Re: Request for comments [voting amendment]

[Branden Robinson]

On Tue, Nov 12, 2002 at 06:03:54PM -0500, Raul Miller wrote:
> This is not a full draft.  In this post, I'm only including
> text for replacing A.6 of the constitution.  I wanted to
> also rewrite the changes to A.3, but I've got to run some
> errands tonight and I'm not going to have time to write up
> a full draft.

It's just as well that we review the changes separately, IMO.

I concur with all of Anthony's revisions from Message-ID:
<[EMAIL PROTECTED]>, except that I would say
"among" instead of "amongst"[1].

>   Definition: An option F is in the beat path of option G if
>   option G defeats option F or if there is some other option
>   H where option H is in the beat path of G AND option F is in
>   the beat path of H.

I'm not crazy about recursive definitions.

  Definition: An option F is in the beat path of option G if option G
  defeats option F, or if there is another option H which defeats G, AND
  option F defeats H.

With this definition you can mentally "build up" a beat path, applying
F, G, and H to different options as you iterate.  Your definition does
have the advantage of functioning better as pseudocode, though.  :)

I suggest this because, being American and thus unaccustomed to
preferential voting mechanisms, I was unfamiliar with the concept of
"beat path" when I was first exposed to it.

>  The more votes in favor of a defeated option, the weaker
>  the defeat.  Where two pairs of options have the same number
>  of votes in favor of the defeated option, the fewer votes in
>  favor of the defeating option, the weaker the defeat.

I find the second sentence awkward even if it is grammatical.

I suggest:

  Where two pairs of options have the same number of votes in favor of
  the defeated option, the pair with fewer number of votes in favor of
  the defeating option is the weaker defeat.

I have made these suggestions because I think it is important that
people have a firm understanding of how the proposed new voting
procedure works.  We will require a lot of votes to successfully pass
this GR, and while those who have taken the time to educate themselves
on election methods seem unanimously convinced that this GR is a good
idea, we need to able to rely on more than faith in authority figures to
persuade the developers.

[1] How small a nit can I pick?  Only Ian Jackson knows for sure...

-- 
G. Branden Robinson|I just wanted to see what it looked
Debian GNU/Linux   |like in a spotlight.
[EMAIL PROTECTED] |-- Jim Morrison
http://people.debian.org/~branden/ |


pgpGhYCdeHWdz.pgp
Description: PGP signature

Re: Proposal - non-free software removal

[John Goerzen]

I accept Branden's amendment.

On Tue, Nov 12, 2002 at 04:48:04AM -0500, Branden Robinson wrote:
> I would like to a very minor amendment to this proposal.  I will not
> withdraw my second if you elect not to accept it.
> 
> > D. That the maintainer of the Debian Policy Manual, or an appointee of
> > the Debian Project Leader, be directed to update that manual
> [...]
> > E. That the maintainers of the Debian archives and website, or an
> > appointee of the Debian Project Leader, be directed to implement the
> 
> s/appointee/delegate/
> 
> I think it is preferable that we employ in this resolution the term used
> by the Constitution for such people.
> 
> -- 
> G. Branden Robinson|People are equally horrified at
> Debian GNU/Linux   |hearing the Christian religion
> [EMAIL PROTECTED] |doubted, and at seeing it
> http://people.debian.org/~branden/ |practiced. -- Samuel Butler




pgp69LbD5H3YB.pgp
Description: PGP signature

Re: Request for comments [voting amendment]

[Anthony Towns]

On Wed, Nov 13, 2002 at 12:54:59PM -0500, Branden Robinson wrote:
> >   Definition: An option F is in the beat path of option G if
> >   option G defeats option F or if there is some other option
> >   H where option H is in the beat path of G AND option F is in
> >   the beat path of H.
> I'm not crazy about recursive definitions.
>   Definition: An option F is in the beat path of option G if option G
>   defeats option F, or if there is another option H which defeats G, AND
>   option F defeats H.

This isn't equivalent.

First, it's wrong: G defeats H and H defeats F, for F to be in the beat
path of G. I really dislike the phrase "in the beat path of", since it
makes exactly this sort of mistake easy to make. Please let us switch
to "transitively beats" or "dominates" or something with a similarly
intuitive meaning.

Slightly more subtly, though, it's not equivalent: if you've got A
defeats B, B defeats C, C defeats D, (and C defeats A, D defeats A,
and D defeats B), then D is still in the beat path of A, even though
neither of the following are true:

B defeats D and A defeats B   (F=D, G=A, H=B -- B doesn't defeat D)
C defeats D and A defeats C   (F=D, G=A, H=C -- C doesn't defeat D)

This is possible in an election where people vote as follows:

50 DABC
40 BCDA
30 CDAB

A defeats B, 80 to 40
B defeats C, 90 to 30
C defeats D, 70 to 50
C defeats A, 70 to 50
D defeats A, 120 to 0
D defeats B, 80 to 40

> With this definition you can mentally "build up" a beat path,

If you want to avoid recursion, you need explicit iteration, something
like:

Option F is said to transitively beat option G if F beats G, or if
there are a sequence of options, H_1, H_2, ..., H_n, such that F
beats H_1, H_i beats H_i+1, and H_n beats G.

