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



On Wed, Nov 29, 2000 at 09:05:09AM -0500, Raul Miller wrote:
> > Please reread: [...] for the explanation.
> Eh?  All I see is that my proposal is less ambiguous than the current
> constitution for this kind of case.
>
> [Those specific messages are where we were talking at cross purposes --

*sigh*

I'll repeat myself then.

Taking the obvious, verbatim, `I have no initiative of my own, nor
any idea what's gone before' interpretation of the constitution, then
the non-free problem would be dealt with as follows:

	* An initial vote, with no supermajority or quorum requirements,
	  on whether the resolution takes the form "A: The developers
	  resolve to remove non-free from the social contract, etc" or "B:
	  The developers resolve to move non-free to a separate server"
	  or whether further discussion should take place.

	* Depending on the result of the initial vote, either:
		+ further discussion would take place
		+ if A won the initial vote, a final vote would take place
		  with options Yes/No/Further Discussion, with (let us assume)
		  3:1 supermajority requirements, and a quorum of 3Q.
		+ if B won the initial vote, a final vote would take place
		  with options Y/N/F with a mere majority requirement, and
		  a quorum of 3Q.

The first vote might end up going like this:

	60 voters vote ABF  (people who want to get rid of non-free)
	40 voters vote BAF  (people who want to de-emphasise it somehow)
	10 voters vote F    (people who like non-free how it is)

Without quorum or supermajority requirements coming in to play, this
results in A dominating B, 60 to 40, and both A and B dominating F 100
to 10, so A wins. The second vote, presumably results in:

	100 votes Y
	10 votes N

and A wins with a clear supermajority.

With your rule, you instead just have an initial vote, with the initial
pairwise preferences:

	A dominates B, 60 to 40
	A dominates F, 100 to 10
	B dominates F, 100 to 10

which are then scaled with supermajority requirements to be:

	B dominates A, 40 to 20
	A dominates F, 33.3 to 10
	B dominates F, 100 to 10

and B wins by dominating all other options.

If the majority of people prefer option A to option B, and a supermajority
of people are willing to accept option A, I don't see any reason to do
B instead, merely becase A doesn't have a supermajority over B as well.

Scaling only in comparison to "Further Discussion" does not have this
problem.


The other, independent, question is what to do when the Condorcet winner
doesn't meet it's supermajority requirement. That is, a simple majority
of people prefer some particular option to all others, but there isn't a
supermajority that's willing to accept it. There are two ways of handling
it I can think of: either try the next preferred option, or go back to
further discussion.

My initial impression was that further discussion was the safer choice,
but I'm not convinced of that, at the moment.

Something akin to:

	* Scale pair-wise comparisons against further discussion according
	  to each option's supermajority requirement
	* Find the Smith set
	* If the Smith set is empty, or contains the default option, the
	  default option wins
	* Otherwise the winner is determined by applying STV to the Smith set

would allow you to fall back to some less preferred choice that does
meet its supermajority requirements, if that's appropriate. I'm not
sure what the exact effect of the third point (either using it as such,
or replacing it with some other rule to remove options that don't meet
their supermajority requirement) would be in general.

> > A much fairer supermajority requirement would simply be:
> > 
> > A.6(3) A supermajority of N:M for an option A is met when the number of
> >        votes ranking A higher than the default option, divided by N is 
> >        greater than than the number of votes ranking the default option
> >        higher than A.
> So, a 3:1 supermajority is required to pass a constitutional amendment,
> 101 ballots YES:NO
> 100 ballots NO:YES
> [No one wants to talk about it any more, and the results are almost
> even.]

Those aren't realistic votes: there's no default option listed, which there
must be.

One possible interpretation would be:

	101 ballots YNF
	100 ballots NYF

in which case Y wins, with a supermajority of 201 to 0.

Another would be:

	101 ballots YNF
	100 ballots NFY

in which case Y loses because 101:100 is not a 3:1 supermajority, and either
the vote defaults to further discussion, or falls back to N (preferred 201
to 0 over F).

> Now, if you're trying to say that my version has some ambiguity about
> it, well.. that might be true.  But I'm not quite seeing it, yet.

No, your version has results inconsistent with the system roughly as it
stands. At worst, mine is overly encouraging of further discussion.

I should further note that this matches how the system described by the
constitution essentially behaves:
	- An initial majority makes the resolution take the form of Y
	- That majority can then vote YFN, and, if it's enough of a
	supermajority the vote will pass, if not, it will devolve to
	further discussion and they'll get a second chance.

> > However it's not clear what should happen when the clear winner of
> > a set of options doesn't meet its supermajority requirement, yet
> > a loser (with a different supermajority requirement) does. It's
> > similarly unclear what should happen if the winner doesn't meet its
> > supermajority requirments, but some other member of the Smith set
> > does.
> My version makes that clear. 

It's quite clear what *does* happen. It's not clear what *should* happen.
It's easy to pick an answer from the air, it's harder to see if that
answer is actually going to be helpful in the context of Debian.

> And, I'll assert: it's reasonable
> to interpret the current constitution in that fashion.  

As long as you ignore or muddy all the specifics about supermajorities
only applying to the final vote, and the final vote having exactly
the options Yes, No and Further Discussion, and if you furthermore
aren't worried about having the results of votes change depending on
the procedure used to conduct them (rather than, say, the merits of the
options or the preferences of the voters).

> > I would suggest something to the effect of:
> > 	* Reduce to the Smith Set
> > 	* Eliminate options that don't meet the supermajority requirement
> > 	* If none left -> default option wins
> > 	* If one left -> it wins
> > 	* If many left, use some tie-breaker, eg STV, Tideman, Schulze
> This directly contradicts the last sentence of A.6(7).  Do you have some
> reason for this contradiction?

A.6(7) is written assuming supermajorities only apply to the final vote,
and that the final vote only has options that are either "Make the change"
or "Stick with the status-quo". If you violate that assumption, A.6(7) is
no longer an appropriate method of handling supermajorities.

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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