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



On Mon, Dec 04, 2000 at 11:20:15PM -0500, Raul Miller wrote:
> > > My point of view is that these two are essentially equivalent: in the
> > > N+1 style of voting, a person who thinks that the option isn't the best
> > > would vote for "further discussion".
> > Well, they might do that, yes. Or else they might think to themselves, 
> > "well, I'm never going to get my preferred choice, and this isn't bad, so 
> > yeah, let's do that". I think that's a valid point of view to hold.
> Indeed, things could happen this way.  [Personally, I'm not sure I'd
> say "Oh well" -- if "My First Preference" was important to me, I'd very
> likely vote 1: further discussion, 2: yes, 3: no -- this wouldn't have a
> substantially different effect, unless some of the people who had voted
> the other way had second thoughts, or unless more people participated
> in the second vote.]

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.

> > 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.

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".

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.

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.

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.

Consider it more as an example of a way to conduct a single vote that
has less flaws than yours, rather than one that's useful as is.

> > No, your view of supermajority isn't good because it affects other
> > options than the status-quo options, and raises the odds that they'll win.
> > An alternative way of looking at it is that there's no way to express
> > a preference towards a non-supermajority vote without that preference
> > counting for three preferences the other way. What if I *don't* feel
> > that strongly about it?
> Well.. if supermajority decreases the chance that an option will win,
> then, yes, that does tend to bias things in the direction of alternatives.

It's also possible to simply bias the vote towards the status-quo, rather
than simply biassing it away from some other option.

> To avoid this "bias", you seem to want to bias things away from the
> alternatives, and in favor of the choice between the supermajority option,
> and what you call the "status quo" option.

No, I don't want to avoid bias entirely; if I did I'd be saying "let's
do away with supermajorities and quorums and just use a straight out
Condorcet method of some description".

But I think the main benefit of a quorum and supermajority is to bias towards
the status-quo, not to bias against that particular possibility.

> > Well, again, my reading explicitly requires a vote with Yes/No/Further
> > Discussion as the only options, and only applies supermajority and quorum
> > to those options.
> Oh?
> The only way I see to get that interpretation requires I either:
> [A] Completely ignore A.3(3), or
> [B] imagine that A.6(7) somehow says that X stands for only "no" or
> "further discussion"
> What have I missed?

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.

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).
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. 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. 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
   [ _ ] [___] Original proposal
   [ _ ] [___] First amendment
   [ _ ] [___] Second amendment
   [ _ ] [___] Third amendment
   [ _ ]       Further discussion

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.

(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
)

That's how I would interpret A.3(1..3) anyway.

> > > > 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.
> > > Do you agree that "preferred by more people" really means "preferred
> > > by a majority of relevant votes"?
> > Sure. If people want their preferences to count, they have to vote.
> > If they choose not to, we have to assume the votes we do get are
> > representative (unless we miss quorum).
> Good enough.  Second question: is there some reason to imagine that the
> second preference should override the first preference in cases where
> the first preference clearly favors one of the options?

Well, consider a vote like:

	60 favour A, B, Status-Quo
	30 favour B, A, Status-Quo

where A requires a 3:1 supermajority but B doesn't. By scaling the
preferences for A over B down to 20, you end up overriding the first
preferences of 60 people by choosing B, rather than overriding the first
preferences of of only 30 people by choosing A.

But I still don't see any reason why the first preference is more crucial
than any other preference.

> > > > 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.
> > > By "easier" do you mean "closest to what the constitution says", or
> > > do you mean something else?  [If you mean something else, I don't
> > > see that "easier" has anything to do with it.]
> > Doing something that doesn't require a supermajority is easier as far
> > as the constitution is concerned. It's easier, for example, to overrule
> > the DPL or a delegate than the technical ctte.
> Ok, so by "implement" you mean "agree on in a vote".

Well, I mean "to get something done". If that something requires a GR,
then yes, I mean "agree on a vote".

> And, it looks like what you want is some kind of "sea level" sort of
> option -- if you've ranked an option with a supermajority above that "sea
> level", you'd like your vote to count as a vote towards the supermajority
> requirement.  And, if you happened to rank some other option above the
> option with the supermajority requirement, that doesn't enter into it.

Yeah, that's not a bad analogy. Let me stretch it a bit and see if it
snaps:

Most options are naturally about as dense as the ocean: if there are
more people pushing it down than holding it up, it sinks, otherwise it
rises up out of the water.

But some options are denser than that: options requiring a supermajority
turn out to require, say, twice as many people pushing it up and those
pushing it down to stay afloat. Some of them require three times as many
people pushing it up as pulling it down.

We don't want a waterlogged or drowned option to win the vote.

Sea-level is how we do things at the moment.

Not really sure that's helpful at all.

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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