[EM] New Condorcet/RP variant

[Paul Crowley]

On Fri, 5 Nov 2004 13:33:03 +0000, Paul Crowley <ciphergoth at gmail.com> wrote:
> > On Thu, 04 Nov 2004 21:33:19 +0100, Markus Schulze
> > <markus.schulze at alumni.tu-berlin.de> wrote:
> > > your Condorcet/RP variant sounds like Steve Eppley's
> > > "minimize thwarted majorities" (MTM) method.

> MTM is exactly equivalent to my method.

Found the definition of MTM:

http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-February/003600.html

   Minimize Thwarted Majorities (MTM)
   ----------------------------------
   If Vij > Vji and the social ordering ranks j ahead of i, 
   then the social ordering "thwarts" the Vij majority who 
   ranked i ahead of j.

   Select as the social ordering the ordering which 
   minimizes thwarted majorities.

It turns out not to be exactly equivalent.  Using Eppley's notation,
if #R(a, b) > #R(b,a), then #R(b,a) plays no role in MTM as far as I
can tell.  My method (call it SortAffirmed) treats #R(a, b) the same
way no matter what its relation to #R(b, a) and so is somewhat simpler
and cleaner.

Proven weak Pareto.  Also proven a sort of "spirit of Pareto" property
which says that if a particular ordering wins, then there is no
ordering that makes no-one any less happy and at least one person
strictly happier.  Still working on strong Pareto - I suspect that
spirit of Pareto implies strong Pareto where voters have no "don't
care" option but I can't see how to prove it.
-- 
  __
\/ o\ Paul Crowley
/\__/ www.ciphergoth.org