[EM] eliminations methods like IRV

[Forest Simmons]

That'll teach me to say,"Nobody can deny!"


On Fri, 23 Feb 2001, Bart Ingles wrote:

> 
> 
> Forest Simmons wrote:
> > 
> > 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.
> 
> 
> Not necessarily; suppose ratings or utilities are considered:
> 
>      1.0              0.5               0.0
>      --------------------------------------
> 40   B                             UVWCXYZA
> 25   UVWCABXY                             Z
> 35   A                             UVWBXYZC
> 
> We can safely infer from the rankings that U is strongly preferred over
> Z by the middle group, at least as strongly as that group prefers anyone
> over anyone, only because U and Z contain both the first and last
> choice.  For the two larger groups it's not possible to make that
> inference.
> 
> Bart
> 

So let's think of a new example starting with ratings to remove the
ambiguity.  How about Bart's layout with everybody spread out:

       1.0                  0.5                    0
       ---------------------------------------------
40     B    U     V    W     C     X    Y     Z    A
25     U    V     W    C     A     B    X     Y    Z
35     A    U     V    W     B     X    Y     Z    C


And we'll assume zero information, so that insincere voting doesn't mess
up the nice lay out.

The point is that it is easy to make up an example where IRV picks the
same choice frontwards and backwards even when it is obvious that not all
of the candidates are equally acceptable.

Forest