[EM] New Condorcet/RP variant

[Paul Crowley]

On Fri, 05 Nov 2004 11:09:24 -0800, Steve Eppley
<seppley at alumni.caltech.edu> wrote:
> Hi,
> 
> Markus S wrote about Paul Crowley's proposed voting method:
> > your Condorcet/RP variant sounds like Steve Eppley's
> > "minimize thwarted majorities" (MTM) method.
> 
> I think of the name MTM as an old name for MAM, which stands
> for "maximize affirmed majorities."

They seem quite different to me - LargestAffirmedMajorities has been
defined in quite a different way in order to provide cloneproofness.

> The tiebreaking in Paul's method sounds different than MAM's.
> But I'd appreciate seeing examples to clarify each case Paul
> wrote about.  I got the impression his tiebreaker is not
> independent of clones, but I'm not confident I understand
> what he intended.

OK, I'll explain it with an example.  Consider
http://www5.cs.cornell.edu/cgi-bin/andru/civs/results?id=E_4dcecf4df0550b93
as before, and to simplify things further let's suppose the only
candidates are Dean, Clark, and Kuchnich, and Edwards

The upper triangle for the ordering DCKE reads 61, 50, 60/ 43, 39/ 43.
So the "sorted affirmed list" for this ordering is (61, 60, 50, 43,
43, 39).

If instead we order the candidates EDCK, we get the upper triangle 21,
35, 36/ 61,50/ 43. The SAL for this ordering is thus (61, 50, 43, 36,
35, 21).

We compare these lists element by element until we find two that are
nonequal.  First element, 61 == 61, so step on to the second element,
60 > 50, so DCKE beats EDCK.

The winning ordering is the one that is "best" by this measure of
goodness.  If more than one ordering is equally good, one is chosen at
random.

This is not cloneproof, given the example

10 A > B1, B2
10 B1, B2 > C
10 C > A

but I'm not sure cloneproofness in the face of ties is necessarily good.

> I'd appreciate if Paul would elaborate on why he thinks its
> tiebreaking is "fairer" and "cleaner" than MAM's.  Are there
> any criteria we can use to more clearly define "fairer"
> and/or "cleaner?"

I think "fairer" is defined in terms of the criteria.  "cleaner" is
borne out if the proofs of the criteria are shorter and easier to
follow.

> There's also the issue of execution time.  There's no inherent
> upper bound on the number of alternatives in an election
> (particularly when voting on propositions).  I don't want to
> have to defend a voting method from attacks by "hired gun"
> academics who argue that its worst case execution time blows up
> as the number of alternatives increases.

I think it's pretty clear that it will never happen that time taken to
run the algorithm will even be noticeable. I think you can drive
yourself mad with this sort of worry if you take it too seriously. 
You'll start to worry that the definition of your method contains the
subsequence "a" "l" "q" "a" "e" "d" "a" in that order, and that
pundits will thus conclude that it's a terrorist plot.  Let's look for
a method that really seems good according to the things we really care
about first, and worry about selling it second.
-- 
  __
\/ o\ Paul Crowley
/\__/ www.ciphergoth.org