Re: current A.6 draft [examples]

[Anthony Towns]

On Sat, Dec 07, 2002 at 07:44:55PM -0500, Raul Miller wrote:
> On Sat, Dec 07, 2002 at 12:12:48PM -0500, Raul Miller wrote:
> > > I'm critiquing the axiom, not the example.  By his rules some elections
> > > with quorums do not have a democratic outcome.
> On Sun, Dec 08, 2002 at 09:40:21AM +1000, Anthony Towns wrote:
> > That's not what's important: by his rules some elections that _meet_
> > quorum don't have a "democratic" outcome. The quorum issue's irrelevant.
>  ax?i?om NOUN: 1. A self-evident or universally recognized truth; a maxim:

Raul, I did a degree in pure maths, I know what an axiom is. If you're
aiming to be insulting, you're going about it in just the right way. If
you're aiming to demonstrate you know what you're talking about, or if
you're trying to understand what I'm saying you're not.

> It's not fair to base an argument on an axiom which is known to be false.

It doesn't matter whether the axiom is false as written: it's trivial
to salvage its intended meaning (by either dropping quorum requirements,
or qualifying the axiom to apply only when the quorum requirements have
already been met for all the options listed).

> The argument may be perfectly well formed, but if the underlying axioms
> are not unconditionally true the argument itself is meaningless.

Yes, you can refuse to talk to people who dare to end sentences in
prepositions, or otherwise don't make "correctly formed" arguments,
but you just end up missing the point.

> The clause I would add to his axioms, to make them always true, is:
> "unless the election is defaulted".

You could do that, but it entirely defeats the point that's trying to be
made, which is to examine when the election should be defaulted and when
it shouldn't be. You have a situation where the majority of voters think
the _worst_ possible option is to default the election. The question
is why you would want to go ahead and default the election anyway,
when there is an option that can be accepted (it meets quorum, doesn't
require a supermajority, and obviously a majority prefer it to defaulting
the election)?

> Let's take the example you proposed in
> http://lists.debian.org/debian-vote/2000/debian-vote-200011/msg00203.html
> and examine its outcome using Clinton's
> proposed resolution system as defined in
> http://lists.debian.org/debian-vote/2002/debian-vote-200212/msg00020.html

I haven't read through Clinton's proposed resolution system; it started
making up too many arbitrary new terms without any justification.

It's _much_ better to work out the principles first, then the mechanisms.

> > > > Which is to say that "if option X doesn't defeat the default option by
> > > > its supermajority requirement, it is ignored" seems to be fairer than
> > > > considering defeats by the default option as especially strong.
> > > Define "fairer" -- the definition of "fair" is the crux of this issue.
> > That's easy: most in line with what the voters actually want.
> And what does "most in line" mean in the context of:

We already have a context: "what does it mean in terms of the given
election"? I don't see how you can say anything other than: "it means
that we go with the majority decision that B is better than defaulting".

> * multiple elections [which may change the rules about how votes are
>   conducted] and/or

I have no idea what you mean.

> * elections which have supermajority requirements [which is a way
>   we reduce the risk of changes in the rules by which we determine
>   fairness]?

I've already indicated what I think this should be: that any sufficiently
sized "super" minority should be able to block any given options with
supermajority requirements.

Cheers,
aj

-- 
Anthony Towns <[EMAIL PROTECTED]> 
I don't speak for anyone save myself. GPG signed mail preferred.

 ``If you don't do it now, you'll be one year older when you do.''


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Re: current A.6 draft [examples]

[Raul Miller]

> > It's not fair to base an argument on an axiom which is known to be false.

On Sun, Dec 08, 2002 at 04:45:07PM +1000, Anthony Towns wrote:
> It doesn't matter whether the axiom is false as written: it's trivial
> to salvage its intended meaning (by either dropping quorum requirements,
> or qualifying the axiom to apply only when the quorum requirements have
> already been met for all the options listed).

I can accept, with that clause added, the axiom that the option ranked
first must win the election.

I am uncomfortable this for the axiom that the option ranked last must
lose.  It's just too arbitrary.  For example, consider also a ballot with
only one option (not that our current system allows this).  The resulting
statement is rather akward to accept as being true without proof.

> The question
> is why you would want to go ahead and default the election anyway,
> when there is an option that can be accepted (it meets quorum, doesn't
> require a supermajority, and obviously a majority prefer it to defaulting
> the election)?

I think I've got a proposal which addresses this problem.  [next message]
 
> It's _much_ better to work out the principles first, then the mechanisms.

Ok, but bear with me a bit when I ask questions to help me sort out
implicit questions.

> We already have a context: "what does it mean in terms of the given
> election"? I don't see how you can say anything other than: "it means
> that we go with the majority decision that B is better than defaulting".
...
> ... any sufficiently
> sized "super" minority should be able to block any given options with
> supermajority requirements.

This helps.

Thanks,

-- 
Raul

Re: current A.6 draft [examples]

[Anthony Towns]

On Sun, Dec 08, 2002 at 07:57:09AM -0500, Raul Miller wrote:
> I am uncomfortable this for the axiom that the option ranked last must
> lose.  It's just too arbitrary.  For example, consider also a ballot with
> only one option (not that our current system allows this).  The resulting
> statement is rather akward to accept as being true without proof.

Assume you have a non-trivial election, ie with multiple options. A
given majority vote some particular option, X, last. 

That means there are N/2+1 ballots of the form "abcde...X", "edcba...X",
etc, where X is always the last option. In this case _any_ of options a,
b, c, d, e, ... are preferred over X by that majority, and further, in
the traditional Condorcet sense, there can't be any cycles involving X
(ie, A beats X, X beats B, B beats A, etc), since that would requires
N/2+1 ballots to have the form "...X...Y" -- but there are only N/2-1
ballots left. Indeed, there can't be _any_ options that beat X in the
traditional Condorcet sense.

Another way of looking at the undemocratic example is to say that the
original vote was "B versus D", and that a few people who wanted to stymie
the outcome (50:10 in favour of B) introduced a new option "A". In the
example given, A fails, but in so doing, also knocks B out of the running.

Another way of looking at it is a restatement of the "Condorcet loser
criterion", or a modification of the "local independence from irrelevant
alternatives criterion" to deal with supermajority requirements. (see
http://www.condorcet.org/emr/criteria.shtml)

Cheers,
aj

-- 
Anthony Towns <[EMAIL PROTECTED]> 
I don't speak for anyone save myself. GPG signed mail preferred.

 ``If you don't do it now, you'll be one year older when you do.''


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Re: current A.6 draft [examples]

[Clinton Mead]

Raul Miller wrote:


It's not fair to base an argument on an axiom which is known to be false.
 



On Sun, Dec 08, 2002 at 04:45:07PM +1000, Anthony Towns wrote:
 


It doesn't matter whether the axiom is false as written: it's trivial
to salvage its intended meaning (by either dropping quorum requirements,
or qualifying the axiom to apply only when the quorum requirements have
already been met for all the options listed).
   



I can accept, with that clause added, the axiom that the option ranked
first must win the election.
 

Quorum requirements was not intended to be in the scope of my argument. 
I didn't mention quorum requirements, but I should of mentioned 
explicitally that they were out of its scope. The argument deals with a 
set of votes, a set of options with optional supermajority requirements, 
one of which may optionally be the default option. It doesn't deal with 
quorum requirements, supression of free speech, violence, vote rigging 
or anything else that may effect the democraticness of a method. 
Admitidly, it was reasonable to assume quorum requirements to be part of 
the arguments scope, but I did not intend that.



I am uncomfortable this for the axiom that the option ranked last must
lose.  It's just too arbitrary.  For example, consider also a ballot with
only one option (not that our current system allows this).  The resulting
statement is rather akward to accept as being true without proof.


Myself wrote:
> Minority Loses Axiom - "In a non-supermajority election, if there are 
options A and B, and option B is solely ranked last on a majority of 
votes, then if option B must not win."


Note the minimum inclusion of two options A and B for 'majority loses' 
axiom to have an effect. These are intended to be two different options.


Personally, I'm more unconfortable the idea of an option not losing when 
a majority of votes rank it last and there are other non-supermajority 
options. But which is more unconfortable is for debate.




In any case, later on I'll define another criteria in my opinion an 
election system should follow, and will attempt to prove that CCSSD (and 
newly defined DPCCSSD) does follow and the Dec 7 draft does not. This 
criteria 'Consistancy', is basically that if an option wins when it is 
not the default option, it should win when it is the default option.


---

Firstly, I'm going to define "Default Protection CCSSD", which I will 
call DPCCSSD. Its the same as my old CCSSD, except for rule 9.


Plain CCSSD is defined at 
http://lists.debian.org/debian-vote/2002/debian-vote-200212/msg00020.html.


Its all leading up to another proof, I'll get there...

---

Definition of "Default Protection Considered Clone-Proof Schwartz 
Sequential Dropping" (DPCCSSD).


(1) A defeats B if more votes prefer A over B than B prefer over A.
(2) A challenges B if more than or an equal number of votes prefer A 
over B than prefer B over A.


(3) A defeats B by X, where X is equal to the number of votes that 
prefer A over B, if A defeats B.


(4) A superchalleges B, where A has a supermajority requirement of (X:Y) 
if the number of votes that prefer A over B multiplied by Y is greater 
than or equal to the number of votes that prefer B over A multiplied by X.


(5) A is considered if A superchallenges all options with supermajority 
requirements less than A.
(6) A is considered if A challenges B, where B has supermajority 
requirements greater than or equal to A.


(7) A has a beatpath to B of strength X, if A and B are considered and A 
defeats B by X, or if A, B and C are considered and A defeats C by Y and 
C has a beatpath to B of strength Z, where X is equal to the minimum of 
Y and Z.


