[EM] independence form covered alternatives is incompatible with monotonicity

[fsimmons at pcc.edu]

Kristopher,

That's an interesting question.  I feel confident that a stronger result holds than the one I have given, but I 
don't know how much stronger.

Forest

----- Original Message -----
From: Kristofer Munsterhjelm 
Date: Saturday, July 17, 2010 0:59 am
Subject: Re: [EM] independence form covered alternatives is incompatible with monotonicity
To: fsimmons at pcc.edu
Cc: election-methods at lists.electorama.com

> fsimmons at pcc.edu wrote:
> > Suppose that we have a method that satisfies independence form 
> covered alternatives, and that gives 
> > greater winning probability to alternative B in this scenario
> > 
> > 40 B>C>A
> > 30 C>A>B
> > 30 A>B>C
> > 
> > than in this scenario
> > 
> > 40 D>B>C
> > 30 B>C>D
> > 30 C>D>B
> > 
> > as any decent method would.
> 
> Could one make a deliberately perverse method that would return 
> bad 
> results but would technically pass both independence from 
> covered 
> alternatives and monotonicity, or is it possible to make an 
> absolute 
> incompatibility proof?
>