Later-no-harm is a property of some

ranked-choice voting Ranked-choice voting may be used as a synonym for: * Ranked voting, a term used for any voting system in which voters are asked to rank candidates in order of preference * Instant-runoff voting (IRV), a specific ranked voting system with single-wi ...

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. It is a common property in the

plurality-rule family In social choice theory, the majority rule (MR) is a social choice rule which says that, when comparing two options (such as Bill (law), bills or Candidate, candidates), the option preferred by more than half of the voters (a ''majority'') shoul ...

of voting systems. 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 may be confused as implying

center squeeze A center squeeze is a kind of spoiler effect shared by rules like the two-round system, plurality-with-primaries, and instant-runoff voting (IRV). In a center squeeze, the Majority-preferred candidate, majority-preferred and Social utility effic ...

, since later-no-harm is a defining characteristic of first-preference plurality (FPP) and instant-runoff voting (IRV), and descending solid coalitions (DSC), systems that have similar mechanics that are based on first preference counting. These systems pass later-no-harm compliance by making sure the results either do not depend on lower preferences at all (

plurality Plurality may refer to: Law and politics * Plurality decision, in a decision by a multi-member court, an opinion held by more judges than any other but not by an overall majority * Plurality (voting), when a candidate or proposition polls more ...

) or only depend on them if all higher preferences have been eliminated ( IRV and DSC), and thus exhibit a

effect. However, this does not mean that methods that pass later-no-harm must be vulnerable to center squeezes. The properties are distinct, as Minimax opposition also passes later-no-harm. Later-no-harm is also often confused with immunity to a kind of

strategic voting Strategic or tactical voting is voting in consideration of possible ballots cast by other voters in order to maximize one's satisfaction with the election's results. Gibbard's theorem shows that no voting system has a single "always-best" strat ...

called strategic truncation or

bullet voting Bullet, single-shot, or plump voting is when a voter supports only a single candidate, typically to show strong support for a single favorite. Every voting method that does not satisfy either later-no-harm (most methods) or monotonicity (suc ...

. Satisfying later-no-harm does not provide immunity to such strategies. Systems like instant runoff that pass later-no-harm but fail

monotonicity In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of orde ...

still incentivize truncation or bullet voting in some situations.

Later-no-harm methods

The

plurality vote Plurality may refer to: Law and politics * Plurality decision, in a decision by a multi-member court, an opinion held by more judges than any other but not by an overall majority * Plurality (voting), when a candidate or proposition polls more ...

two-round system The two-round system (TRS or 2RS), sometimes called ballotage, top-two runoff, or two-round plurality, is a single-winner electoral system which aims to elect a member who has support of the majority of voters. The two-round system involves one ...

instant-runoff voting Instant-runoff voting (IRV; ranked-choice voting (RCV), preferential voting, alternative vote) is a single-winner ranked voting election system where Sequential loser method, one or more eliminations are used to simulate Runoff (election), ...

, and descending solid coalitions satisfy the later-no-harm criterion.

First-preference plurality First-past-the-post (FPTP)—also called choose-one, first-preference plurality (FPP), or simply plurality—is a single-winner voting rule. Voters mark one candidate as their favorite, or first-preference, and the candidate with more first- ...

satisfies later-no-harm trivially, by ignoring every preference after the first.

Non-LNH methods

Nearly all voting methods not discussed above fail LNH, including

score voting Score voting, sometimes called range voting, is an electoral system for single-seat elections. Voters give each candidate a numerical score, and the candidate with the highest average score is elected. Score voting includes the well-known approva ...

, highest medians,

Borda count The Borda method or order of merit is a positional voting rule that gives each candidate a number of points equal to the number of candidates ranked below them: the lowest-ranked candidate gets 0 points, the second-lowest gets 1 point, and so on ...

, and all

Condorcet method A Condorcet method (; ) is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, whenever there is such a candidate. A candidate with this property, the ...

s. The

Condorcet criterion A Condorcet winner (, ) is a candidate who would receive the support of more than half of the electorate in a one-on-one race against any one of their opponents. Voting systems where a majority winner will always win are said to satisfy the Condo ...

is incompatible with later-no-harm (assuming the

resolvability criterion A voting system is called decisive, resolvable, or resolute if it ensures a low probability of tied elections. There are two different criterion that formalize this. * In Nicolaus Tideman's version of the criterion, adding one extra vote (with no ...

, i.e. any tie can be removed by a single voter changing their rating).Douglas Woodall (1997)
Monotonicity of Single-Seat Election Rules
Theorem 2 (b) 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 Single non-transferable vote or SNTV is a multi-winner electoral system in which each voter casts a single vote. Being a semi-proportional variant of first-past-the-post voting, under SNTV small parties, as well as large parties, have a chance t ...

does.

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.

Borda count

Copeland

Schulze method

Criticism

Douglas Woodall writes:

Notes

Bibliography

* D R Woodall, "Properties of Preferential Election Rules", ''

Voting matters ''Voting matters'' was a peer-reviewed academic journal whose purpose is "To advance the understanding of preferential voting systems". Originally published by the Electoral Reform Society (1994–2003), ''Voting matters'' then became a publication ...

'', Issue 3, December 199

* Tony Anderson Solgard and Paul Landskroener, Bench and Bar of Minnesota, Vol 59, No 9, October 2002

John Brown, Jr. v. W. H. Smallwood
130 Minn. 492, 153 N.W. 953 (July 30, 1915)

References

{{voting systems Electoral system criteria