(8) A has a beatpath to B of strength 0 if there is no non-zero X such 
that A has a beatpath to B of strength X


(9a) A has a beatpath win to B if A and B are both not default options 
and the largest X such that A has a beatpath to B of X is greater than 
the largest Y such that B has a beatpath to A of Y.


(9b) A has a beatpath win to B if A is the default option, and there is 
a non-zero X such that A has a beatpath to B of strength X.


(9c) A has a beatpath win to B if B is the default option, and there is 
non-zero X such that A has a beatpath to B of X, and there is no 
non-zero Y such that B has a beatpath to A of Y.


(10) A is a finalist if A is considered and there is no B such that B 
has a beatpath win to A.


(11) A is a winner if A is a finalist and there is no B such that the 
casting vote prefers B over A.


Consistancy Criteria - "If election X and election Y have identical 
votes and supermajority requirements, and election X has a default 
option of A, and election Y has a default option of B, and B is the 
winner of election X, then B must be the winner of election Y."


---

Consider this election, with no supermajority requirements.

4 CBA
3 BAC
2 ACB

B defeats A 7:2
C defeats B 6:3
A defeats C 5:4

---

Default option 

Hybrid Theory

[Raul Miller]

Focusing on just A.6 again, in this draft:

(*) Weakest defeats can now be eliminated: before a defeat of the default
option is eliminated, all options which fail to meet their supermajority
requirements are deleted.
(*) When artificial supermajority defeats are eliminated the corresponding
option is also deleted.
(*) Terms expressed using mathematical shorthand have been named.
(*) Other minor fixes

__

   A.6 Vote Counting

 1. Each voter's ballot ranks the options being voted on.  Not all
options need be ranked.  Ranked options are considered preferred
to all unranked options.  Voters may rank options equally.
Options left unranked by the voter are considered to be ranked
equally with one another and below any ranked options.  The other
details of how ballots may be filled out will be included in
the Call For Votes.

 2. We construct the Schwartz set based on undropped options and
defeats:

  a. An option A is in the Schwartz set if A has not been dropped
 and if for all options B, either A transitively defeats B,
 or B does not transitively defeat A.

  b. An option A transitively defeats an option C if A defeats C
 or if there is some other option B, where A defeats B AND
 B transitively defeats C.

  c. An option A defeats an option B, if the strength
 N(A,B)*V(A,B) is larger than N(B,A)*V(B,A), and if the
 (A,B) defeat has not been dropped.

  d. Given two options A and B, the votes V(A,B) is the number
 of voters who prefer option A over option B.

  e. If a majority of n:1 is required for A, and if B is the
 default option, majority requirement N(B,A) is n.  In all
 other cases, N(B,A) is 1.

 3. If any options involved in the weakest defeats between options
in the Schwartz set are options in superdefeats, we drop the
corresponding superdefeated options then return to step 2.

  a. A defeat (A,X) is weaker than a defeat (B,Y) if V(A,X)
 is less than V(B,Y).  Also, (A,X) is weaker than (B,Y) if
 V(A,X) is equal to V(B,Y) AND V(X,A) is larger than V(Y,B).

  b. A weakest defeat is a defeat that has no other defeat weaker
 than it. There may be more than one such defeat.

  c. An option B is superdefeated by an option A if A defeats B,
 and if V(A,B) is not larger than V(B,A).

  c. Given a defeat (A,B) the options A and B are involved in
 this defeat.

  d. An option A is dropped by dropping all defeats which involve
 A and also stipulating that option A is not a member of
 the Schwartz set.

 4. If there are defeats between members of the Schwartz set, we
drop the weakest defeats then return to step 2.

 5. If there are no defeats within the Schwartz set, then the winner
is chosen from the undropped options in the Schwartz set where
at least Q voters ranked that option above default option, where
Q is the quorum requirement for the ballot. If there is only one
such option, it is the winner. If there are multiple options, the
elector with a casting vote chooses which of those options wins.

 "RATIONALE": Options which voters rank above the default option are
 options they find acceptable.  Options ranked below the default
 option are unacceptable options.  Supermajority options require
 some approximation of unanimity before they can be accepted.

__

This changes a few of the outcomes for tests posted in 
http://lists.debian.org/debian-vote/2002/debian-vote-200211/msg00321.html

Here's the test cases which have changed:

A requires 2:1 majority; D is the default option
3 ABD
1 BDA
1 DAB

A defeats B 4:1
B defeats D 4:1
D superdefeats A 4:3

eliminate A

B defeats D 4:1

B wins
in previous draft, this was a tie between B and D
the requirement was that D did not win



Z is the default option
40 A
25 B
35 ZBA

B defeats A 60:40
A defeats Z 40:35
Z defeats B 35:25

eliminate 35:25

B defeats A 60:40
A defeats Z 40:35

B wins
in previous draft, Z won
the requirement was that A not win



Quorum of n, no supermajorities, D is the default option:
25 DAB
30 BDA
35 ABD

B defeats D 65:25
A defeats B 60:30
D defeats A 55:35

eliminate 55:35

B defeats D 65:25
A defeats B 60:30

A wins unless quorum is not met in which case D wins.
In the previous draft B won unless quorum was not met in which case D wins.


Additionally, here's the result of the test proposed by Clinton Mead in
http://lists.debian.org/debian-vote/2002/debian-vote-200212/msg00020.html

A requires 3:1 majority; D is the default option
4 ABD
1 ADB
1 BDA
1 DAB

A defeats B 6:1
D superdefeat

Re: current A.6 draft [examples]

[Anthony Towns]

On Mon, Dec 09, 2002 at 03:03:33AM +1100, Clinton Mead wrote:
> Consistancy Criteria - "If election X and election Y have identical 
> votes and supermajority requirements, and election X has a default 
> option of A, and election Y has a default option of B, and B is the 
> winner of election X, then B must be the winner of election Y."

This criterion doesn't really make any sense: the default option doesn't
change, it's always "further discussion" or "none of the above". It's
just not meaningful to say "consider the same votes when X is the default
option instead of Y".

Cheers,
aj

-- 
Anthony Towns <[EMAIL PROTECTED]> 
I don't speak for anyone save myself. GPG signed mail preferred.

 ``If you don't do it now, you'll be one year older when you do.''


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Re: current A.6 draft [examples]

[Raul Miller]

On Mon, Dec 09, 2002 at 03:03:33AM +1100, Clinton Mead wrote:
> In any case, later on I'll define another criteria in my opinion an 
> election system should follow, and will attempt to prove that CCSSD (and 
> newly defined DPCCSSD) does follow and the Dec 7 draft does not. This 
> criteria 'Consistancy', is basically that if an option wins when it is 
> not the default option, it should win when it is the default option.

What's the rationale for this system?

In other words, you're stipulating that for an election where A has 3:1
supermajority, and D is the default option, and the votes are

100 ABD
 35 BAD

that B should win, even though every voter considers A to be an acceptable
option.  Why is this a good idea?

That said, here's how the test case you've proposed here plays out with
the draft I submitted today:

__

A is the default option
4 CBA
3 BAC
2 ACB

B defeats A 7:2
C defeats B 6:3
A defeats C 5:4

eliminate 5:4

B defeats A 7:2
C defeats B 6:3

C wins
__

B is the default option
4 CBA
3 BAC
2 ACB

B defeats A 7:2
C defeats B 6:3
A defeats C 5:4

eliminate 5:4

B defeats A 7:2
C defeats B 6:3

C wins
__

Finally, as an aside: I've been avoiding the beatpath strength mechanism
because I'm not confident of the logic which proves it's equivalent to
CpSSD in an election with supermajorities.

Good enough?

Thanks,

-- 
Raul

Re: Hybrid Theory

[Anthony Towns]

On Sun, Dec 08, 2002 at 11:13:23AM -0500, Raul Miller wrote:
>  "RATIONALE": Options which voters rank above the default option are
>  options they find acceptable.  Options ranked below the default
>  option are unacceptable options.  Supermajority options require
>  some approximation of unanimity before they can be accepted.

That's really more of an extended explanation than a rationale, per
se. I'm inclined to think that phrasing it as instructions to the voters
is probably more useful.

Can we possibly stop coming up with full blown voting systems while
we still don't have a firm idea of the underlying things we're trying
to achieve? Seriously: if we can't come up with a list of acceptable,
mutually understood criteria by which we can judge our voting systems,
getting bogged down in implementation details is just confusing the issue.

Here's a start:

(0) The default option should be to leave the vote unresolved;
if people wish to actively preserve the status quo, they should
ensure that is listed as a separate option on the ballot.

(1) We want a voting system that handles quorums.
(1a) Quorums are handled on a per-option basis.
(1b) Electors are counted toward the quorum if they vote, and if they
 rank the option above the default option.

(2) We want a voting system that handles supermajorities.
(2a) An option requiring an N:1 supermajority means that 1/(N+1) of
 the voters may block that option from passing.
(2b) An option that does not meet its supermajority requirement does
 not affect the outcome of the vote.
(2c) Options with a supermajority requirement should be treated as
 similarly to other options as possible.
(2c.i) The supermajority requirement should be satisfied by more
   than N/(N+1) voters ranking that option above the default
   option.
(2c.ii) All other comparisons, including transitive comparisons,
should not be scaled.

I presume there are some people on this list who would say "actually, I
don't want (1)" or "(2) is undesirable and unnecessary". That's fine: we
can list those as alternatives on the vote we eventually have if there's
support for them; what's *important* is to make sure we're all on the
same page as to what we're trying to achieve and _why_ we're trying to
achieve it.

