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

Only Instant-runoff voting and Single transferable vote satisfy the later-no-harm criterion.

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

Commentary

Examples of later-no-harm failure.

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 520

B 480

C 100

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:

A 520

B 530

C 100

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.

Condorcet compliant methods

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

49: A

25: B

26: C>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:

49: A

25: B>C

26: C>B

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.

Relevance

In 1915, in the case of Brown v. Smallwood, the Bucklin electoral system adopted by the city of Duluth in 1912 was declared unconstitutional by the Minnesota Supreme Court partly because Bucklin violates later-no-ham.

“The preferential system (Bucklin) directly diminishes the right of an elector to give an effective vote for the candidate of his choice. If he votes for him once, his power to help him is exhausted. If he votes for other candidates he may harm his choice, but cannot help him.”

Brown v. Smallwood 1915

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]