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.

[edit] 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.

[edit] 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.

[edit] Examples

[edit] 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.

A is the most approved candidate and therefore the winner.

Suppose 50 of the A>B>C voters approve both candidates A and B instead of just candidate A. The result is now:

B is now the most approved candidate and therefore the winner.

By approving an additional less preferred candidate the 50 AB voters have caused their favourite candidate to lose.

[edit] Condorcet compliant methods

For example in an election conducted using the Condorcet compliant method Ranked pairs the following votes are cast:

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:

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

C is now the Condorcet winner and therefore the Ranked pairs winner.

By giving a second preference to candidate C the 25 B voters have caused their first choice to be defeated.

[edit] Effect of majority requirement

In a Single transferable vote election with majority required, and full ranking is not required, the votes are as follows (for simplicity, all voters plump for their favorites):

If this majority failure results in a runoff between A and B, B could win.

However, suppose the B voters decide to add a second preference for A:

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.

[edit] 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.'"

[edit] References

• D R Woodall, "Properties of Preferential Election Rules", Voting Matters, Issue 3, December 1994 [1]
• Tony Anderson Solgard and Paul Landskroener, Bench and Bar of Minnesota, Vol 59, No 9, October 2002. [2]
• Brown v. Smallwood, 1915