In particular, dropping the options that don't meet their supermajority
requirement before applying CpSSD meets the above criteria better than
strengthening the default versus supermajority-option defeat: it avoids
scaling transitive comparisons and ensures that options that don't meet
the supermajority requirement don't prejudice other options. There may
be other reasons to go the other way, but if we're going to stop going
round and round in circles on this, we need to be *explicit* about them.

Raul, can you give a good a priori reason for declaring the vote:
30 ABD  (A requires a 2:1 supermajority, B a simple majority)
10 BDA
10 DAB
to be a draw between B and D [0], when the vote:
40 BD   (ie, how the vote would've gone if A had not been an option)
10 DB
would have been a clear win to option B?

Cheers,
aj

[0] There's a tie amongst B,D,A, and A defeats B 40:10 and B defeats D
40:10 are equally weakest defeats, so both are dropped, if A is
kept around.

-- 
Anthony Towns <[EMAIL PROTECTED]> 
I don't speak for anyone save myself. GPG signed mail preferred.

 ``If you don't do it now, you'll be one year older when you do.''


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Re: Hybrid Theory

[Raul Miller]

On Mon, Dec 09, 2002 at 03:20:20AM +1000, Anthony Towns wrote:
[what are the underlying things we're trying to achieve]:

> Here's a start:
> 
>   (0) The default option should be to leave the vote unresolved;
>   if people wish to actively preserve the status quo, they should
>   ensure that is listed as a separate option on the ballot.
> 
>   (1) We want a voting system that handles quorums.
>   (1a) Quorums are handled on a per-option basis.
>   (1b) Electors are counted toward the quorum if they vote, and if they
>rank the option above the default option.
> 
>   (2) We want a voting system that handles supermajorities.
>   (2a) An option requiring an N:1 supermajority means that 1/(N+1) of
>the voters may block that option from passing.
>   (2b) An option that does not meet its supermajority requirement does
>not affect the outcome of the vote.
>   (2c) Options with a supermajority requirement should be treated as
>similarly to other options as possible.
>   (2c.i) The supermajority requirement should be satisfied by more
>  than N/(N+1) voters ranking that option above the default
>  option.
>   (2c.ii) All other comparisons, including transitive comparisons,
>   should not be scaled.

Here's my view:

[A] The default option represents voter approval of the ballot -- options
ranked below the default option are options that voter would rather have
been left off the ballot, options ranked above the default option are
options the voter considers acceptable.

[B] We want to use quorum and supermajority.

Looking back at your items,

(0) follows from [A] as options which are not on the ballot
can not be resolutions from that ballot.

(1) follows from [B].
(1a) and (1b) Follow from [A] and [B}.

(2) follows from [B].
(2a) stands alone, and seems fine to me.
(2b) and (2c) stand alone and conflict with each other.
(2d) follows from (2a).
(2e) follows from [A] and (2a).

Interestingly enough, the problem which has lead to all these voting
mechanics proposals very much has to do with the conflict expressed here
between (2b) and (2c).

As an aside: I have been to trying find a theory for using condorcet
to choose between options with sufficiant approval with respect to the
default option.  My requirement has been: don't give bad results for
any of the cases people have brought up where earlier systems could not
be justified.  I've been expressing my understanding of this theory as
voting mechanics drafts.

> In particular, dropping the options that don't meet their supermajority
> requirement before applying CpSSD meets the above criteria better than
> strengthening the default versus supermajority-option defeat: it avoids
> scaling transitive comparisons and ensures that options that don't meet
> the supermajority requirement don't prejudice other options. There may
> be other reasons to go the other way, but if we're going to stop going
> round and round in circles on this, we need to be *explicit* about them.

I've rejected this idea because it introduces
problems which Buddha illustrated in
http://lists.debian.org/debian-vote/2002/debian-vote-200211/msg00162.html

I think it's better to strengthen the defeat of the default vs
supermajority option and to wait to drop related supermajority options
until the point where the presence or absence of this scaled defeat
would cause a problem.

> Raul, can you give a good a priori reason for declaring the vote:
>   30 ABD  (A requires a 2:1 supermajority, B a simple majority)
>   10 BDA
>   10 DAB
> to be a draw between B and D [0], when the vote:
>   40 BD   (ie, how the vote would've gone if A had not been an option)
>   10 DB
> would have been a clear win to option B?

No, I can't give a good a priori reason for declaring this to be a tie
between D and A.

As an aside, the message you're responding to has an explicit example
with a clear win for option B where A requires 2:1, B 1:1, D is default,
with 1 BDA and 1 DAB and 3 ABD votes.

> [0] There's a tie amongst B,D,A, and A defeats B 40:10 and B defeats D
> 40:10 are equally weakest defeats, so both are dropped, if A is
> kept around.

As an aside, the system I proposed earlier today drops A for exactly
that reason.

-- 
Raul

debian unmanageable?

[David N. Welton]

A few poorly-formed thoughts:

It seems we aren't even able to pick a system to let us vote, let
alone actually debating and voting on issues.

Maybe the answer isn't hyper-democracy, where everyone who maintains a
package gets to decide on every issue.

Maybe we ought to recognize that the power is already in the hands of
those who *do* things, and align our control structures accordingly.

Ever more technical and detailed voting schemes seem like a bad
management hack to me.  Maybe some sort of hierarchical structure is
better.  I can see how these appeal to the inner geek, but they strike
me as heading off in a direction that is potentially very different
from "rough consensus and working code".

One really important role Debian fulfills that makes it somewhat
different from other open source projects is that of a place to ramp
up and get involved, even if you're not an expert C hacker.  I know I
didn't know half of what I know now when I started.  More like 1/10th?
I think this is very important for the free software comunity at
large.  On the other hand, is it fair to entrust the project to a
(potential) majority of developers who are still learning as they go,
and who haven't been around that long?  Not that these people are in
any way bad - as I state above, I think they are terribly important
for the future of free software.

Me?  I'm not that involved in Debian any more, except for a few
packages.  Most of my work these days is for the Apache Software
Foundation.  I have been around Debian since 1997.

If Debian happens to need an supreme and feared emperor-for-life, I'd
be happy to volunteer.  I want minions as part of the deal, though.

Ciao,
-- 
David N. Welton
   Consulting: http://www.dedasys.com/
 Personal: http://www.dedasys.com/davidw/
Free Software: http://www.dedasys.com/freesoftware/
   Apache Tcl: http://tcl.apache.org/

Re: Hybrid Theory

[Jochen Voss]

Hello

On Mon, Dec 09, 2002 at 03:20:20AM +1000, Anthony Towns wrote:
> Can we possibly stop coming up with full blown voting systems while
> we still don't have a firm idea of the underlying things we're trying
> to achieve?
Good idea :-)

>   (1) We want a voting system that handles quorums.
>   (1a) Quorums are handled on a per-option basis.
>   (1b) Electors are counted toward the quorum if they vote, and if they
>rank the option above the default option.

Can you give reasons for (1a) and (1b)?  As far as I
understood the debate, the reason for a quorum is to avoid
"stealth-decision-making", i.e. to assert that enough
developers notice the election and take part in it.  Because
of this for me the concept of a per-option quorum does not
make much sense.  What do you think?

Some other goal I would propose:

(3) In the absence of a quorum/supermajority requirement our
voting system should behave identical to textbook Condorcet
voting with Cloneproof Schwartz sequential dropping.

This may be clear (is it?) but I think that some of the
previous drafts did not have this property.

And finally: the reason way we want Condorcet voting is,
that this system is a "good" voting system in the sense of

http://electionmethods.org/evaluation.htm

I append a list of good properties of Condorecet voting
below (summarized from the election-methods page).  To
handle quorum and supermajority requirements we have to make
changes to the voting system.  In my opionion we should find
out which of the properties we loose because of the changes.
Remember: these properties were the reason why we want
Condorcet voting instead of competing systems.

What do you think?

Jochen



A list of good properties of Condorcet Voting
(from http://electionmethods.org/evaluation.htm)

  * Monotonicity Criterion (MC):
If a single voter changes his mind and ranks an option higher,
this option can not stop being the winner because of this

  * Condorcet Criterion (CC):
If one candidate is preferred over each of the other
candidates, that candidate is the Ideal Democratic Winner
(IDW).  If all votes are sincere, the Ideal Democratic
Winner should win if one exists.

  * Generalized Condorcet Criterion (GCC):
If all votes are sincere, the winner should be a member
of the Smith set.
   ^
this is what we call "Schwartz set".

  * Strategy-Free Criterion (SFC):
If an Ideal Democratic Winner (IDW) exists, and if a
majority prefers the IDW to another candidate, then the
other candidate should not win if that majority votes
sincerely and no other voter falsifies any preferences.

Note: sometimes (When good options are ranked equal) and
IDW can be not preferred by a majority of voters over
another candidate.

  * Generalized Strategy-Free Criterion (GSFC)

If an Ideal Democratic Winner (IDW) exists, and if a
majority prefers the IDW to another candidate, then the
other candidate should not win if that majority votes
sincerely and no other voter falsifies any preferences.

  * Strong Defensive Strategy Criterion (SDSC)

If a majority prefers one particular candidate to
another, then they should have a way of voting that will
ensure that the other cannot win, without any member of
that majority reversing a preference for one candidate
over another or falsely voting two candidates equal.

This seems to be a weaker form of what we want to achive
with supermajority requirements.

  * Weak Defensive Strategy Criterion (WDSC)

If a majority prefers one particular candidate to
another, then they should have a way of voting that will
ensure that the other cannot win, without any member of
that majority reversing a preference for one candidate
over another.

