[EM] IRV clone-independent?

[Markus Schulze]

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