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



On Thu, Dec 07, 2000 at 12:45:24AM -0500, Raul Miller wrote:

[Status-quo versus Further Discussion and No]
> I still maintain there's a difference (because the intent of the
> developers is more obvious), but you're right about the minimum discussion
> period.

Okay, let's ignore what I've said previously about introducing more facets
and go into this a little deeper.

In our past votes, we've variously had:

	Constituion: Yes/No/Further Discussion
	Election 1: [nominees] + None of the above
	Logo License: Single/Dual/Further Discussion
	New Logo: [submissions, including current logo] + Further Discussion
	Swap Logo: For/Against/Further Discussion
	Election 2: [nominees] + Further Discussion

and in our current pending vote we've currently got two ways of modifying
the constitution, and further discussion (with no "No" option at all).

Note, for example, that after the new logo vote, even though further
discussion didn't win, we were quite happy to continue discussing the
matter and change the logo a bit (although it probably would've been
easier to just include the swapped swirl in the "New Logo" vote).

So given that in the past we've not really had any benefit from the
distinct options (and often haven't even bothered having distinct
options), and that it doesn't make any actual difference in the result
(if enough interested people want to keep discussing the matter and make
a new proposal, they can; if no one's interested in discussing more,
they don'thave) I really don't see any benefit in having separate options.

For reference, the things I can think of that need
fixing/disambiguating/discussing/whatever:

	* How to resolve the vote when you don't have a Condorcet winner
	  (working assumption: find the Smith set and apply STV to it)

	* How to conduct a vote in a single ballot, as simply and fairly
	  as possible
	  (working assumption for votes where there are no independent
	   options: allow voters to rank each option as well as either
	   Status-Quo, or (Further Discussion and No))

	* What to require for an option to meet quorum
	  (working assumption: count the number of votes that mention
	   the option, and compare against quorum)

	* What to require of an option for it to meet a supermajority
	  requirement

	* How to formulate a ballot / set of ballots to decide amongst
	  related but independent options

	* Whether to use a single Status-quo option or both Further
	  discussion and No on each vote (or what).

> > > > > > 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).
> > > Supermajority options which don't meet supermajority requirement but
> > > do meet a lesser majority requirement will (by definition) pairwise
> > > beat other options [which don't have that requirement].

Let me start from the top, perhaps.

There's no such "majority requirement", though, per se. This is why I avoided
answering when you asked this before. Instead, preference for majority support
is just handled by how you count votes. For example, if you have a vote:

	30 ABC
	35 BCA
	40 CAB

then none of these options meet its majority wrt *all* other options
(75/105 people prefer C over A, 70/105 people prefer A over B, and 65/105
people prefer B over C). But we choose a winner anyway by using STV
(A disappears, and B wins with 65/105 votes).

What you could end up with (using my scheme) is a vote that goes
something like:

	60 ABS
	40 BSA

where A requires 3:1 supermajority. You get:

	A dominates B 60 to 40
	B dominates S 100 to 0
	S dominates A 40 to 20 (reduced 3:1)

which would be a circular tie. For the moment, I'm just declaring that S
(the Status-quo) wins (by claiming S wins whenever it's in the Smith set),
but it would also be possible (and probably reasonable) to make B win (by
having dropped A for not meeting its supermajority right at the start).

Now, if we go back to:

> > > > > [...] And, I presume that a bias towards options
> > > > > with supermajority requirements is something that you don't
> > > > > really care about.

then I'm afraid I still don't know what you're talking about. There's no
way of voting that would have an option requiring a supermajority win,
that wouldn't have had a non-supermajority option also win if the roles
were switched.

> I'll agree that quorum biases against any change (when there aren't
> enough voters).  I'll also note, here, that quorum is different from
> supermajority.

Right. I'm using "bias" as a general term to analyse the effects of any
extra requirements we might add beyond just saying `take the Smith set,
apply STV'.

> I'll only agree that supermajority biases against certain forms of
> change (changing the constitution, for example).

Well, yes, but I'd rather consider biasses in a pairwise manner. That is,
that when considering any two options, A and B, you're biassed towards
the one that doesn't require the supermajority.