Condorcet voting with Cloneproof Schwartz sequential dropping
additionally has the "cloneproof" property (from
http://electionmethods.org/CondorcetEx.htm)

  * The Schwartz Sequential Dropping (SSD) method has a
``plain'' version and the ``cloneproof'' version. The
cloneproof version gives no group or party any advantage
or disadvantage for having additional candidates that
are essentially ``clones'' of each other.  Except for
the case of ties, the two versions give the same result.
-- 
 Omm
  (0)-(0)
http://www.mathematik.uni-kl.de/~wwwstoch/voss/index.html


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Re: Hybrid Theory

[Raul Miller]

On Sun, Dec 08, 2002 at 09:03:22PM +0100, Jochen Voss wrote:
> Can you give reasons for (1a) and (1b)?  As far as I understood the
> debate, the reason for a quorum is to avoid "stealth-decision-making",
> i.e. to assert that enough developers notice the election and take part
> in it.  Because of this for me the concept of a per-option quorum does
> not make much sense.  What do you think?

Ballot contains A and D, A has 1:1 majority, D is default option.
Quorum is 45.

23 people vote for A.

A defeats D, but A doesn't meet quorum, default option wins.

23 people vote for A.
22 people vote for D.

A defeats D, A meets quorum, A wins.

Or: the addition of 22 people voting against A caused A to win.  In my
opinion, this is very wrong.

Note also that the process of ballot creation needs protection from
lack of interest.  We can't assume, just because someone submits a
ballot, that they participated during the creation of that ballot.
I use comparison with the default option to determine whether or not
the voter approves of that option being on the ballot.

Aside: I'm in favor of an analysis of the voting system based on the
electionmethods principles you referred to.  I expect [hope] that
without quorum and supermajority requirements the system I proposed
earlier today meets all the criteria of condorcet.  With quorum and
supermajority I expect there to be edge cases where we lose criteria
which aren't criteria of approval.  I hope someone can prove that my
expectations are right [or wrong, if they are indeed wrong].

Thanks,

-- 
Raul

Re: Hybrid Theory

[Sven Luther]

On Sun, Dec 08, 2002 at 03:18:16PM -0500, Raul Miller wrote:
> On Sun, Dec 08, 2002 at 09:03:22PM +0100, Jochen Voss wrote:
> > Can you give reasons for (1a) and (1b)?  As far as I understood the
> > debate, the reason for a quorum is to avoid "stealth-decision-making",
> > i.e. to assert that enough developers notice the election and take part
> > in it.  Because of this for me the concept of a per-option quorum does
> > not make much sense.  What do you think?
> 
> Ballot contains A and D, A has 1:1 majority, D is default option.
> Quorum is 45.
> 
> 23 people vote for A.
> 
> A defeats D, but A doesn't meet quorum, default option wins.
> 
> 23 people vote for A.
> 22 people vote for D.
> 
> A defeats D, A meets quorum, A wins.
> 
> Or: the addition of 22 people voting against A caused A to win.  In my
> opinion, this is very wrong.

Why ?

You are trying to use the quorum for something it is not for.

A quorum (in traditional elections) is just a mean of ensuring that
enough people are present so that the election is meaningfull.

Also, there is no way you are going to be able to explicitly exploit
this weakness you pointed out, unless you are the project voting
secretary (or whatever it is called) or you did manage to get access to
the already voted ballot.

Let's say you are against option A, and you have two choices :

  o not vote, in hope the quorum will not be met.

  o vote against A (or DA in this case).

if you do not vote, like you suppose, you can only do this in a
meaningfull way if you are sure that the quorum will not be met, which
should not be possible. And if you don't vote and the quorum is met,
then you have one less vote against A, and if A wins, you deserve it.

Friendly,

Sven Luther

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Re: Hybrid Theory

[Raul Miller]

> > Or: the addition of 22 people voting against A caused A to win.  In my
> > opinion, this is very wrong.

On Sun, Dec 08, 2002 at 09:38:46PM +0100, Sven Luther wrote:
> Why ?

I answered this in the message you were responding to, immediately
following the paragraph you quoted.

> You are trying to use the quorum for something it is not for.

I disagree.

> A quorum (in traditional elections) is just a mean of ensuring that
> enough people are present so that the election is meaningfull.

And that's what I'm using quorum for.

Except my proposal for quorum satisfys the monotonicity criterion
(http://www.electionmethods.org/evaluation.html#MC) while the mechanism
you're proposing would have cases where an option wins *because* of
votes against it.

> Also, there is no way you are going to be able to explicitly exploit
> this weakness you pointed out, unless you are the project voting
> secretary (or whatever it is called) or you did manage to get access to
> the already voted ballot.

I'm concerned about the effects of lack-of-interest.  I don't want people
deciding to not submit a ballot because of the chance that they'll cause
something they're opposed to to win.  If this happens even once it will
be very upsetting.

> Let's say you are against option A, and you have two choices :
> 
>   o not vote, in hope the quorum will not be met.
> 
>   o vote against A (or DA in this case).
> 
> if you do not vote, like you suppose, you can only do this in a
> meaningfull way if you are sure that the quorum will not be met, which
> should not be possible. And if you don't vote and the quorum is met,
> then you have one less vote against A, and if A wins, you deserve it.

Your argument is valid if quorum is never used.

Imagine that quorum is relevant at some point in time: imagine that we
have a set of elections which default because they don't meet quorum.

At this point: you wouldn't be certain that the some elections will meet
quorum.  Neither could you be certain that voting against an amendment
in some elections would not cause that amendment to win.

-- 
Raul

Debian voting system resources

[Jochen Voss]

Hello,

I set up a web page with Debian voting system resources.
My page tries to cover everything which is important for
the planned rewrite of our voting system.  I hope that
the page provides a good starting point for anybody who
wants to join the voting system discussion.

The address of my web page is

http://www.mathematik.uni-kl.de/~wwwstoch/voss/comp/vote.html

I hope this helps,
Jochen
-- 
 Omm
  (0)-(0)
http://www.mathematik.uni-kl.de/~wwwstoch/voss/index.html


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Re: Hybrid Theory

[Matthias Urlichs]

Hi,

Raul Miller:
> Anthony Towns:
> > In particular, dropping the options that don't meet their supermajority
> > requirement before applying CpSSD meets the above criteria better than
> > strengthening the default versus supermajority-option defeat: it avoids
> > scaling transitive comparisons and ensures that options that don't meet
> > the supermajority requirement don't prejudice other options.
> 
> I've rejected this idea because it introduces
> problems which Buddha illustrated in
> http://lists.debian.org/debian-vote/2002/debian-vote-200211/msg00162.html
> 
It's a known fact that dropping (or adding) an option from a Condorcet
election may change its result if there's a cycle.

You want an election method where this cannot happen?
Don't use Condorcet voting.  It's that simple.  :-/

I don't like to play around with ratios when considering the supermajority
requirement. It already has led to one unforeseen effect (the rule about
not dropping the default, because otherwise the supermajority-requiring
option might _still_ win -- which gives the default option a strength it
IMHO does NOT deserve); nobody can guarantee that there are no others.

-- 
Matthias Urlichs | noris network AG | http://smurf.noris.de/


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Re: Hybrid Theory

[Anthony Towns]

On Sun, Dec 08, 2002 at 09:03:22PM +0100, Jochen Voss wrote:
> > (1) We want a voting system that handles quorums.
> > (1a) Quorums are handled on a per-option basis.
> > (1b) Electors are counted toward the quorum if they vote, and if they
> >  rank the option above the default option.
> Can you give reasons for (1a) and (1b)? 

I can't give a reason for (1); quorums in real meetings are used to
make sure enough people are able to participate in decisions for them
to be meaningful.  Since we do everything over mailing lists and have a
couple of weeks for every issue to be considered, I'm not sure there's
any benefit to making sure there are at least a given number of votes.

But on the assumption that there is, then we need to take account of
the differences between Debian's system than real life meetings. First,
in a real life meeting, everyone who's present is counted for a quorum:
they're locked in a room and can't leave afterall, so it doesn't matter
how they vote. For Debian, you don't have any "presence" to count, and
you don't want to discourage people from voting, which means allowing
them to vote in such a way that options they don't like are given no
support whatsoever.

Additionally, this gives us the minimum change from what we have now.

> Some other goal I would propose:
> (3) In the absence of a quorum/supermajority requirement our
> voting system should behave identical to textbook Condorcet
> voting with Cloneproof Schwartz sequential dropping.
> This may be clear (is it?) but I think that some of the
> previous drafts did not have this property.

It's irrelevant, we don't have votes without quorum/supermajority
requirement.

Note that as stated our votes are a combination of approval and Condorcet
voting: an option is "approved" by the number of ballots that rank it
above the default option.

One way to think about this is to say:

(1) First we use approval voting to handle the default option,
quorum and supermajority. An option is "approved" by the
number of votes that rank it above the default option. An
option is "disapproved" by the number of votes that rank it
below the default option.

If an option is approved by fewer votes than its quorum, it
is dropped.

If an option requiring a supermajority of N:1 is approved by
fewer than N times the number of votes it is disapproved by, it
is dropped.

If an option is approved by no more than the number of votes
it is disapproved by, it is dropped.

If the only remaining option is the default option, it wins.

Otherwise, the default option is dropped.

(2) The Cloneproof Schwartz Sequential Dropping method is applied to
the remaining options. In the event of a tie, the elector with a
casting vote decides amongst the tied options.

> What do you think?

I think the above is a counterexample to your idea: it obviously has the
good properties of CpSSD that we want: we're using it and nothing else
to choose between all the real options -- we don't have any fake options,
we don't have any scaling, we don't have any special rules hacked in.

Again, the default option is fundamentally special. It's not there
because people want it to win -- if they want the status quo they need
to specifically nominate that -- it's there to handle our additional
requirements that Condorcet systems don't manage.

