths have to be identified, e.g. the path A > C > B is stronger than the direct path A > B (which is nullified, since it is a loss for A).

Result: The full ranking is A > C > B. Thus, A is elected Schulze winner.

By hiding their later preferences about B and C, the three voters could change their first preference A from loser to winner. Thus, the Schulze method doesn't satisfy the Later-no-harm criterion.
 * Conclusion
 * }

Criticism
Douglas Woodall writes:

"[U]nder STV the later preferences on a ballot are not even considered until the fates of all candidates of earlier preference have been decided. Thus a voter can be certain that adding extra preferences to his or her preference listing can neither help nor harm any candidate already listed. Supporters of STV usually regard this as a very important property, although it has to be said that not everyone agrees; the property has been described (by Michael Dummett, in a letter to Robert Newland) as "quite unreasonable", and (by an anonymous referee) as "unpalatable"."