Later-no-harm criterion

An election method satisfies the later-no-harm criterion if by ranking, rating or voting for 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, all methods that comply with the Condorcet criterion satisfy later-no-harm if a Condorcet winner exists.

Approval voting, Borda count, Range voting and Bucklin do not satisfy later-no-harm. If no Condorcet winner exists for a set of election data then Condorcet compliant methods can also fail later-no-harm.

Commentary

Examples of later-no-harm failure.

Approval voting

Suppose 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

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

Condorcet compliant methods

Suppose in an election conducted using the Condorcet compliant method Ranked pairs (winning votes) the following votes are cast:

49: A

25: B

26: C>B

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

There is no Condorcet winner and B is the Ranked pairs (winning votes) winner (the 51:49 B>A win is kept because B has the greatest number of winning votes, the 49:26 A>C win is kept because A has the second largest number of winning votes, the 26:25 C>B win is ignored because C has the lowest number of winning votes giving a ranking of B>A>C).

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 to 49. C is preferred to B by 26 to 25.

C is now the Condorcet winner and therefore elected.

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

References

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