Cheers,
aj

-- 
Anthony Towns <[EMAIL PROTECTED]> 
I don't speak for anyone save myself. GPG signed mail preferred.

 ``If you don't do it now, you'll be one year older when you do.''


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Re: Hybrid Theory

[Anthony DeRobertis]

On Sun, 2002-12-08 at 23:51, Anthony Towns wrote:

> I can't give a reason for (1); quorums in real meetings are used to
> make sure enough people are able to participate in decisions for them
> to be meaningful.  Since we do everything over mailing lists and have a
> couple of weeks for every issue to be considered, I'm not sure there's
> any benefit to making sure there are at least a given number of votes.

Not to mention with 1000 developers 3Q = e(1/2*l(1000))/2*3 = ~47.4. I
don't think fewer than 48 out of 1000 people will vote ever, and
www.debian.org/vote bears me out. No decided issues have less than 100
votes.

So, suggest go ahead with it: Drop all ocurances of "Q" and quorum from
the Consitution.

BTW:  has the quorum
calculated wrong. "Q is HALF of the square root of the number of current
Developers"; someone forgot the half part when calculating Q on that
page. Q is really ~11.15, making the quorum 33.44, not 67.
 has the same problem. And
.

 and
 have the proper calculation,
and  didn't bother.




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Re: current A.6 draft [examples]

[Raul Miller]

> > It's not fair to base an argument on an axiom which is known to be false.

On Sun, Dec 08, 2002 at 04:45:07PM +1000, Anthony Towns wrote:
> It doesn't matter whether the axiom is false as written: it's trivial
> to salvage its intended meaning (by either dropping quorum requirements,
> or qualifying the axiom to apply only when the quorum requirements have
> already been met for all the options listed).

I can accept, with that clause added, the axiom that the option ranked
first must win the election.

I am uncomfortable this for the axiom that the option ranked last must
lose.  It's just too arbitrary.  For example, consider also a ballot with
only one option (not that our current system allows this).  The resulting
statement is rather akward to accept as being true without proof.

> The question
> is why you would want to go ahead and default the election anyway,
> when there is an option that can be accepted (it meets quorum, doesn't
> require a supermajority, and obviously a majority prefer it to defaulting
> the election)?

I think I've got a proposal which addresses this problem.  [next message]
 
> It's _much_ better to work out the principles first, then the mechanisms.

Ok, but bear with me a bit when I ask questions to help me sort out
implicit questions.

> We already have a context: "what does it mean in terms of the given
> election"? I don't see how you can say anything other than: "it means
> that we go with the majority decision that B is better than defaulting".
...
> ... any sufficiently
> sized "super" minority should be able to block any given options with
> supermajority requirements.

This helps.

Thanks,

-- 
Raul


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Re: current A.6 draft [examples]

[Anthony Towns]

On Sun, Dec 08, 2002 at 07:57:09AM -0500, Raul Miller wrote:
> I am uncomfortable this for the axiom that the option ranked last must
> lose.  It's just too arbitrary.  For example, consider also a ballot with
> only one option (not that our current system allows this).  The resulting
> statement is rather akward to accept as being true without proof.

Assume you have a non-trivial election, ie with multiple options. A
given majority vote some particular option, X, last. 

That means there are N/2+1 ballots of the form "abcde...X", "edcba...X",
etc, where X is always the last option. In this case _any_ of options a,
b, c, d, e, ... are preferred over X by that majority, and further, in
the traditional Condorcet sense, there can't be any cycles involving X
(ie, A beats X, X beats B, B beats A, etc), since that would requires
N/2+1 ballots to have the form "...X...Y" -- but there are only N/2-1
ballots left. Indeed, there can't be _any_ options that beat X in the
traditional Condorcet sense.

Another way of looking at the undemocratic example is to say that the
original vote was "B versus D", and that a few people who wanted to stymie
the outcome (50:10 in favour of B) introduced a new option "A". In the
example given, A fails, but in so doing, also knocks B out of the running.

Another way of looking at it is a restatement of the "Condorcet loser
criterion", or a modification of the "local independence from irrelevant
alternatives criterion" to deal with supermajority requirements. (see
http://www.condorcet.org/emr/criteria.shtml)

Cheers,
aj

-- 
Anthony Towns <[EMAIL PROTECTED]> 
I don't speak for anyone save myself. GPG signed mail preferred.

 ``If you don't do it now, you'll be one year older when you do.''



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Re: current A.6 draft [examples]

[Clinton Mead]

Raul Miller wrote:


It's not fair to base an argument on an axiom which is known to be false.
 


On Sun, Dec 08, 2002 at 04:45:07PM +1000, Anthony Towns wrote:
 

It doesn't matter whether the axiom is false as written: it's trivial
to salvage its intended meaning (by either dropping quorum requirements,
or qualifying the axiom to apply only when the quorum requirements have
already been met for all the options listed).
   


I can accept, with that clause added, the axiom that the option ranked
first must win the election.
 

Quorum requirements was not intended to be in the scope of my argument. 
I didn't mention quorum requirements, but I should of mentioned 
explicitally that they were out of its scope. The argument deals with a 
set of votes, a set of options with optional supermajority requirements, 
one of which may optionally be the default option. It doesn't deal with 
quorum requirements, supression of free speech, violence, vote rigging 
or anything else that may effect the democraticness of a method. 
Admitidly, it was reasonable to assume quorum requirements to be part of 
the arguments scope, but I did not intend that.

I am uncomfortable this for the axiom that the option ranked last must
lose.  It's just too arbitrary.  For example, consider also a ballot with
only one option (not that our current system allows this).  The resulting
statement is rather akward to accept as being true without proof.


Myself wrote:
> Minority Loses Axiom - "In a non-supermajority election, if there are 
options A and B, and option B is solely ranked last on a majority of 
votes, then if option B must not win."

Note the minimum inclusion of two options A and B for 'majority loses' 
axiom to have an effect. These are intended to be two different options.

Personally, I'm more unconfortable the idea of an option not losing when 
a majority of votes rank it last and there are other non-supermajority 
options. But which is more unconfortable is for debate.



In any case, later on I'll define another criteria in my opinion an 
election system should follow, and will attempt to prove that CCSSD (and 
newly defined DPCCSSD) does follow and the Dec 7 draft does not. This 
criteria 'Consistancy', is basically that if an option wins when it is 
not the default option, it should win when it is the default option.

---

Firstly, I'm going to define "Default Protection CCSSD", which I will 
call DPCCSSD. Its the same as my old CCSSD, except for rule 9.

Plain CCSSD is defined at 
http://lists.debian.org/debian-vote/2002/debian-vote-200212/msg00020.html.

Its all leading up to another proof, I'll get there...

---

Definition of "Default Protection Considered Clone-Proof Schwartz 
Sequential Dropping" (DPCCSSD).

(1) A defeats B if more votes prefer A over B than B prefer over A.
(2) A challenges B if more than or an equal number of votes prefer A 
over B than prefer B over A.

(3) A defeats B by X, where X is equal to the number of votes that 
prefer A over B, if A defeats B.

(4) A superchalleges B, where A has a supermajority requirement of (X:Y) 
if the number of votes that prefer A over B multiplied by Y is greater 
than or equal to the number of votes that prefer B over A multiplied by X.

(5) A is considered if A superchallenges all options with supermajority 
requirements less than A.
(6) A is considered if A challenges B, where B has supermajority 
requirements greater than or equal to A.

(7) A has a beatpath to B of strength X, if A and B are considered and A 
defeats B by X, or if A, B and C are considered and A defeats C by Y and 
C has a beatpath to B of strength Z, where X is equal to the minimum of 
Y and Z.

(8) A has a beatpath to B of strength 0 if there is no non-zero X such 
that A has a beatpath to B of strength X

(9a) A has a beatpath win to B if A and B are both not default options 
and the largest X such that A has a beatpath to B of X is greater than 
the largest Y such that B has a beatpath to A of Y.

(9b) A has a beatpath win to B if A is the default option, and there is 
a non-zero X such that A has a beatpath to B of strength X.

(9c) A has a beatpath win to B if B is the default option, and there is 
non-zero X such that A has a beatpath to B of X, and there is no 
non-zero Y such that B has a beatpath to A of Y.

(10) A is a finalist if A is considered and there is no B such that B 
has a beatpath win to A.

(11) A is a winner if A is a finalist and there is no B such that the 
casting vote prefers B over A.

Consistancy Criteria - "If election X and election Y have identical 
votes and supermajority requirements, and election X has a default 
option of A, and election Y has a default option of B, and B is the 
winner of election X, then B must be the winner of election Y."

---

Consider this election, with no supermajority requirements.

4 CBA
3 BAC
2 ACB

B defeats A 7:2
C defeats B 6:3
A defeats C 5:4

---

Default option A.

-

Dec 7 Draft: Drop 

Hybrid Theory

[Raul Miller]

Focusing on just A.6 again, in this draft:

(*) Weakest defeats can now be eliminated: before a defeat of the default
option is eliminated, all options which fail to meet their supermajority
requirements are deleted.
(*) When artificial supermajority defeats are eliminated the corresponding
option is also deleted.
(*) Terms expressed using mathematical shorthand have been named.
(*) Other minor fixes

__

   A.6 Vote Counting

 1. Each voter's ballot ranks the options being voted on.  Not all
options need be ranked.  Ranked options are considered preferred
to all unranked options.  Voters may rank options equally.
Options left unranked by the voter are considered to be ranked
equally with one another and below any ranked options.  The other
details of how ballots may be filled out will be included in
the Call For Votes.

