[EM] eliminations methods like IRV

[Blake Cretney]

On Thu, 22 Feb 2001 00:02:12 +0000
Martin Harper <mcnh2 at cam.ac.uk> wrote:

> Forest Simmons wrote
> 
> 
> > is it possible for IRV to pick the same candidate as both the best
and the
> > worst?  In other words, is there a pair of examples which are
identical
> > except for the reversal of preference directions, that both have
the same
> > winner when IRV is applied?
> 
> According to
http://www.fortunecity.com/meltingpot/harrow/124/criteria.html
> 
> IRV fails the "Reverse Symmetry Criterion", so yes, there apparently
is 
> such a pair. But don't believe everything you read... ;-)
> 

Your skepticism is not without cause (I have been known to make
mistakes).  However, IRV does fail Reverse Symmetry.  Consider this
example:

40 BCA 
25 CAB 
35 ABC 

The winner is A.  Now, for the reverse:

40 ACB 
25 BAC 
35 CBA

The winner is still A.

Actually, this criterion is more often failed than you might think.  I
happen to notice that Ranked Pairs passes it though.

---
Blake Cretney