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



Damn, I've got to stop postponing and forgetting these things.

On Fri, Dec 01, 2000 at 06:08:50AM -0500, Raul Miller wrote:
> > I suspect we've also agreed that the Condorcet winner (if there is
> > one) should always win. And we seem to have agreed that the winner
> > should be from the Smith set, although that's apparently considered
> > debatable amongst the pairwise voting cognescenti.
> I'm uncomfortable saying if I've agreed to this.  The Smith/Condorcet
> criteria that Buddha posted is not something I've agreed to.

The Condorcet criterion says that if there's a single option that pairwise
beats every other option, it should win (assuming there's no supermajority
requirement, and quorum is met).

It's what the current A.6(2) and A.6(3) are for. (The Condorcet criterion
doesn't say anything about the ambiguous cases we've been talking about)

> > There are two reasonable ways of treating supermajorities, that I can
> > think of:
> > 	a) A supermajority of developers believe this option is acceptable.
> > 	b) A supermajority of developers support this option above all
> > 	   others.
> > I believe (a) is the better case, and I think it's essentially what the
> > N+1 scheme described in the constitution achieves. From some of your
> > mails, I'm lead to believe you might prefer (b).
> Er.. you've lost me here.
> (*scratches head*)

I, uh, don't see how... [0]

Ignore all the procedures established in the appendices, and just
note that a consitutional amendment requires a `3:1 supermajority'
to succeed. I can only see two things this can be attempting to require:

	* For every person who wouldn't accept it as a resolution, there
	  must be three who will for it to pass.

	* For every person who would prefer some other solution, there
	  must be three who think this is the best solution possible.

The way the N+1 style of voting behave, you're effectively requiring the
former.

The way your proposed clarification behaves, you're requiring (I think)
that if you have an option, S, requiring a supermajority, that it be
preferred by a supermajority over every option, A, B, C that don't require
a supermajority (of which "No" and "Further Discussion" are examples,
but others are possible too). I don't think this is particularly useful.

> Ok, I think you're basing this off of my earlier response to a specific
> example where I thought, at the time, you were talking about a vote
> which mixed a supermajority option with a non-supermajority option.

That's the main (sole?) example where it behaves differently to the
other methods.

> > (b) isn't quite what your system does, though (aiui). If you consider
> > the Manoj and Branden's proposed vote, we might end up with people holding
> > preferences like:
> > 	120 people prefer M, B, S, F  (Manoj, Branden, Status-Quo, F.Disc)
> > 	100 people prefer B, M, S, F
> > This means that the ratio between M and B would be only 6:5, rather than
> > 3:1, so presumably neither should win (that's what (b) would imply to me)?
> 
> If we're talking about *my* interpretation of what the constitution
> is saying, and what it's trying to say, and *my* understanding of that
> particular vote.  And, if we agree that a 3:1 supermajority applies to
> changing the social contract:

(By Manoj's and Branden's proposals, I mean the amendments to the
constitution to provide a procedure for changing the constitution,
not any of the non-free votes themselves, since both would change
the constitution if accepted, both require a supermajority to pass)

> The way I see it, when determining which votes Dominate which others,
> votes which prefer an option with a supermajority are reduced to an
> appropriate fraction (in this case 1/3).  But, 40 Dominates 33 1/3,
> so M wins.

Yes, that's how I understand your interpretation too; it just doesn't
seem sensible to me to have the voting system be biassed towards options
that don't require a supermajority (or require a lesser one).

That is, given two options, A and B, both of which pass quorum, both of
which are acceptable to their respective supermajorities, then the one
that's picked should be the one that's preferred by more people, simple
as that.

There's an obvious justification for choosing A: more people prefer
it. I can't see one for being biassed towards B (anywhere up to a 2.99:1
majority for A:B would still make B the winner), merely because it's
easier, constitutionally, to implement.

> [Also, 73 1/3 -- the total number of votes for M, exceeds
> quorum of 37, so there's not a problem with not enough people voting.]

Eh? Supermajorities and quorum requirments are usually distinct,
aren't they?  You'll note the constitution currently says ``For votes
requiring a supermajority, the actual number of Yes votes is used when
checking whether the quorum has been reached.'' So there's 220 votes
"for" M, as far as quorum is concerned, unless I've missed something.

Did any of that make any more sense?

Cheers,
aj

[0] If it's just the terms, I'm using N+1 / "the current scheme" to talk
    about the method where we first vote (using simple majority and
    no quorum) on what the form of the amendment is, and we then vote
    on whether it's passed or not, with options Y/N/F. I'm using "your
    scheme" or "your interpretation" to refer to the method you describe
    of handling all the options on a single ballot, simply by ordering the
    options [1]. I'm using "my scheme" to refer to the method I describe
    of doing the same thing, but which certainly isn't supported by the
    constitution as it stands.

[1] As opposed to a single ballot that lets you say:

	[2] Remove non-free [NYF]
	[1] Support non-free [YNF]
	[3] Further Discussion

    which is effectively just incorporating the N+1 votes into a single
    message (which is how I'd have interpreted A.3(3)).

-- 
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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