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



On Fri, Nov 24, 2000 at 12:22:31PM -0500, Raul Miller wrote:
> > If you consider how:
> > 	60 votes, ABF
> > 	30 votes, BFA
> > might turn out under the current constitution (again where A requires
> > 3:1 supermajority, B requires simple majority to pass), you'd have:
> > 	A dominates B, 60 to 30
> My guess here is that you think that A.6(2) applies sequentially before
> A.6(7).

A.6(2) is just defining a term.

> Which would mean that A.6(7) doesn't really apply to anything at
> all (since A.6(5) and A.6(6) both would apply before A.6(7)).  Personally,
> I'm uncomfortable with the idea that A.6(7) is a part of the constitution
> that should never be applied.
> 
> With a 3:1 supermajority over B, and 60 ABF votes, B dominates A, 30 to 20.

This isn't the case at all: A.6(7) applies only to the final ballot
(``If a supermajority is required the number f Yes votes in the *final
ballot*..''). From A.3(1) and A.3(2), presuming there's more than one
possible change that could be made (say, "A: Remove non-free" and "B:
Move non-free to unofficial.debian.org"), they form a set of related
amendments and are first voted on in a separate ballot, the winner of
which becomes the final form of the resolution as is `voted on in a
final ballot', at which point supermajority requirements become relevant.

> [By the way
> since you didn't specify it, I'm going to imagine a quorum of 25 on
> these ballots -- which doesn't affect this particular sample ballot.]

Apparently the quorum would actually be closer to 37 these days. If it's a
problem, just assume the number of votes are multiplied by 2 or 10 or so.

> > and a final vote something like:
> > 	~80 votes for
> > 	~15 votes against
> > which is a successful 3:1 supermajority, so it'd pass.
> Obviously, I disagree.  Your interpretation seems to rely on
> applying the stanzas of A.6 in sequence, which effectively
> nullifies the higher-numbered stanzas.

I'm applying them as follows:

	A.6(1), A.6(2) are definitional, not procedural

	From A.3(1) there is an initial vote (or votes) to determine
	which (set of independent) related amendments apply. This vote
	(if necessary) is counted as follows:

		A.6(3) is applied to remove all dominated options

		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)

			A.6(6) is applied if A.6(5) didn't result in a clear
			       winner [0]

		(from A.3(1), no quorum is required for this vote)

	From A.3(2) there is a final vote to determine whether the resolution
	is passed, which has options "Yes", "No" and "Further Discussion."
	It is counted as follows:

		If a supermajority is required, A.6(7) is applied.

		A.6(3) is applied to remove all dominated options.

		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
			A.6(6) is applied if A.6(5) didn't result in a clear
			       winner [0]

		If a quorum is required, A.6(8) is applied (to the original
		vote count, without options dropped, or counts scaled).

(I don't particularly care about the ambiguities in tie situations in this case, so the vote numbers I made up simply avoided them).

> > > If that turns out to be too ambiguous, perhaps we need a
> > > constitutional ammendment?
> > 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.

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.

A.6(4) and A.6(5) should be applied in order.

I'm not at all clear on when exactly A.6(6) is intended to apply. 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. Usually casting votes are
considered to have less weight than any normal vote, so this doesn't seem
entirely reasonable. It's also possible A.6(6) is intended to apply only
when STV vote fails with all options having an equal number of votes,
in which case the casting vote would be a more normal one, and A.6(6)
would come after A.6(5).

So, what I'd assume is something like the following order:

	A.6(1), A.6(2)
	A.6(7)
	A.6(3), A.6(4), A.6(5)
	A.6(8)

If all of those fail to select a winner, I don't think it's at all clear
what the constitution says should happen.

> [Aside: have you ever done any frames-based ai programming?]

No?

> 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?

> I take the "now" in A.6(5) as an important part of the fact that A.6(5)
> can be applied more than once, and those iterative applications must be
> in sequence.

I don't think the word "now" is much justification for continually
repeating the process (it seems to me to simply indicate that those things
are done in sequence, not how many times they're done), that's not the
issue: if you *ever* do A.6(3), you're required to immediately discard
*all* votes in some situations, whether one of them has been chosen or
not. I don't think it's at all clear in the constitution that A.6(3)
should be ignored in any circumstances, and I don't particularly think
it's a good idea to have to rely on the secretary's interpretation in
counting the votes, generally speaking.

Fortunately, the circumstances where any ambiguities occur are pretty
rare.

Cheers,
aj

[0] A.6(6) claims it applies "in the case of ties". I don't consider `all
    options have been eliminated' to be a tie, but since it's not defined,
    the secretary could well do that. A.6(5) already seems to be being
    used to resolve ties, but only in very rare cases (where there are
    a couple of options which dominate all others, but which are exactly
    equally preferred (ie, n people prefer A over B, and n people prefer
    B over A).

-- 
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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