> I suggest this because, being American and thus unaccustomed to
> preferential voting mechanisms, I was unfamiliar with the concept of
> "beat path" when I was first exposed to it.

"beat paths" are exclusive to Condorcet style voting, and Debian's still
the sole group to actually use one of those, outside of election-method
geeks. So it ain't just yankees who aren't familiar with it.

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.''

Re: Request for comments [voting amendment]

[Aaron M. Ucko]

Branden Robinson <[EMAIL PROTECTED]> writes:

> On Tue, Nov 12, 2002 at 06:03:54PM -0500, Raul Miller wrote:
[...]
> >   Definition: An option F is in the beat path of option G if
> >   option G defeats option F or if there is some other option
> >   H where option H is in the beat path of G AND option F is in
> >   the beat path of H.
> 
> I'm not crazy about recursive definitions.
> 
>   Definition: An option F is in the beat path of option G if option G
>   defeats option F, or if there is another option H which defeats G, AND
>   option F defeats H.
> 
> With this definition you can mentally "build up" a beat path, applying
> F, G, and H to different options as you iterate.  Your definition does
> have the advantage of functioning better as pseudocode, though.  :)

AFAICT, your version only gives one level of transitivity, which does
not necessarily suffice.  An explicitly iterative version would have
to read along the lines of

  Definition: An option F is in the beat path of option G if option G
  defeats option F, or if there is a sequence of other options H_1,
  ..., H_n (where n may be 1) such that H_1 defeats F, G defeats H_n,
  AND for every i from 1 to n-1, H_{i+1} defeats H_i.

which I'm not convinced is better.

-- 
Aaron M. Ucko, KB1CJC (amu at alum.mit.edu, ucko at debian.org)
Finger [EMAIL PROTECTED] (NOT a valid e-mail address) for more info.

Re: Request for comments [voting amendment]

[Buddha Buck]

Raul Miller wrote:

This is not a full draft.  In this post, I'm only including
text for replacing A.6 of the constitution.  I wanted to
also rewrite the changes to A.3, but I've got to run some
errands tonight and I'm not going to have time to write up
a full draft.

Please let me know of any flaws in the following partial draft:


I'd like some clarifications...



  A.6 Vote Counting

1. Each ballot orders the options being voted on in the order
   specified by the voter.  Any options unranked by the voter are
   treated as being equal to any other unranked options and below
   all options ranked by the voter.


Definition:  A "ballot" consists of a ranking A>B>C>D>... of options 
submitted by a voter.  It defines a total ordering of options for a 
particular voter (i.e., for any pair of options A and B, we can claim 
that a particular voter feels either A>B, AB, then 
B

Let |A>B| be the number of voters who voted A>B.
Similarly, for |A(Obviously, |A>B| + |A=B| + |Athe definition of a ballot.)



2. Options which do not defeat the default option are eliminated.

   Definition: Option A defeats option B if more voters prefer optio
   A over option B than prefer option B over option A.


Let A>>B ("A defeats B")if |A>B| > |B>A|
Let A==B ("A ties B")   if |A>B| = |B>A|
Let AA|
(Note: A==A, for all options A)

Eliminate all options A if Default>>A.

Clarification:  What if Default==A?


3. If an option has a quorum requirement, that option must defeat
   the default option by the number of votes specified in the quorum
   requirement or the option is eliminated.


Does is mean:

Eliminate A if |A>Default| < Quorum

or

Eliminate A if |A>Default| - |Default>A| < Quorum

Again, how do we deal with that |A=Default| case?



4. If an option has a supermajority requirement, that option must
   defeat the default option by the ratio of votes specified in the
   quorum requirement or the option is eliminated.


(?) Eliminate A if |A>Default| / |A

5. If one remaining option defeats any other remaining options,
   that option wins.


s/any/all/

"Condorcet Winner"

If there is a remaining option A, such that for all remaining options B, 
either A=B, or A>>B.



6. If more than one option remains after the above steps, we use
   Cloneproof Schultz Sequential Dropping to eliminate any cyclic
   ambiguities and then pick the winner.  These represent a procedure
   and must be carried out in the specified order:

   i. All options not in the Schultz set are eliminated.

  Definition: An option C is in the Schultz set if there is no
  other option D such that C is in the beat path of D AND D is
  not in the beat path of C.


