Re: Hybrid Theory
[I just noticed that my reply to this message never got sent.]
> > http://lists.debian.org/debian-vote/2002/debian-vote-200211/msg00162.html
On Sun, Dec 08, 2002 at 10:54:50PM +0100, Matthias Urlichs wrote:
> It's a known fact that dropping (or adding) an option from a Condorcet
> election may change its result if there's a cycle.
Yes. However, this doesn't make all such results equivalent.
> I don't like to play around with ratios when considering the supermajority
> requirement. It already has led to one unforeseen effect (the rule about
> not dropping the default, because otherwise the supermajority-requiring
> option might _still_ win -- which gives the default option a strength it
> IMHO does NOT deserve); nobody can guarantee that there are no others.
That artifact of that system was not because of "playing around with
ratios", it was because in that draft I had stipulated that defeats by
the default option could not be dropped. This had a couple effects that
I wanted [preventing insufficient-supermajority options from winning, and
defeating options which resoundingly defeated by supermajority options],
but it had some bad effects as well [defeating options which should not
have been defeated].
The mechanism in "Hybrid Theory" starts out using an artificial defeat
of insufficient-supermajority options. This has less effect on the
outcome than eliminating that supermajority entirely.
At one end of the spectrum, where the first defeat which would be
eliminated is a defeat of the default option, "Hybrid Theory" is exactly
equivalent to deleting all options with failed supermajority before
using CpSSD. In all other cases with failed supermajority, I'm retaining
defeats which which CpSSD would normally treat as significant, and which
"drop failed supermajority before CpSSD" would treat as insignificant.
This is very different from the prior draft, which treated defeats by the
default option as significant when CpSSD treated them as insignificant.
And, I've yet to see any cases where "Hybrid Theory" either:
[a] Does not treat supermajority properly, or
[b] Gives a result which is less like condorcet than "drop all failed
supermajority before CpSSD".
I don't think such cases exist (I'm working on how to show this). On the
other hand, there are cases where "drop all failed supermajority before
CpSSD" gives results which are less like condorcet than "Hybrid Theory".
Thanks,
--
Raul
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