[EM] New Condorcet/RP variant
ciphergoth at gmail.com
Fri Nov 5 06:44:08 PST 2004
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:
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
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
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