Later-no-harm criterion
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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.
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[edit] 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.
[edit] Commentary
Examples of later-no-harm failure.
[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 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.
[edit] 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.
[edit] References
- D R Woodall Properties of Preferential Election Rules, Voting Matters issue 3 December 1994 [1]
