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



On Tue, Dec 05, 2000 at 02:25:26PM -0500, Raul Miller wrote:
> On Tue, Dec 05, 2000 at 05:58:47PM +1000, Anthony Towns wrote:
> > It'd have a substantial effect if a supermajority was required: if 60
> > of 100 people preferred your second preference, and voted Yes/Further
> > Discussion/No, while 40 people voted Further Discussion/Yes/No, the
> > vote would fail, and you'd be back at the start again.
> > Personally, I doubt this would do you any good: everyone's already
> > likely to have decided on their preference, so you may as well take
> > the compromise rather than trying again and again and again.
> Depends on how I felt on the issue -- I rate things based on my
> preferences, not based on some abstract expectation about other people's
> preferences.

Certainly, you can vote however you like. But be aware that other people
might _not_ want to hinder their second preference just because they've
got no chance of getting their first preference.

> > > > Similarly, in the counting scheme I proposed, you'd vote:
> > > Er.. I've been trying to find your proposal.  
> > Let me restate it, then.
> > A single vote is called, with each alternative option in its full form
> > as an option, along with a "Status-quo" option. Developers submit ballots
> > with each option numbered according to their relative preferences.
> First note: you don't attempt to distinguish between "this is worth
> redoing" and "this is not worth redoing", in your "status quo".

As I've said, I don't see any benefit in doing it. Whichever's selected,
as far as the constitution's concerned, you'll get the same result (ie
nothing will change). As far as people are concerned, I don't believe
it's appropriate to try to silence discussion by a vote. I'll also note we
haven't consistently distinguished between "no" and "further discussion"
in past votes.

> > Votes are counted by first counting how many individual votes rank one
> > option above another option, and a matrix is formed, where M[a,b] is the
> > number of votes that rank option "a" over option "b", and M[b,a] is the
> > number of votes that rank option "b" over option "a".
> Second note: this mechanism won't work for STV (which you suggest using,
> below).

Eh? The matrix won't help you working out STV, but so what? You can just
ignore it later, if you want to.

> > An option has quorum if the number of individual ballots mentioning that
> > option is greater than or equal to the quorum required.
> > 
> > An option, a, meets a supermajority of N:1 if M[a,S] > M[S,a] * N, where
> > S is the Status-Quo option.
> Third note: this is something we're still debating.

Yes, and I'm using this scheme as an example of a single-ballot
preferential system that has the properties of supermajority I
describe. That's its whole point.

> > The vote is counted by first finding the Smith set, then eliminating
> > all options from the Smith set that don't make quorum or their
> > respective supermajority requirement. If no options remain, the
> > default option, Status-quo wins. If many options remain, they're
> > chosen amongst by using STV, or something similar.
> It's interesting that you're throwing quorum into the middle of the
> vote instead of at the begining or the end.  I'm curious: do you
> have any describable reason for this choice?

If you throw it in at the very end, you don't have an opportunity to
select an alternative winner. If you put it at the start, I *believe*
it tends to encourage insincere votes unnecessarily.

> > This isn't entirely ideal: it'll select the status-quo more often
> > than is probably desirable, but otherwise it's fairly expressive, and
> > doesn't weight any preferences any more than others wherever possible.
> I presume, here, you're talking about the case where we're picking between
> an option with a supermajority requirement and a case where we're not.
> And, I presume that a bias towards options with supermajority requirements
> is something that you don't really care about.

_Huh_?! Where did that come from?

The only biasses in the above are towards options that pairwise beat other
options, and towards the status-quo options (in the event others don't
meet their supermajority requirements).

That is there isn't a bias towards options with supermajority
requirements.  I don't care about problems that don't exist, if that's
what you mean, I guess...

Let me try a different explanation for what a "bias" is.

Suppose you had a vote amongst only two options, Foo and Bar, that went
something like:
	60 votes F over B
	40 votes B over F
then you would expect F to beat B, right? And if the vote went the other
way,
	60 votes B over F
	40 votes F over B
you'd expect B to win. That would be a completely unbiassed vote.

If, instead, you had a "Yes" and a "No" vote, and "Yes" required 3:1
supermajority to win, then clearly:
	60 votes N over Y
	40 votes Y over N
would be a clear win for N, but then
	60 votes Y over N
	40 votes N over Y
would also be a win for N. So any way of counting votes like this is
biassed towards a "No" answer. Which is justifiable, because things like
changing the constitution or the social contract shouldn't be done on a
whim. Doing what we've always done is at least somewhat effective, you need
to have a strong, convincing argument to take the risk and change. It's
entirely fair and reasonable to be biassed towards what we're already
doing, and to encode that into the way we vote.


