[EM] eliminations methods like IRV

[Forest Simmons]

Thanks to Blake Cretney for the example below!

Immediately below that I beef his example up to show in stark relief
IRV's failure to detect that there actually is a best and a worst. 

On Wed, 21 Feb 2001, Blake Cretney wrote:

> 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.
> 
> --- 

Forest:  An IRV fan might say to Blake's example, "Big deal. The three
candidates are in a Condorcet cycle. How can you expect IRV to distinguish
a winner from a loser?"

The following beefed up version of Blake's example is not subject to that
kind of weasling:

40 BUVWCXYZA
25 UVWCABXYZ
35 AUVWBXYZC

In this version (Blake's example with steroids) nobody can deny that some
of the candidates are much better than others, for example U is strongly
preferred over Z by all the voters.

In an example like this where it is obvious that some candidates
represent the voters uniformly better than others ... in such a case no
decent voting method would pick the same candidate for both the best and
the worst.

Yet in this example, IRV still picks A as both best and worst (i.e. 
whether IRV is applied from left to right or right to left, respectively). 

Not good IRV!

Forest