[EM] New Condorcet/RP variant

[Paul Crowley]

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

Thanks for the pointer!  Having a bit of difficulty finding a
definition of MTM online, but there seems to be this definition:

http://lists.topica.com/lists/RankedPairs/read/message.html?mid=1604391148&sort=d&start=65

which is very similar but reversed.  For each of the n! possible
orderings of the candidates, MTM generates a "sorted thwarted list" by
sorting the lower triangle least first, then picks the ordering with
the least sorted thwarting list; my method generates a "sorted
affirmed list" by sorting the upper triangle greatest first, then
picks the ordering with the greatest sorted affirmed list.

I'd guess given this similarity that both possibilities must have
occured to Eppley - I wonder what the advantages of each are?

I can't resist demonstrating how simple some things are to prove for
this method.  For instance, consider the Smith criterion.  Any
ordering which does not rank all members of the Smith set above all
members must at some point have a non-member immediately above a
member.  Swapping these two is therefore bound to produce an ordering
with a better "sorted affirmed list"; therefore a list that does not
meet this criterion cannot be the winning list.
-- 
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\/ o\ Paul Crowley
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