What you're also saying, though, is that given three options, A, B and
Status-Quo, say, where A requires a 3:1 supermajority, but B doesn't, that
if the vote went like:
	60 votes B over A over S
	40 votes A over B over S
then B should clearly win (which I agree with), but also, if A and B were
swapped, so that you had:
	60 votes A over B over S
	40 votes B over A over S
that B should still win. That is, you're biassed towards accepting any
option that doesn't require a supermajority over any that does.

And while I can see the point of this for favouring the status-quo
(either expressed as "No" or "Further Discussion" or "Status-quo")
can't see any useful reason why we should be *that* scared of changing
the constitution, that we should always favour *anything* else.


I would like some justification of choosing B over A, when most people prefer
A. I can think of one when B means don't change *anything*, but not when
it can involve, say, trashing the FTP site, forbidding any new maintainers
to join, throwing out members randomly, or whatever else.


If we had no choice about it -- if there were *no* method of handling
a supermajority requirement without biassing towards B, say -- I
could understand it, but we *do* have a choice. And yes, I'd like a
justification beyond "Oh, thats how I read the constitution", at least
in part because that's not even remotely how I read the constitution.

> > Okay, let me flesh out how I'd conduct a vote that has multiple related
> > alternatives that should be decided on at once.
> > First, since the constitution doesn't say anything about merging distinct
> > votes, I'd require the later alternatives to be phrased as amendments to
> > the first alternative presented, even if this essentially implies ignoring
> > the original proposal and rewriting it from scratch.
> Ok.
> > Once all the alternatives are assembled, and the proposers/sponsors have
> > called for a vote, I'd first form a ballot under A.3(1) that looked like
> > 	[ _ ] Original proposal
> > 	[ _ ] First amendment
> > 	[ _ ] Second amendment
> > 	[ _ ] Third amendment
> > 	[ _ ] Further discussion
> > (assuming there aren't any sensible combinations of two or more amendments).
> An important assumption.  

A simplifying assumption, not an important one. I could instead have just
listed a single amendment and the original proposal and there'd have been
no question.

> Also, if you're talking a constitutional ballot, I think you need an
> explicit "no" option, for people who don't want the original proposal
> with or without any amendments, and don't want to discuss it further.

No, section A.3(1) sets out the options to be included on the initial
ballot, that is all sensible combinations of amendments and options,
and an option Further Discussion. If people want to vote "No", they have
to do so in the final vote (A.3(2)), not the initial vote/s.

> > Under A.3(2), I'd be required to issue a ballot that allowed people to choose
> > amongst:
> > 	[ _ ] Yes
> > 	[ _ ] No
> > 	[ _ ] Further discussion
> > to whichever of the above won.
> Yes.

> > Under A.3(3) I'd be permitted to issue these ballots in a single
> > message, as long as each voter could choose a different final vote no
> > matter which original option won.
> A.3(3) says: 
>     3. The vote taker (if there is one) or the voters (if voting is done
>        by public pronouncement) may arrange for these ballots to be held
>        simultaneously, even (for example) using a single voting message.
>        If amendment ballot(s) and the final ballot are combined in this
>        way then it must be possible for a voter to vote differently in
>        the final ballot for each of the possible forms of the final draft
>        resolution.
> I believe the case you're talking about is where the amendment
> ballot(s) are combined with the final ballot.  

What it says is that the ballots may be `held using a single voting
message', not that the ballots can be combined into a single ballot.
It further requires that the voter must be able to express a different
vote in the final ballot for each of the possible forms of the final
draft resolution.

That is, they must first be able to rank the various options for how
the final form of the resolution may look, and then, depending on the
result of that vote, must be able to choose their ordering of Yes,
No and Further Discussion on the final vote.

> > I'd this make a message that
> > looked like:
> >       ,-- Preference for this option to win
> >      |     ,-- Preference for "Yes" in the final ballot if this option wins
> >      |    | ,--- Preference for "No" ...
> >      |    || ,---- Preference for "Further Discussion" ...
> >      V    VVV
> >    [ A ] [_B_] Original proposal
> >    [ _ ] [_C_] First amendment
> >    [ _ ] [_D_] Second amendment
> >    [ _ ] [_E_] Third amendment
> >    [ _ ]       Further discussion

(identifiers A,B,C,D,E added)

This form of ballot achieves that by allowing you to first consider the
preferences stated by each voter in the A vote, then, depending on which
option won, counting the votes made in only one of the B,C,D or E options.