 2. We construct the Schwartz set based on undropped options and
defeats:

  a. An option A is in the Schwartz set if A has not been dropped
 and if for all options B, either A transitively defeats B,
 or B does not transitively defeat A.

  b. An option A transitively defeats an option C if A defeats C
 or if there is some other option B, where A defeats B AND
 B transitively defeats C.

  c. An option A defeats an option B, if the strength
 N(A,B)*V(A,B) is larger than N(B,A)*V(B,A), and if the
 (A,B) defeat has not been dropped.

  d. Given two options A and B, the votes V(A,B) is the number
 of voters who prefer option A over option B.

  e. If a majority of n:1 is required for A, and if B is the
 default option, majority requirement N(B,A) is n.  In all
 other cases, N(B,A) is 1.

 3. If any options involved in the weakest defeats between options
in the Schwartz set are options in superdefeats, we drop the
corresponding superdefeated options then return to step 2.

  a. A defeat (A,X) is weaker than a defeat (B,Y) if V(A,X)
 is less than V(B,Y).  Also, (A,X) is weaker than (B,Y) if
 V(A,X) is equal to V(B,Y) AND V(X,A) is larger than V(Y,B).

  b. A weakest defeat is a defeat that has no other defeat weaker
 than it. There may be more than one such defeat.

  c. An option B is superdefeated by an option A if A defeats B,
 and if V(A,B) is not larger than V(B,A).

  c. Given a defeat (A,B) the options A and B are involved in
 this defeat.

  d. An option A is dropped by dropping all defeats which involve
 A and also stipulating that option A is not a member of
 the Schwartz set.

 4. If there are defeats between members of the Schwartz set, we
drop the weakest defeats then return to step 2.

 5. If there are no defeats within the Schwartz set, then the winner
is chosen from the undropped options in the Schwartz set where
at least Q voters ranked that option above default option, where
Q is the quorum requirement for the ballot. If there is only one
such option, it is the winner. If there are multiple options, the
elector with a casting vote chooses which of those options wins.

 "RATIONALE": Options which voters rank above the default option are
 options they find acceptable.  Options ranked below the default
 option are unacceptable options.  Supermajority options require
 some approximation of unanimity before they can be accepted.

__

This changes a few of the outcomes for tests posted in 
http://lists.debian.org/debian-vote/2002/debian-vote-200211/msg00321.html

Here's the test cases which have changed:

A requires 2:1 majority; D is the default option
3 ABD
1 BDA
1 DAB

A defeats B 4:1
B defeats D 4:1
D superdefeats A 4:3

eliminate A

B defeats D 4:1

B wins
in previous draft, this was a tie between B and D
the requirement was that D did not win



Z is the default option
40 A
25 B
35 ZBA

B defeats A 60:40
A defeats Z 40:35
Z defeats B 35:25

eliminate 35:25

B defeats A 60:40
A defeats Z 40:35

B wins
in previous draft, Z won
the requirement was that A not win



Quorum of n, no supermajorities, D is the default option:
25 DAB
30 BDA
35 ABD

B defeats D 65:25
A defeats B 60:30
D defeats A 55:35

eliminate 55:35

B defeats D 65:25
A defeats B 60:30

A wins unless quorum is not met in which case D wins.
In the previous draft B won unless quorum was not met in which case D wins.


Additionally, here's the result of the test proposed by Clinton Mead in
http://lists.debian.org/debian-vote/2002/debian-vote-200212/msg00020.html

A requires 3:1 majority; D is the default option
4 ABD
1 ADB
1 BDA
1 DAB

A defeats B 6:1
D superdefeat

Re: current A.6 draft [examples]

[Raul Miller]

On Mon, Dec 09, 2002 at 03:03:33AM +1100, Clinton Mead wrote:
> In any case, later on I'll define another criteria in my opinion an 
> election system should follow, and will attempt to prove that CCSSD (and 
> newly defined DPCCSSD) does follow and the Dec 7 draft does not. This 
> criteria 'Consistancy', is basically that if an option wins when it is 
> not the default option, it should win when it is the default option.

What's the rationale for this system?

In other words, you're stipulating that for an election where A has 3:1
supermajority, and D is the default option, and the votes are

100 ABD
 35 BAD

that B should win, even though every voter considers A to be an acceptable
option.  Why is this a good idea?

That said, here's how the test case you've proposed here plays out with
the draft I submitted today:

__

A is the default option
4 CBA
3 BAC
2 ACB

B defeats A 7:2
C defeats B 6:3
A defeats C 5:4

eliminate 5:4

B defeats A 7:2
C defeats B 6:3

C wins
__

B is the default option
4 CBA
3 BAC
2 ACB

B defeats A 7:2
C defeats B 6:3
A defeats C 5:4

eliminate 5:4

B defeats A 7:2
C defeats B 6:3

C wins
__

Finally, as an aside: I've been avoiding the beatpath strength mechanism
because I'm not confident of the logic which proves it's equivalent to
CpSSD in an election with supermajorities.

Good enough?

Thanks,

-- 
Raul


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Re: current A.6 draft [examples]

[Anthony Towns]

On Mon, Dec 09, 2002 at 03:03:33AM +1100, Clinton Mead wrote:
> Consistancy Criteria - "If election X and election Y have identical 
> votes and supermajority requirements, and election X has a default 
> option of A, and election Y has a default option of B, and B is the 
> winner of election X, then B must be the winner of election Y."

This criterion doesn't really make any sense: the default option doesn't
change, it's always "further discussion" or "none of the above". It's
just not meaningful to say "consider the same votes when X is the default
option instead of Y".

Cheers,
aj

-- 
Anthony Towns <[EMAIL PROTECTED]> 
I don't speak for anyone save myself. GPG signed mail preferred.

 ``If you don't do it now, you'll be one year older when you do.''



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Re: Hybrid Theory

[Anthony Towns]

On Sun, Dec 08, 2002 at 11:13:23AM -0500, Raul Miller wrote:
>  "RATIONALE": Options which voters rank above the default option are
>  options they find acceptable.  Options ranked below the default
>  option are unacceptable options.  Supermajority options require
>  some approximation of unanimity before they can be accepted.

That's really more of an extended explanation than a rationale, per
se. I'm inclined to think that phrasing it as instructions to the voters
is probably more useful.

Can we possibly stop coming up with full blown voting systems while
we still don't have a firm idea of the underlying things we're trying
to achieve? Seriously: if we can't come up with a list of acceptable,
mutually understood criteria by which we can judge our voting systems,
getting bogged down in implementation details is just confusing the issue.

Here's a start:

(0) The default option should be to leave the vote unresolved;
if people wish to actively preserve the status quo, they should
ensure that is listed as a separate option on the ballot.

(1) We want a voting system that handles quorums.
(1a) Quorums are handled on a per-option basis.
(1b) Electors are counted toward the quorum if they vote, and if they
 rank the option above the default option.

(2) We want a voting system that handles supermajorities.
(2a) An option requiring an N:1 supermajority means that 1/(N+1) of
 the voters may block that option from passing.
(2b) An option that does not meet its supermajority requirement does
 not affect the outcome of the vote.
(2c) Options with a supermajority requirement should be treated as
 similarly to other options as possible.
(2c.i) The supermajority requirement should be satisfied by more
   than N/(N+1) voters ranking that option above the default
   option.
(2c.ii) All other comparisons, including transitive comparisons,
should not be scaled.

I presume there are some people on this list who would say "actually, I
don't want (1)" or "(2) is undesirable and unnecessary". That's fine: we
can list those as alternatives on the vote we eventually have if there's
support for them; what's *important* is to make sure we're all on the
same page as to what we're trying to achieve and _why_ we're trying to
achieve it.

In particular, dropping the options that don't meet their supermajority
requirement before applying CpSSD meets the above criteria better than
strengthening the default versus supermajority-option defeat: it avoids
scaling transitive comparisons and ensures that options that don't meet
the supermajority requirement don't prejudice other options. There may
be other reasons to go the other way, but if we're going to stop going
round and round in circles on this, we need to be *explicit* about them.

Raul, can you give a good a priori reason for declaring the vote:
30 ABD  (A requires a 2:1 supermajority, B a simple majority)
10 BDA
10 DAB
to be a draw between B and D [0], when the vote:
40 BD   (ie, how the vote would've gone if A had not been an option)
10 DB
would have been a clear win to option B?

Cheers,
aj

[0] There's a tie amongst B,D,A, and A defeats B 40:10 and B defeats D
40:10 are equally weakest defeats, so both are dropped, if A is
kept around.

-- 
Anthony Towns <[EMAIL PROTECTED]> 
I don't speak for anyone save myself. GPG signed mail preferred.

 ``If you don't do it now, you'll be one year older when you do.''



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Re: Hybrid Theory

[Raul Miller]

On Mon, Dec 09, 2002 at 03:20:20AM +1000, Anthony Towns wrote:
[what are the underlying things we're trying to achieve]:

> Here's a start:
> 
>   (0) The default option should be to leave the vote unresolved;
>   if people wish to actively preserve the status quo, they should
>   ensure that is listed as a separate option on the ballot.
> 
>   (1) We want a voting system that handles quorums.
>   (1a) Quorums are handled on a per-option basis.
>   (1b) Electors are counted toward the quorum if they vote, and if they
>rank the option above the default option.
> 
>   (2) We want a voting system that handles supermajorities.
>   (2a) An option requiring an N:1 supermajority means that 1/(N+1) of
>the voters may block that option from passing.
>   (2b) An option that does not meet its supermajority requirement does
>not affect the outcome of the vote.
>   (2c) Options with a supermajority requirement should be treated as
>similarly to other options as possible.
>   (2c.i) The supermajority requirement should be satisfied by more
>  than N/(N+1) voters ranking that option above the default
>  option.
>   (2c.ii) All other comparisons, including transitive comparisons,
>   should not be scaled.

