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 cannot cause a more preferred candidate to lose.

Complying methods

Single transferable vote (including
Instant Runoff Voting and Contingent vote), Minimax Condorcet (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.

However, if a method permits incomplete ranking of candidates, and if a majority of votes is required for election, it cannot satisfy Later-no-harm, because a lower preference vote cast may create a majority for that lower preference, whereas if the vote was not cast, the election could fail, proceed to a runoff, repeated ballot or other process, and the favored candidate could possibly win.

The later-no-harm criterion is by definition inapplicable to any voting system in which a voter is not allowed to express more than one choice, including plurality voting, the system most commonly used in Canada, India, the UK, and the USA.

Noncomplying methods

Approval voting, Borda count, Range voting, Schulze method and Bucklin voting do not satisfy later-no-harm. The Condorcet criterion is incompatible with later-no-harm.

When Plurality is being used to fill two or more seats in a single district (Plurality-at-large) it fails later-no-harm.

Examples

Approval voting

For example in an election using Approval voting 520 voters prefer candidates in the order A>B>C and approve only candidate A. 380 voters prefer candidates in the order B>C>A and approve only candidate B. 100 voters prefer candidates in the order C>B>A and approve candidates C and B.

B is preferred to A by 51 votes to 49 votes.A is preferred to C by 49 votes to 26 votes.C is preferred to B by 26 votes to 25 votes.

There is no Condorcet winner and B is the Ranked pairs winner.

Suppose the 25 B voters give an additional preference to their second choice C.

The votes are now:

In the Preferential voting method described as an example in Robert's Rules of Order, elimination continues iteratively until "one pile contains more than half the ballots." So C would be eliminated, then B, and the B ballots would be counted for A, who would thereby obtain a majority and be elected. (If no candidate gains a majority, this will "require the voting to be repeated.") By adding a second preference vote for A, the B voters eliminated the election possibility for B.

Commentary

Woodall writes about Later-no-harm, "... under 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.'"

References

* D R Woodall, "Properties of Preferential Election Rules", "Voting Matters", Issue 3, December 1994 [http://www.votingmatters.org.uk/ISSUE3/P5.HTM]
* Tony Anderson Solgard and Paul Landskroener, Bench and Bar of Minnesota, Vol 59, No 9, October 2002. [http://www2.mnbar.org/benchandbar/2002/oct02/voting.htm]
* [http://rangevoting.org/BrownVsmallwood.pdf Brown v. Smallwood, 1915]