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



On Sun, Nov 26, 2000 at 09:02:51AM -0500, Raul Miller wrote:
> > > 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.
> We seem to be having a serious communication problem here.

Not helped by me making up my own terminology now and then, by the looks.

What I've been randomly calling the "schwartz" set, is actually meant
to be called the Smith set, and the Smith condition is that whoever wins
the vote should be a member of the Smith set.

The definitions link from http://www.fortunecity.com/meltingpot/harrow/124/
defines what I've been calling "circular ties" as cycles.

> You're calling the above situation a circular tie.
> I'm saying that in the above situation there's no strict preference.

I'm not sure what you mean by a "strict" preference. The only use in
the constitution is A.6(2), which is just referring to there having to
be *more* votes preferring A to B than prefer B to A, rather than the
same number.

> In essense, you're saying that in the above situation there is a strict
> preference. 

So a preference has been expressed by the voters, but it's not easy to
see what that preference is meant to mean (since a majority of voters
specifically prefer some other solution to any one you might pick). If
that's what you'd call "non-strict" or something, I think we're saying
the same thing.

> > 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 describes a method of voting on an issue where there are first N
(presumably concurrent) ballots on each of the independent aspects of
the issue under discussion, and then a final ballot on whether the final
form of the resolution should be passed or not (which has only Yes,
No and Further Discussion as options). It further allows these ballots
to be issued in a single message, but requires that voters be able to
vote differently on the final ballot depending on the result of the N
initial ballots.

There are other possible ways of conducting the vote, and, according
to precedent and the secretary's (presumable) interpretation these are
legitimate and constitutional -- the judgement call you're referring to
above is exactly how to handle these options -- but they're not written
down anywhere. I don't think it's a good thing that how our ballots are
done, or how our votes are interpreted and counted is a judgement call.

> > 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).

A.6(2) defines the term "Dominate" (albeit with a capital), as "Option
A is said to Dominate option B if strictly more ballots prefer A to
B than prefer B to A." That's the sense in which I'm using the word,
you don't need to assume anything there.

> > 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.

What concept of "strict preference" are you referring to, exactly? Please
cite.

If the constitution's to mean anything at all, surely someone other than
the secretary or his replacement should be able to read it?

> > > 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.
> Are you saying that you refuse to allow "strict" to mean anything
> because it's not spelled "transitive"?

Well, I've never seen "strict" used to mean "transitive" before. Is that
all you mean by it?

> Try it again with something meaningful for the definition of "strict"
> and see if you get similar conclusions?

You're the one using the term, you're welcome to define it if you want me
to know exactly what you mean by it. For reference,

       adj 1: rigidly accurate; allowing no deviation from a standard;
              "rigorous application of the law"; "a strict
              vegetarian" [syn: {rigorous}]

is what wordnet says it means, which doesn't seem particularly relevant.

Hmmm.

If you're claiming that A.6(2) should be read as meaning "Option A is
said to Dominate option B is [transitively] more ballots prefer A to B
than prefer B to A.", then... Well, I'm at a loss. I suppose it makes
some sort of sense, but it doesn't seem any sort of reasonable use of
the word "strict" [0], and even then it's not clear how transitive votes
should be counted [1]. 

In essence, you seem to be saying "the constitution should be
interpreted in whatever manner allows the vote to come up with the right
answer". Which is irrefutable (by definition the right option is chosen
by every vote count, which is essentially the perfect voting system),
but doesn't seem like a good idea.

Cheers,
aj

[0] In the same way that saying ``Oh, this sentence doesn't make sense
    with the word "fish" there, it should be interpreted as having the
    word "antidisestablishmentarianism" there instead'' doesn't seem
    reasonable.

[1] Suppose you have:
	35 ABC
	30 BCA
	25 CAB
    Then to work out if A dominates B, you know that:
	60 voters prefer A to B
	30 voters prefer B to A

	35 voters prefer A to C
	25 voters prefer C to B
	65 voters prefer B to C
	55 voters prefer C to A
    If you're going to consider transitivity, are you then meant to count
    the transitive votes somehow, and say something like:
	60 + min(35,25) = 85 votes "strictly" prefer A to B
	30 + min(65,55) = 85 votes "strictly" prefer B to A
    ? Should you use min() there, or max(), or an averaging function? If
    there are multiple paths, what should you do then? What does it mean
    to say 170 votes expressed a "strict" preference between A and B
    when there were only 90 votes in the first place?

-- 
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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