It's more precise, and thus more open to analysis. It's not necessarily
wrong, though.

Yet. ;)

> > > I can accept this definition, but using the terms in the way you've
> > > indicated: I don't see that "taking the bias out of the voting"
> > > system means anything other than "taking the effect of supermajority
> > > out of the voting system".
> > It'd also take quorum out of the voting system too.
> Well, it could mean that, but I didn't think that that was what you were
> arguing for.

No, it's not, but I'm not trying to take the effect of supermajority
out of the voting system.

What I'm trying to do is say that the best interpretation of
"supermajority" is to only use it when comparing an option requiring a
supermajority and an option that changes absolutely *nothing*.

> > Arguably, it'd also take tie-breakers out of the vote, also.
> That's really reaching.

Yes, well, I *did* say "arguably"...

> > It's irrelevant. I'm not trying to remove all bias from the vote, only
> > ones that don't have a reasonable justification.
> What do you consider "a reasonable justification"?

Well, any justification would be a start.

> > _Why_ do you think it's proper or justified or reasonable to be
> > biassed towards B over A? What's the motivation for doing this? Why is
> > B better than A? Why is A more of a risk than B?
> Let's say that we're still talking about a situation where B has no
> supermajority requirement because it does not modify the constitution, and
> A has a supermajority requirement because it modifies the constitution.
> Supermajority is blind to the almost all of the semantics of a change --
> all it cares about is whether or not the requirement is there -- whether
> the constitution is being modified.

Okay, so far you haven't distinguished between the various ways of handling
a supermajority.

> So, a vote in favor of A is a vote in favor of modifying the constitution,
> while a vote in favor of B is a vote in favor of not modifying the
> constitution.

This, however, doesn't make any sense. Again, there is no such thing
as a vote that is simply "for" or "against" modifying the constitution,
unless the vote simply has "yes" and "no" options.

This isn't a plurality system. It's a system where we simply rank
preferences.

It's possible for me to not be against modifying the constitution,
but to think there's a better way of doing things. A vote that rates my
preferences can capture this, easily, while still being able to express
an explicit desire that changing the constitution would be a bad thing
for someone else.

So no, I don't accept the implication that a vote where X isn't your
first preference should be considered a vote "against" X.

> For some reason, you seem to want to argue that a vote which prefers
> B (not modifying the constitution) to A (modifying the constitution)
> should count in favor of modifying the constitution unless "do nothing
> at all, not even B" is ranked higher than A.  I can understand *that*
> this is what you're arguing, but I've yet to see any convincing argument
> that this is a good thing.

Because it can represent the preferences of a voter who thinks "Well,
changing the constitution (A, say) is a bit drastic, but we should move in
this direction; so ideally I'd rather the compromise (B), but I don't mind
if we go all out", because he could vote "BAS", and a voter who thinks
(like you apparently might) "Changing the constitution is too drastic,
we have a compromise, we have to use that instead" could express that
by saying "BSA", and someone who'd rather go all out, but will accept
the compromise if necessary can express *that* by voting "ABS".

Your system doesn't allow someone to express a weak preference for a
compromise without having their vote count, essentially, for three.

> > Note that biassing everything over A isn't the only way of handling a
> > supermajority (and isn't even a common or usual way --- you're welcome
> > to cite one other instance of _anyone_ doing it this way, though),
> > you can simply require a supermajority of people preferring A to the
> > status-quo (by literally having a "Status-quo" option, or by using
> > "No" or "Further Discussion" or both of them as a replacement).
> This looks like what you're advocating, but I still don't see a convincing
> reason to believe that "do nothing" is any less of a change to the
> constitution than "option B" in the above example.

Certainly it's not as much of a change to *the constitution*, but that
doesn't mean it's any less a *change*.

Again, what is so vastly horrible about changing the constitution that
*anything* should be done instead of it?

> > On that grounds, consider a vote that goes like:
> > 	200 A over B over F over N
> > 	 70 B over A over F over N
> > and having B win. Do you really think the 200 people are going to be
> > happy to be overruled by a minority of 70, who *didn't even dislike*
> > option A?
> They disliked it enough to prefer option B.