Here's my view:

[A] The default option represents voter approval of the ballot -- options
ranked below the default option are options that voter would rather have
been left off the ballot, options ranked above the default option are
options the voter considers acceptable.

[B] We want to use quorum and supermajority.

Looking back at your items,

(0) follows from [A] as options which are not on the ballot
can not be resolutions from that ballot.

(1) follows from [B].
(1a) and (1b) Follow from [A] and [B}.

(2) follows from [B].
(2a) stands alone, and seems fine to me.
(2b) and (2c) stand alone and conflict with each other.
(2d) follows from (2a).
(2e) follows from [A] and (2a).

Interestingly enough, the problem which has lead to all these voting
mechanics proposals very much has to do with the conflict expressed here
between (2b) and (2c).

As an aside: I have been to trying find a theory for using condorcet
to choose between options with sufficiant approval with respect to the
default option.  My requirement has been: don't give bad results for
any of the cases people have brought up where earlier systems could not
be justified.  I've been expressing my understanding of this theory as
voting mechanics drafts.

> In particular, dropping the options that don't meet their supermajority
> requirement before applying CpSSD meets the above criteria better than
> strengthening the default versus supermajority-option defeat: it avoids
> scaling transitive comparisons and ensures that options that don't meet
> the supermajority requirement don't prejudice other options. There may
> be other reasons to go the other way, but if we're going to stop going
> round and round in circles on this, we need to be *explicit* about them.

I've rejected this idea because it introduces
problems which Buddha illustrated in
http://lists.debian.org/debian-vote/2002/debian-vote-200211/msg00162.html

I think it's better to strengthen the defeat of the default vs
supermajority option and to wait to drop related supermajority options
until the point where the presence or absence of this scaled defeat
would cause a problem.

> Raul, can you give a good a priori reason for declaring the vote:
>   30 ABD  (A requires a 2:1 supermajority, B a simple majority)
>   10 BDA
>   10 DAB
> to be a draw between B and D [0], when the vote:
>   40 BD   (ie, how the vote would've gone if A had not been an option)
>   10 DB
> would have been a clear win to option B?

No, I can't give a good a priori reason for declaring this to be a tie
between D and A.

As an aside, the message you're responding to has an explicit example
with a clear win for option B where A requires 2:1, B 1:1, D is default,
with 1 BDA and 1 DAB and 3 ABD votes.

> [0] There's a tie amongst B,D,A, and A defeats B 40:10 and B defeats D
> 40:10 are equally weakest defeats, so both are dropped, if A is
> kept around.

As an aside, the system I proposed earlier today drops A for exactly
that reason.

-- 
Raul


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debian unmanageable?

[David N. Welton]

A few poorly-formed thoughts:

It seems we aren't even able to pick a system to let us vote, let
alone actually debating and voting on issues.

Maybe the answer isn't hyper-democracy, where everyone who maintains a
package gets to decide on every issue.

Maybe we ought to recognize that the power is already in the hands of
those who *do* things, and align our control structures accordingly.

Ever more technical and detailed voting schemes seem like a bad
management hack to me.  Maybe some sort of hierarchical structure is
better.  I can see how these appeal to the inner geek, but they strike
me as heading off in a direction that is potentially very different
from "rough consensus and working code".

One really important role Debian fulfills that makes it somewhat
different from other open source projects is that of a place to ramp
up and get involved, even if you're not an expert C hacker.  I know I
didn't know half of what I know now when I started.  More like 1/10th?
I think this is very important for the free software comunity at
large.  On the other hand, is it fair to entrust the project to a
(potential) majority of developers who are still learning as they go,
and who haven't been around that long?  Not that these people are in
any way bad - as I state above, I think they are terribly important
for the future of free software.

Me?  I'm not that involved in Debian any more, except for a few
packages.  Most of my work these days is for the Apache Software
Foundation.  I have been around Debian since 1997.

If Debian happens to need an supreme and feared emperor-for-life, I'd
be happy to volunteer.  I want minions as part of the deal, though.

Ciao,
-- 
David N. Welton
   Consulting: http://www.dedasys.com/
 Personal: http://www.dedasys.com/davidw/
Free Software: http://www.dedasys.com/freesoftware/
   Apache Tcl: http://tcl.apache.org/


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Re: Hybrid Theory

[Jochen Voss]

Hello

On Mon, Dec 09, 2002 at 03:20:20AM +1000, Anthony Towns wrote:
> Can we possibly stop coming up with full blown voting systems while
> we still don't have a firm idea of the underlying things we're trying
> to achieve?
Good idea :-)

>   (1) We want a voting system that handles quorums.
>   (1a) Quorums are handled on a per-option basis.
>   (1b) Electors are counted toward the quorum if they vote, and if they
>rank the option above the default option.

Can you give reasons for (1a) and (1b)?  As far as I
understood the debate, the reason for a quorum is to avoid
"stealth-decision-making", i.e. to assert that enough
developers notice the election and take part in it.  Because
of this for me the concept of a per-option quorum does not
make much sense.  What do you think?

Some other goal I would propose:

(3) In the absence of a quorum/supermajority requirement our
voting system should behave identical to textbook Condorcet
voting with Cloneproof Schwartz sequential dropping.

This may be clear (is it?) but I think that some of the
previous drafts did not have this property.

And finally: the reason way we want Condorcet voting is,
that this system is a "good" voting system in the sense of

http://electionmethods.org/evaluation.htm

I append a list of good properties of Condorecet voting
below (summarized from the election-methods page).  To
handle quorum and supermajority requirements we have to make
changes to the voting system.  In my opionion we should find
out which of the properties we loose because of the changes.
Remember: these properties were the reason why we want
Condorcet voting instead of competing systems.

What do you think?

Jochen



A list of good properties of Condorcet Voting
(from http://electionmethods.org/evaluation.htm)

  * Monotonicity Criterion (MC):
If a single voter changes his mind and ranks an option higher,
this option can not stop being the winner because of this

  * Condorcet Criterion (CC):
If one candidate is preferred over each of the other
candidates, that candidate is the Ideal Democratic Winner
(IDW).  If all votes are sincere, the Ideal Democratic
Winner should win if one exists.

  * Generalized Condorcet Criterion (GCC):
If all votes are sincere, the winner should be a member
of the Smith set.
   ^
this is what we call "Schwartz set".

  * Strategy-Free Criterion (SFC):
If an Ideal Democratic Winner (IDW) exists, and if a
majority prefers the IDW to another candidate, then the
other candidate should not win if that majority votes
sincerely and no other voter falsifies any preferences.

Note: sometimes (When good options are ranked equal) and
IDW can be not preferred by a majority of voters over
another candidate.

  * Generalized Strategy-Free Criterion (GSFC)

If an Ideal Democratic Winner (IDW) exists, and if a
majority prefers the IDW to another candidate, then the
other candidate should not win if that majority votes
sincerely and no other voter falsifies any preferences.

  * Strong Defensive Strategy Criterion (SDSC)

If a majority prefers one particular candidate to
another, then they should have a way of voting that will
ensure that the other cannot win, without any member of
that majority reversing a preference for one candidate
over another or falsely voting two candidates equal.

This seems to be a weaker form of what we want to achive
with supermajority requirements.

  * Weak Defensive Strategy Criterion (WDSC)

If a majority prefers one particular candidate to
another, then they should have a way of voting that will
ensure that the other cannot win, without any member of
that majority reversing a preference for one candidate
over another.

Condorcet voting with Cloneproof Schwartz sequential dropping
additionally has the "cloneproof" property (from
http://electionmethods.org/CondorcetEx.htm)

  * The Schwartz Sequential Dropping (SSD) method has a
``plain'' version and the ``cloneproof'' version. The
cloneproof version gives no group or party any advantage
or disadvantage for having additional candidates that
are essentially ``clones'' of each other.  Except for
the case of ties, the two versions give the same result.
-- 
 Omm
  (0)-(0)
http://www.mathematik.uni-kl.de/~wwwstoch/voss/index.html



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Re: Hybrid Theory

[Raul Miller]

On Sun, Dec 08, 2002 at 09:03:22PM +0100, Jochen Voss wrote:
> Can you give reasons for (1a) and (1b)?  As far as I understood the
> debate, the reason for a quorum is to avoid "stealth-decision-making",
> i.e. to assert that enough developers notice the election and take part
> in it.  Because of this for me the concept of a per-option quorum does
> not make much sense.  What do you think?

Ballot contains A and D, A has 1:1 majority, D is default option.
Quorum is 45.

23 people vote for A.

A defeats D, but A doesn't meet quorum, default option wins.

23 people vote for A.
22 people vote for D.

A defeats D, A meets quorum, A wins.

Or: the addition of 22 people voting against A caused A to win.  In my
opinion, this is very wrong.

Note also that the process of ballot creation needs protection from
lack of interest.  We can't assume, just because someone submits a
ballot, that they participated during the creation of that ballot.
I use comparison with the default option to determine whether or not
the voter approves of that option being on the ballot.

Aside: I'm in favor of an analysis of the voting system based on the
electionmethods principles you referred to.  I expect [hope] that
without quorum and supermajority requirements the system I proposed
earlier today meets all the criteria of condorcet.  With quorum and
supermajority I expect there to be edge cases where we lose criteria
which aren't criteria of approval.  I hope someone can prove that my
expectations are right [or wrong, if they are indeed wrong].

