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Re: Condorcet Voting and Supermajorities (Re: [CONSTITUTIONAL AMENDMENT] Disambiguation of 4.1.5)



On Sat, Nov 25, 2000 at 06:07:30AM -0500, Raul Miller wrote:
> > 		A.6(3) is applied to remove all dominated options
> But remember that an option is only dominated if strictly more ballots
> prefer the dominating option. 

Yes, sure.

> 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.

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.

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.

> > 		if there is one option left:
> > 			A.6(4) is applied
> > 		else if there's more than one option left:
> > 			A.6(5) is applied if there is more than one option left
> > 				(in which case, there is an exact tie
> > 				 between two or more options, that is n
> > 				 votes prefer A to B, and n votes prefer
> > 				 B to A)
> And, A.6(4) still applies if there is then one option left.

That's not particularly meaningful, in any way I can see. The way I see
it, the purpose of A.6 is to determine a winner, which can be done by
any of:

	* eliminating all the ballots but one, and choosing the one that's
	  left as the winner
	* applying STV and choosing whichever it says is the winner as
	  the winner
	* allowing the casting vote to break a tie that isn't resolved by
	  STV

STV doesn't seem to be used to eliminate options so A.6(4) can apply,
it's just used to select a winner. Once you've got a winner, you're done,
you don't need to go back to some other clause to make doubly sure you've
got a winner.

> > 			A.6(6) is applied if A.6(5) didn't result in a clear
> > 			       winner [0]
> After which A.6(4) still applies.

Of course, if you're in a position to act as secretary and make a
determination on this, then apparently what you say goes, but this
doesn't seem a particularly obvious interpretation.

> > 	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.

Again, as someone who may end up acting as secretary, you might be in a
position to interpret the fact the constitution doesn't explicitly forbid
it (especially along with all the previous votes we've had as precedent)
as allowing it, but it seems worthwhile to have a system that's explicitly
spelled out, rather than one interpreted in.

> > > > > If that turns out to be too ambiguous, perhaps we need a
> > > > > constitutional amendment?
> > > > That's the general idea.
> > > Do you have a problem with my view -- that A.6(1..8) apply simultaneously
> > > (as applicable), or are you going to insist that they be applied in
> > > a rigid order?
> > Well, if you apply them in random orders you'll get different results.
> Ok.  But I'm guessing that the real problem was that I was
> misunderstanding your underlying point.  But now let me ask you: are
> you comfortable with A.3(3)?

Depends what you mean by "comfortable".

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).

> > A.6(1) and A.6(2), are definitional, so they apply at all times.
> > A.6(3) and A.6(7) are the only options which change how ballots are
> >   interpreted, so which order you do those in will change things,
> >   as will whether you do them. I'm assuming A.6(7) is the first thing
> >   that done, and it's done in the final vote when a supermajority is
> >   required. Given A.6(7) is done first, A.6(3) will then remove the
> >   same votes whenever it is applied.
> I prefer to think of these as applying wherever they make sense,
> but yours is a perfectly valid way of looking at things.

Well, I think of them applying whenever their preconditions make sense,
and not taking into account at all whether they end up with a sensible
result or not. For A.6(4), A.6(5) and A.6(6) these preconditions can't
be checked until the previous options have been done.

> > 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)

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.

A.6(4) doesn't apply either way (since there's either none or five options
left).

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

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.

Note that if we'd just had a single alternative, A, instead of the
three similar options, A, B and C (if the supporters of those options
got together off list to work on a single solution that they could all
agreed on), we'd have had:
	60 votes DAE
	57 votes EAD
	15 votes ADE
and A would've won by dominating both D (72 to 57) and E (75 to 57).

Which doesn't seem like a good way for a voting system to behave.

> > > I don't see how eliminating all the options makes sense.  I'm much more
> > > comfortable eliminating no options than I am eliminating all options.
> > Well, sure, but it's not what your comfortable with that matters, it's
> > what the constitution says that matters, surely? Isn't that why we have
> > it in the first place?
> 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.

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):

	* the constitution doesn't describe any way of having a single
	  vote to resolve a situation where there're many possible
	  outcomes to be decided amongst.

	* the constitution is unclear on how circular ties should
	  be handled if they occur, and reasonable interpretations don't
	  necessarily result in logical outcomes (which usually means the
	  vote's outcome can be manipulated, for example by introducing
	  false alternatives B and C to try to make an option D win, say,
	  when A would have won normally).

	* the mechanism for handling supermajorities described in the
	  constitution works fine where the only options are Yes,
	  No and Further Discussion, and also when the options all
	  have the same supermajority requirements, but doesn't handle
	  votes where different options have different supermajority
	  requirements well.

I think all these are flaws in the constitution, and that the former
and the latter are definitely worth fixing (since both applied to the
aborted non-free vote, and the former also applies to the currently
pending constitutional amendment).

Cheers,
aj

-- 
Anthony Towns <aj@humbug.org.au> <http://azure.humbug.org.au/~aj/>
I don't speak for anyone save myself. GPG signed mail preferred.

     ``Thanks to all avid pokers out there''
                       -- linux.conf.au, 17-20 January 2001

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