> > Which I'd then issue. When counting, I'd first use the preferences in
> > the first column, then depending on which option won, the preferences
> > in the second column to work out the outcome of the two simultaneously
> > held votes.
> I don't see that this "secondary preference" info is meaningful.

Of course it is. You could vote, say:
	[1] [312] Modify social contract and remove non-free
	[3] [312] Continue supporting non-free but try to distance it
	[2]       Further discussion
in the hopes that if the first option wins, it'll be voted against with
a substantial majority and never be brought up again, but if it doesn't
win, then the second option might actually have a chance at winning, so
try not to let it go to a vote ever. This style of voting was advocated
during the non-free vote discussion.

Alternatively, you could vote:
	[1] [132] Modify social contract and remove non-free
	[3] [132] Continue supporting non-free but try to distance it
	[2]       Further discussion
in the hopes that non-free will successfully be removed, and that the
stupid lame-ass "compromise" didn't get taken, but if there's no choice,
better to compromise than not.

And in any event, it doesn't matter whether it's meaningful, it's required
by the constitution.

An alternative, more verbose but otherwise equivalent, way of doing it
would be a single message that read like:

	Please rank these alternatives, in order:
		[   ] Original proposal
		[   ] First amendment
		[   ] Second amendment
		[   ] Further discussion

	If the Original proposal wins the vote, how do you wish to rank
	the following alternatives:
		[   ] Yes: pass original proposal
		[   ] No: don't pass original proposal
		[   ] Further disucssion

	If the First amendment wins the vote, how do you wish to rank the
	following alternatives:
		[   ] Yes: pass original proposal modified by first amendment
		[   ] No: don't pass original proposal as modified by first
		          amendment
		[   ] Further discussion

	If the Second amendment wins the vote, how do you wish to rank the
	following alternatives:
		[   ] Yes: pass original proposal modified by second amendment
		[   ] No: don't pass original proposal as modified by second 
		          amendment
		[   ] Further discussion

> If it's reasonable to vote:
> > (A valid vote would be something like:
> >    [ 3 ] [213] Original proposal
> >    [ 5 ] [312] First amendment
> >    [ 1 ] [132] Second amendment
> >    [ 2 ] [132] Third amendment
> >    [ 4 ]       Further discussion
> > )
> This doesn't even make sense. What does it mean to rank "no on the
> unammended proposal" as your third choice, and "yes on the proposal
> amended by the second amendment" as the first choice?  

Only one of the secondary preferences is actually ever considered. Which
one is decided once the primary preferences of all the voters have
been tallied.

> > That's how I would interpret A.3(1..3) anyway.
> But.. uh.. I don't see that you've pointed out anything in the 
> constitution that favors your interpretation above mine.

Well, of course not. I have no idea what you would consider a valid
basis for interpretation of the constitution. You seem to be quite happy
to say things like "Well sure, it doesn't say you can combine separate
votes in a single ballot, but it doesn't say you can't, so why not?",
and it doesn't seem much of a step from that to "Well sure, it doesn't
say you can count the votes like this, but it doesn't say you can't,
so why not?", which seems like it essentially means anything you do with
the votes would be valid. I'm sure you don't go so far as to think that,
but I can't tell where you'd draw the line, and I don't see how I could
possibly guess. I could just ask you, but if I'm going to do that, I might
as well just accept you as an Oracle, and take your word as gospel anyway.
And there is, at least, constitutional support for doing _that_.

So I don't really see the point of this digression, but you did ask.

> I think we need to talk about what it means to have distinct options on
> the ballot.  [I recognize, from your "Status-Quo" option, that you're
> not talking about the constitutional mechanism, but are talking about
> some hypothetical mechanism.  But, from your explanation of how you
> understand the constitution, I think we need to talk a bit more about
> the difference between independent alternatives and distinct choices.
> Wait until we've agreed on the more fundamental concepts before you
> teach me about your view of supermajorities.]

Considering we've already attempted to have a vote that (was deemed
to) require a supermajority, and had two options on a single ballot
with different supermajority requirements, yet we've never had a single
ballot with independent alternatives, I'm inclined to disagree with your
assertion as to what's more fundamental.

I suspect deciding fairly amongst a number of independent options will
probably be as difficult to understand as the stuff we've discussed so
far, so I'm inclined against wandering into that fray and having to come
back and start this all over again.

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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