That doesn't mean they actually disliked it however.

If they really did detest the option, they could have voted B over N
over F over A, and there'd have been no question.

> > > > > > 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.  

If you would rather, "an assumption no more important than that there were
three amendments to the proposal rather than four, ten or one".

> > > > 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.
> > > Given your interpretation -- that a person could be against the
> > > original proposal but for the amendment, I'd still have a serious
> > > question.
> That wasn't the form of the question.  The question is how can you have
> an amendment without having an original proposal to amend?

Eh? Are you just saying it would've been clearer if I'd said:
	[ _ ] Original proposal
	[ _ ] Original proposal after having the first amendment applied
	[ _ ] Original proposal after having the second amendment applied
	[ _ ] Original proposal after having the third amendment applied
	[ _ ] Further discussion
?

> Also, A.3(2) only applies "When the final form of the resolution has
> been determined".  It doesn't make sense to apply A.3(2) when there
> remain distinct possibilities for the final form of the resolution.

A.3(3) then overrides this by discussing how the amendment ballot(s)
and the final ballot can be combined into a single message.

> > The constitution never says that multiple ballots can be combined into
> > a single ballot, merely that the ballots can be "held simultaneously,
> > even using a single voting message".
> I guess I see what you're saying here -- but I feel that your conclusion
> is completely nonsensical, and therefore an incorrect interpretation.

Using a similar basis, I suppose you would declare "This sentence is
false" to have a completely meaningful interpretation. ("Interpreting
it to refer to *itself* is just completely nonsensical so therefore
incorrect, so when it says "this" it actually refers to some other clause,
namely this one over here").

> > > Now, as I understand it, your feelings about this ballot are:
> > > [1] It's unconstitutional,
> > ...because it has no basis in the constitution.
> I've yet to see you propose a more sensible interpretation for combining
> amendment and final ballots.  I'll stick with mine until then.

So we can drop this digression?

> The constitution is specifying the properties of that voting message.
> You seem to want to use it as some kind of procedural statement -- but
> in doing so you seem to be failing to be fulfilling all the requirements.

Well, the section is titled `A.3. Voting procedure' so it doesn't seem
completely unreasonable to take it as "some kind of procedural statement".

> > Because the constitution specifically requires that ``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'', even though
> > only _one_ of the possible forms of the final draft resolution will
> > actually win the initial vote.
> The constitution doesn't say that you create a final ballot where
> some of the individual options are themselves unresolved ballots.

No, it doesn't it says you create a final *message* that includes many
ballots.

It seems a reasonable interpretation to me that a single message can contain
many distinct ballots, eg:

From: gecko@debian.org
To: debian-vote@lists.debian.org

Ballot 1:
	[ _ ] Kick Raul in the Nutz
	[ _ ] Kick aj in the Nutz
	[ _ ] Kick both Raul and aj in the Nutz
	[ _ ] Don't kick anyone in the Nutz
	[ _ ] Further discussion

Ballot 2: On the matter of requiring a bug to be fixed and closed by the
          poster for each post made to -vote:
	[ _ ] Yes
	[ _ ] No
	[ _ ] Further discussion

(Now, how many smart-alecs do you reckon will second these?)

If the constitution had meant a single ballot should be constructed that
suffices for the A.3(1) and the A.3(2) ballots both, it would have said
so. It didn't. Instead it said they can be combined in a single message
(in spite of the fact that the final form of the draft resolution couldn't
possibly be known for the final vote in this case), and then discusses
how to cope with the fact that the final form of the draft resolution
*isn't* known by then.

> > > > 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.
> > > Nope.
> > > The constitution says: 
> > >        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.
> > > You're talking about creating a final ballot for rating each of a
> > > set of possible *ballots*. You're supposed to be creating a ballot
> > > for rating each of the possible *resolutions*.
> > No. The form of the *ballots* are defined by A.3(1) and A.3(2). I am
> > simply combining these ballots in a single message.
> Actually, you're creating a new "ballot of ballots" in the process.

