Re: Condorcet Voting and Supermajorities (Re: [CONSTITUTIONAL AMENDMENT] Disambiguation of 4.1.5)
> > So, really, you're abusing the terminology
> > to say that A dominates B, B dominates C and C dominates A. A more
> > accurate way of describing that situation would be to say that more
> > ballots prefer A to B, more prefer B to C and more prefer C to A, but
> > that, strictly speaking, there is no unambiguous preference.
On Sun, Nov 26, 2000 at 06:30:59PM +1000, Anthony Towns wrote:
> That's no more accurate, it's just more verbose. "A dominates B, B
> dominates C, and C dominates A" is *defined* to mean what you wrote above.
> There's no difference in accuracy at all.
We seem to be having a serious communication problem here.
You're calling the above situation a circular tie.
I'm saying that in the above situation there's no strict preference.
In essense, you're saying that in the above situation there is a strict
preference. [I think?] If that's what you're saying, please confirm.
If you're saying something else, please explain.
> If you want something more accurate than my restatement of A.6(3) above,
> you can just take A.6(3) straight from the consitution. No big deal.
Ok, but I don't want to overlook the word "strict" in "strict preference."
> > > From A.3(2) there is a final vote to determine whether the resolution
> > > is passed, which has options "Yes", "No" and "Further Discussion."
> > A.3(3) indicates that other sets of options are also possible (for
> > example, combining the amendment ballots and the final ballots), as long
> > as all the options of all the potential final ballots are represented.
>
> Not exactly: it says the two ballots can be combined in a single message
> for convenience, but it doesn't say you can add other options, or allow
> different semantics as far as counting the vote goes.
What are you talking about? A.3(3) doesn't even use the word "two".
And, nowhere did I suggest that the semantics would be different that
what's specified in appendix A.
> In the sense that it (loosely) requires two votes on most issues,
> no not really because I think that's overly complicated, inefficient
> (more effort on the part of developers, and takes longer to get an issue
> resolved) and seems to allow amendments to be made and voted for more
> to stymie other options than to be particularly productive (or at the
> very least that they can be seen that way).
No.
It loosely *specifies* N votes on most issues, where the last vote
*might* be a simple yes/no vote. It also *allows* those votes to
be collapsed into fewer votes -- no fewer than 1. In no place does
it *require* any any specific number of votes take place. That's
a judgement call (or, a series of judgement calls).
> > > It could well be intended as a response to circular ties, which
> > > means it should apply somewhat concurrently with A.6(3) (if there's
> > > a circular tie go to A.6(6), if not, apply A.6(3) then A.6(4) or
> > > A.6(5)), but if so it means a "casting vote" can be equivalent to 10
> > > or 20 or however many "normal" votes it may need to resolve the tie.
> > Nope, A.6(5) makes sense for what you're calling "circular ties".
> > A.6(3) doesn't [because none are dominated], and A.6(6) doesn't
> > [because it's not really a tie].
>
> You could end up with a circular tie something like, let me see:
>
> 20 votes for each of DABCE DBCAE DCABE
> 19 votes for each of EABCD EBCAD ECABD
> 4 votes for ABCDE
> 5 votes for BCADE
> 6 votes for CABDE
>
> giving you:
>
> A dominates B, 88 to 44 (2x20 + 2x19 + 4+6, to 20 + 19 + 5)
> B dominates C, 87 to 45 (2x20 + 2x19 + 4+5, to 20 + 19 + 6)
> C dominates A, 89 to 43 (2x20 + 2x19 + 5+6, to 20 + 19 + 4)
>
> A,B,C dominates D, 63 to 60 (3x19 + 3x5 to 3x20)
> A,B,C dominates E, 66 to 57 (3x20 + 3x5 to 3x19)
>
> D dominates E, 66 to 57 (3x20 + 3x2 to 3x9)
I've not counted for myself, but I'll assume that your numbers are correct
(and I'm mentally asuming by "dominates" you mean "is preferred over"
since clearly you have what you call a circular tie between A B and C, and
I claim that that means that there's no strict preference between them).
> This is essentially saying that there are three options which are
> essentially equivalent (A, B and C) and which everyone seems likely to
> accept as a compromise, and two which most people are horribly split
> between (D and E).
>
> Note that every option is preferred to E (A,B,C and D dominate it),
> and that everything but E is preferred to D (A,B and C dominate D).
>
> If we try to process this vote with the constitution, we have something
> like (assuming supermajorities and quorums aren't relevant for this vote):
>
> A.6(3) either eliminates all options (since they're all dominated by some
> other option), and we give up; or A.6(3) doesn't apply at all, leaving
> all options open for consideration.
Nope. If you allow for the concept of "strict preference" in the
definition of Dominated, D and E are eliminated.
> A.6(4) doesn't apply either way (since there's either none or five options
> left).
3, but yes.
> A.6(5) could be made to apply, in which case you'd end up with:
>
> 60 votes with D as first preference
> 57 votes with E as first preference
> 6 votes with C as first preference
> 5 votes with B as first preference
> 4 votes with A as first preference
With D and E eliminated, you have:
> 43 votes for each of ABC
> 44 votes for each of BCA
> 45 votes for each of CAB
> A would be eliminated, giving B 9 votes. C would then be eliminated, giving
> B 15 votes all up. B would then be eliminated giving D 75 votes, and letting
> D win.
A would be eliminated, resulting in a ballot of:
87 BC
45 CB
B wins.
> > Ok. A better way of tackling this issue is to point out that you were
> > labelling ballots as "dominating" in a situation where there was no
> > strict preference expressed in the ballots.
>
> Hrm? There were strict, and transitive, preferences expressed in all the
> individual ballots; and there were preferences expressed cumulatively,
> they just happened to not be transitive. Domination in Condorcet
> schemes seems to be more of a `paper/rock/scissors' sort of thing,
> that particularly deterministic, at least in very close votes.
Are you saying that you refuse to allow "strict" to mean anything
because it's not spelled "transitive"?
> Which, I should add, we haven't had yet.
>
> So in summary (and in my opinion, although I think I've given decent
> evidence of it in this thread):
Try it again with something meaningful for the definition of "strict"
and see if you get similar conclusions?
--
Raul
Reply to: