Re: stability isn't an issue
> > Once again, I highly recommend that we pay attention to the criteria
> > documented at http://www.electionmethods.org. In particular, monotonicity
On Sat, Dec 14, 2002 at 10:17:15AM +0100, Matthias Urlichs wrote:
> Note that electionmethods.org is biased towards Condorcet. There are a
> bunch of other criteria.
>
> See for example http://www.barnsdle.demon.co.uk/vote/aprove.html
This indeed adds two criteria: the Strong Adverse Results Criterion
(which Condorcet doesn't meet) and the Unanimously Unpreferred Candidate
Criterion (which Condorcet does meet).
As an aside: while Condorcet fails to meet SARC and FBC, the conditions
required are so improbable that it's hard to imagine how anyone could
take advantage of this failure without knowing ahead of time how the
election is going to come out.
> See http://www.google.de/search?q=+site:www.sam.sdu.dk+condorcet+approval
> for a couple of scientific papers. I've not had time to do more than skim
> these, but at least one analyzes the question of which of these criteria
> is actually important in practice.
I've also run across the "Consistency Criterion": if two elections with
the same candidates have the same winner then combining the votes should
still result in the same winner. Near as I can tell, this is equivalent
to monotonicity.
I've been shying away from approval, however, because approval only
allows a binary choice: you like the option or you don't like the option.
Approval doesn't let you say "I like all three of these, but I prefer
this one over that one, ...".
You'll also remember that I tried doing a mix of approval and condorcet
(where the default option could never be the weakest defeat), but a
number of people objected to that. (Perhaps the observed problems could
be remedied using the "drop the option entirely it's defeated by the
default option and either option in the defeat is involved in a weakest
defeat" mechanism. Or, perhaps, simply eliminate any options defeated
by the default option before using CpSSD.)
What I should do, I guess, is set up a sequence of elections and
tests for the various criterion and implementaions of a number of
plausible mechanisms to see which ones tend to be better behaved.
I've got a rough idea of how I could do this, but I've not dedicated
the development/debugging time I'd need to pull this off.
Either that, or I should just settle on CpSSD with quorum and
supermajority eliminating options before they're otherwise considered.
Suggestions?
Thanks,
--
Raul
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