Only if you equate "email containing a ballot" with "ballot". Which I can
see a justification for by looking at dict, but I think the constitution
is reasonably clear in distinguishing the two.

> One which seems to have no constitutional basis whatsoever [where you
> give preference to one amendment ballot preference over another and over
> the original proposal].

Again, you're giving a preference for the final form of the resolution
(which, yes, dictates what you'll be voting on in the final ballot too),
and then giving preferences to Yes, No and Further Discussion in the
final ballot, depending on which form the resolution finally takes.

> And, I still don't see how, using your interpretation, the voter could
> vote differently in the final ballot for each of the possible forms
> of the final draft resolution.

If further discussion fails, the only possible forms of the final
resolution are the three/four listed, for which you could express
different preferences quite explicitly.

If you have a more general case, you're welcome to present it.

> > > > > > 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. 
> > > *blink*
> > > > I have no idea what you would consider a valid basis for
> > > > interpretation of the constitution.
> > > I guess I'd think that the english language would be a valid basis
> > > for interpretation of the constitution.
> > Whatever.
> I notice that you elected to discard my criteria for judging a
> valid interpretation.

Should I compliment you on your powers of observation? You might as well
have just said ``I claim the moral highground, and if you don't like it,
I'll be a grammar/definitions pedant until you bleed''.

> > Please don't bother poring over the constitution and finding that,
> > say, A.3(1) says `combinations of amendments and options', and arguing
> > how clearly it's differentiating amendments and options, and how thus
> > options must mean other proposals, because there's nothing else it can
> > mean, and whatever else. I really don't care at this point.
> I know that A.3(1) doesn't say anything of that sort.

Eh? It most certainly does refer to `combinations of amendments and
options'.

> > Your definition of `using English as a basis for interpretation' and
> > mine are wildly different and probably irreconcilable.
> I'd like to believe otherwise.

I believe, first and foremost, that we should read the constitution
in as if it were written to be straightforward. We shouldn't look for
subtle shadings of the word "strict", say, or try rearranging the order
of clauses to see what result that has.

You seem to believe, first and foremost, that the constitution makes
sense, and if the straightforward reading doesn't support that then the
straightforward reading is wrong.

> > Can we just focus on talking about what would make a good and fair and
> > efficient voting system for Debian?
> Only if we can use English in a mutually understandable fashion.

In a dialogue, subtle shadings can be questioned ("When you say this,
do you mean to imply that...") and they can be cleared up. When you've
got a set document to interpret, you can't do any such thing.

> I have reason to believe that Darren would be available, if needed.
> I have reason to believe that he's waiting for the discussion to draw
> to a close, and for (if nothing else) Manoj+Branden to indicate what
> form they want the ballot to take.

I hope he's not waiting for _this_ discussion to close? Discussion
actually relevant to Manoj/Branden's proposals seems to have died about
a month ago.

> > No, isn't it obvious? I'm trying to destroy Debian from within, by
> > ensuring that no decisions can be made and distracting Raul from
> > doing his other jobs and thus ensuring the continued decline of
> > standards and quality and consensus. I'm completely unreasonable, and
> > am motivated by bad intentions, just like Branden likes to assert.
> And here I thought it was just that your feelings were hurt.

More accurately, it just feels like I'm banging my head against a wall.

I actually tried that in response to this message, but the wall flexed
alarmingly, so I decided to stop.

> I do worry that someone will need to propose a disambiguating amendment
> to the constitution to resolve the ambiguities we're discussing here,
> but I'm not ready to do that yet.  I want to make sure I understand your
> issues before I'd personally be willing to tackle such a thing.

Sure, neither am I. We'll probably have to get to independent options,
but I think we'd be better off if we finished supermajority requirements
first.

> > It would help if you'd not argue from a basis of "that's what
> > supermajority means so that's how supermajority works" for a few
> > messages, perhaps.
> Was my treatment in this message adequate?

It was closer, but you fell back to talking about votes "for" and
"against" an option, which we don't have. We only have preferences.
And you seem overly attached to discarding all preferences but the
first one.

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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