Later-no-harm criterion

Definition

By giving an additional ranking or rating to a less preferred candidate a voter cannot cause a more preferred candidate to lose.

Complying methods

Instant-runoff voting satisfies the later-no-harm criterion.

Approval voting, Borda count, Range voting and Bucklin do not satisfy later-no-harm. The majority of election methods that comply with the Condorcet criterion fail 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.

Further information

D R Woodall Properties of Preferential Election Rules, Voting Matters issue 3 December 1994 http://www.mcdougall.org.uk/VM/ISSUE3/P5.HTM

Election-methods mailing list http://wiki.electorama.com/wiki/Election-methods_mailing_list