[EM] IRV clone-independent?
Markus Schulze
markus.schulze at alumni.tu-berlin.de
Sat Oct 6 11:51:16 PDT 2001
Dear Rob,
you wrote (4 Oct 2001):
> Is it possible for a method based purely on ranked ballots to be both
> clone-independent and nonmonotonic? In particular, can anyone come up
> with an IRV example that violates independence of clones? I don't
> remember having seen one.
When there are no ties (for candidate with fewest number of actual
first preferences), then IRV is clone-independent. Whether IRV is
clone-independent in the case of ties depends on the used tiebreaker.
Example
3 voters vote A > B > C.
2 voters vote B > C > A.
1 voter votes C > B > A.
Step 1: A has 3 votes; B has 2 votes; C has one vote.
Step 2: C is eliminated. A has 3 votes; B has 3 votes.
Most IRV supporters suggest that when there is a tie then that
candidate should be eliminated who had fewer votes in the latest
step; this means that in the example above --as candidate A
had 3 votes in the first step while candidate B had only 2
votes in the first step-- candidate A wins decisively so that
clone-independence is violated. However, with a random tiebreaker
IRV is clone-independent even when there are ties.
******
Another example for a nonmonotonic clone-independent election method
is Pairwise-Elimination:
http://www.fortunecity.com/meltingpot/harrow/124/methods.html
As far as I know, this election method is also called "Arrow-Raynaud
Method." But I am not sure about that.
Markus Schulze
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