Thanks,

-- 
Raul


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Re: Hybrid Theory

[Sven Luther]

On Sun, Dec 08, 2002 at 03:18:16PM -0500, Raul Miller wrote:
> On Sun, Dec 08, 2002 at 09:03:22PM +0100, Jochen Voss wrote:
> > Can you give reasons for (1a) and (1b)?  As far as I understood the
> > debate, the reason for a quorum is to avoid "stealth-decision-making",
> > i.e. to assert that enough developers notice the election and take part
> > in it.  Because of this for me the concept of a per-option quorum does
> > not make much sense.  What do you think?
> 
> Ballot contains A and D, A has 1:1 majority, D is default option.
> Quorum is 45.
> 
> 23 people vote for A.
> 
> A defeats D, but A doesn't meet quorum, default option wins.
> 
> 23 people vote for A.
> 22 people vote for D.
> 
> A defeats D, A meets quorum, A wins.
> 
> Or: the addition of 22 people voting against A caused A to win.  In my
> opinion, this is very wrong.

Why ?

You are trying to use the quorum for something it is not for.

A quorum (in traditional elections) is just a mean of ensuring that
enough people are present so that the election is meaningfull.

Also, there is no way you are going to be able to explicitly exploit
this weakness you pointed out, unless you are the project voting
secretary (or whatever it is called) or you did manage to get access to
the already voted ballot.

Let's say you are against option A, and you have two choices :

  o not vote, in hope the quorum will not be met.

  o vote against A (or DA in this case).

if you do not vote, like you suppose, you can only do this in a
meaningfull way if you are sure that the quorum will not be met, which
should not be possible. And if you don't vote and the quorum is met,
then you have one less vote against A, and if A wins, you deserve it.

Friendly,

Sven Luther


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Re: Hybrid Theory

[Raul Miller]

> > Or: the addition of 22 people voting against A caused A to win.  In my
> > opinion, this is very wrong.

On Sun, Dec 08, 2002 at 09:38:46PM +0100, Sven Luther wrote:
> Why ?

I answered this in the message you were responding to, immediately
following the paragraph you quoted.

> You are trying to use the quorum for something it is not for.

I disagree.

> A quorum (in traditional elections) is just a mean of ensuring that
> enough people are present so that the election is meaningfull.

And that's what I'm using quorum for.

Except my proposal for quorum satisfys the monotonicity criterion
(http://www.electionmethods.org/evaluation.html#MC) while the mechanism
you're proposing would have cases where an option wins *because* of
votes against it.

> Also, there is no way you are going to be able to explicitly exploit
> this weakness you pointed out, unless you are the project voting
> secretary (or whatever it is called) or you did manage to get access to
> the already voted ballot.

I'm concerned about the effects of lack-of-interest.  I don't want people
deciding to not submit a ballot because of the chance that they'll cause
something they're opposed to to win.  If this happens even once it will
be very upsetting.

> Let's say you are against option A, and you have two choices :
> 
>   o not vote, in hope the quorum will not be met.
> 
>   o vote against A (or DA in this case).
> 
> if you do not vote, like you suppose, you can only do this in a
> meaningfull way if you are sure that the quorum will not be met, which
> should not be possible. And if you don't vote and the quorum is met,
> then you have one less vote against A, and if A wins, you deserve it.

Your argument is valid if quorum is never used.

Imagine that quorum is relevant at some point in time: imagine that we
have a set of elections which default because they don't meet quorum.

At this point: you wouldn't be certain that the some elections will meet
quorum.  Neither could you be certain that voting against an amendment
in some elections would not cause that amendment to win.

-- 
Raul


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Debian voting system resources

[Jochen Voss]

Hello,

I set up a web page with Debian voting system resources.
My page tries to cover everything which is important for
the planned rewrite of our voting system.  I hope that
the page provides a good starting point for anybody who
wants to join the voting system discussion.

The address of my web page is

http://www.mathematik.uni-kl.de/~wwwstoch/voss/comp/vote.html

I hope this helps,
Jochen
-- 
 Omm
  (0)-(0)
http://www.mathematik.uni-kl.de/~wwwstoch/voss/index.html



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Re: Hybrid Theory

[Matthias Urlichs]

Hi,

Raul Miller:
> Anthony Towns:
> > In particular, dropping the options that don't meet their supermajority
> > requirement before applying CpSSD meets the above criteria better than
> > strengthening the default versus supermajority-option defeat: it avoids
> > scaling transitive comparisons and ensures that options that don't meet
> > the supermajority requirement don't prejudice other options.
> 
> I've rejected this idea because it introduces
> problems which Buddha illustrated in
> http://lists.debian.org/debian-vote/2002/debian-vote-200211/msg00162.html
> 
It's a known fact that dropping (or adding) an option from a Condorcet
election may change its result if there's a cycle.

You want an election method where this cannot happen?
Don't use Condorcet voting.  It's that simple.  :-/

I don't like to play around with ratios when considering the supermajority
requirement. It already has led to one unforeseen effect (the rule about
not dropping the default, because otherwise the supermajority-requiring
option might _still_ win -- which gives the default option a strength it
IMHO does NOT deserve); nobody can guarantee that there are no others.

-- 
Matthias Urlichs | noris network AG | http://smurf.noris.de/



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Re: Hybrid Theory

[Anthony Towns]

On Sun, Dec 08, 2002 at 09:03:22PM +0100, Jochen Voss wrote:
> > (1) We want a voting system that handles quorums.
> > (1a) Quorums are handled on a per-option basis.
> > (1b) Electors are counted toward the quorum if they vote, and if they
> >  rank the option above the default option.
> Can you give reasons for (1a) and (1b)? 

I can't give a reason for (1); quorums in real meetings are used to
make sure enough people are able to participate in decisions for them
to be meaningful.  Since we do everything over mailing lists and have a
couple of weeks for every issue to be considered, I'm not sure there's
any benefit to making sure there are at least a given number of votes.

But on the assumption that there is, then we need to take account of
the differences between Debian's system than real life meetings. First,
in a real life meeting, everyone who's present is counted for a quorum:
they're locked in a room and can't leave afterall, so it doesn't matter
how they vote. For Debian, you don't have any "presence" to count, and
you don't want to discourage people from voting, which means allowing
them to vote in such a way that options they don't like are given no
support whatsoever.

Additionally, this gives us the minimum change from what we have now.

> Some other goal I would propose:
> (3) In the absence of a quorum/supermajority requirement our
> voting system should behave identical to textbook Condorcet
> voting with Cloneproof Schwartz sequential dropping.
> This may be clear (is it?) but I think that some of the
> previous drafts did not have this property.

It's irrelevant, we don't have votes without quorum/supermajority
requirement.

Note that as stated our votes are a combination of approval and Condorcet
voting: an option is "approved" by the number of ballots that rank it
above the default option.

One way to think about this is to say:

(1) First we use approval voting to handle the default option,
quorum and supermajority. An option is "approved" by the
number of votes that rank it above the default option. An
option is "disapproved" by the number of votes that rank it
below the default option.

If an option is approved by fewer votes than its quorum, it
is dropped.

If an option requiring a supermajority of N:1 is approved by
fewer than N times the number of votes it is disapproved by, it
is dropped.

If an option is approved by no more than the number of votes
it is disapproved by, it is dropped.

If the only remaining option is the default option, it wins.

Otherwise, the default option is dropped.

(2) The Cloneproof Schwartz Sequential Dropping method is applied to
the remaining options. In the event of a tie, the elector with a
casting vote decides amongst the tied options.

> What do you think?

I think the above is a counterexample to your idea: it obviously has the
good properties of CpSSD that we want: we're using it and nothing else
to choose between all the real options -- we don't have any fake options,
we don't have any scaling, we don't have any special rules hacked in.

Again, the default option is fundamentally special. It's not there
because people want it to win -- if they want the status quo they need
to specifically nominate that -- it's there to handle our additional
requirements that Condorcet systems don't manage.

Cheers,
aj

-- 
Anthony Towns <[EMAIL PROTECTED]> 
I don't speak for anyone save myself. GPG signed mail preferred.

 ``If you don't do it now, you'll be one year older when you do.''



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Re: Hybrid Theory

[Anthony DeRobertis]

On Sun, 2002-12-08 at 23:51, Anthony Towns wrote:

> I can't give a reason for (1); quorums in real meetings are used to
> make sure enough people are able to participate in decisions for them
> to be meaningful.  Since we do everything over mailing lists and have a
> couple of weeks for every issue to be considered, I'm not sure there's
> any benefit to making sure there are at least a given number of votes.

Not to mention with 1000 developers 3Q = e(1/2*l(1000))/2*3 = ~47.4. I
don't think fewer than 48 out of 1000 people will vote ever, and
www.debian.org/vote bears me out. No decided issues have less than 100
votes.

So, suggest go ahead with it: Drop all ocurances of "Q" and quorum from
the Consitution.

BTW:  has the quorum
calculated wrong. "Q is HALF of the square root of the number of current
Developers"; someone forgot the half part when calculating Q on that
page. Q is really ~11.15, making the quorum 33.44, not 67.
 has the same problem. And
.

 and
 have the proper calculation,
and  didn't bother.





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Re: Hybrid Theory

[Jochen Voss]

On Mon, Dec 09, 2002 at 02:51:18PM +1000, Anthony Towns wrote:
> It's irrelevant, we don't have votes without quorum/supermajority
> requirement.
Sorry, I didn't know that :-(

> I think the above is a counterexample to your idea:
Which idea?  A counterexample to per-vote (and not pre-option)
quorums?  Or to the idea of being aware what properties of
Condorcet voting we sacrifice?

> it obviously has the good properties of CpSSD that we want: [...]
Sorry, but which properties?  Maybe the presence of quorum and
supermajority?

Jochen
-- 
 Omm
  (0)-(0)
http://www.mathematik.uni-kl.de/~wwwstoch/voss/index.html



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