Let A>>>B mean there is a possibly empty sequence C, D, ..., E, F of 
remaining options such that A>>C, C>>D, ..., E>>F, F>>B


Then B is on the beat path of A.

The Schultz Set = { A | A>>>A }

Note:  Because A==A, it isn't the case that A>>A, so if the Schultz set 
includes A, then there must be a B!=A such that A>>B>>...>>A.  Since 
A>>B, we then have B>>...>>A>>B, so B is also in the Schultz set. 
Therefore, the Schultz Set can't be a Singleton Set.



  Definition: An option F is in the beat path of option G if
  option G defeats option F or if there is some other option
  H where option H is in the beat path of G AND option F is in
  the beat path of H.

   ii. Unless this would eliminate all options in the Schultz set,
   the options which have the weakest defeat are eliminated.

   Definition: The strength of a defeat is represented by two
   numbers: the number of votes for the defeated option and the
   number of votes for the defeating option.

   The more votes in favor of a defeated option, the weaker
   the defeat.  Where two pairs of options have the same number
   of votes in favor of the defeated option, the fewer votes in
   favor of the defeating option, the weaker the defeat.


So if we have two defeats A>>B and C>>D, then we lexigraphically compare 
(|B>A|, -|A>B|) and (|D>C|, -|C>D|)


What do you mean by "options with the weakest defeat"?

My understanding was that we were removing defeats from consideration. 
If, for example, there were four options A, B, C, D in the Schultz Set, 
we'd initially be looking at the following set of defeats, in strongest 
to weakest order:


A>>B
A>>D
B>>C
C>>A
D>>C
B>>D

After eliminating the weakest defeat (in this case, B>>D, we no longer 
consider it when determining the Schultz Set, as if we had declared 
B==D, so that neither B>>D or D>>B held.


So what do we really want to eliminate here?

And...

What if we had |D>C| = |B>D|, |D=C| = |B=D|, |Dneither D>>C nor B>>D was weaker than the other?  Do we eliminate both 
defeats?



   iii. If eliminating the weakest defeat would eliminate all options

Re: Request for comments [voting amendment]

[Branden Robinson]

On Thu, Nov 14, 2002 at 06:24:14AM +1000, Anthony Towns wrote:
> On Wed, Nov 13, 2002 at 12:54:59PM -0500, Branden Robinson wrote:
> >   Definition: An option F is in the beat path of option G if option G
> >   defeats option F, or if there is another option H which defeats G, AND
> >   option F defeats H.
> 
> This isn't equivalent.
> 
> First, it's wrong: G defeats H and H defeats F, for F to be in the beat
> path of G. I really dislike the phrase "in the beat path of", since it
> makes exactly this sort of mistake easy to make. Please let us switch
> to "transitively beats" or "dominates" or something with a similarly
> intuitive meaning.

Sorry about that.  I retract my proposed amendment quoted above.

> Slightly more subtly, though, it's not equivalent: if you've got A
> defeats B, B defeats C, C defeats D, (and C defeats A, D defeats A,
> and D defeats B), then D is still in the beat path of A, even though
> neither of the following are true:
> 
>   B defeats D and A defeats B   (F=D, G=A, H=B -- B doesn't defeat D)
>   C defeats D and A defeats C   (F=D, G=A, H=C -- C doesn't defeat D)
> 
> This is possible in an election where people vote as follows:
> 
>   50 DABC
>   40 BCDA
>   30 CDAB
> 
> A defeats B, 80 to 40
> B defeats C, 90 to 30
> C defeats D, 70 to 50
> C defeats A, 70 to 50
> D defeats A, 120 to 0
> D defeats B, 80 to 40

I see.

> > With this definition you can mentally "build up" a beat path,
> 
> If you want to avoid recursion, you need explicit iteration, something
> like:
> 
> Option F is said to transitively beat option G if F beats G, or if
> there are a sequence of options, H_1, H_2, ..., H_n, such that F
> beats H_1, H_i beats H_i+1, and H_n beats G.

Can we use the term "transitively defeat", and thus leave the term
"beat" out of the proposal altogether.  This way no one will wonder what
an unqualified "beat" is.

While your definition smacks of mathematical notation (which scares some
people), it does seem the most clear way to express this.

> > I suggest this because, being American and thus unaccustomed to
> > preferential voting mechanisms, I was unfamiliar with the concept of
> > "beat path" when I was first exposed to it.
> 
> "beat paths" are exclusive to Condorcet style voting, and Debian's still
> the sole group to actually use one of those, outside of election-method
> geeks. So it ain't just yankees who aren't familiar with it.

Wow, be careful saying charitable things about Americans, it might tempt
W to start a war with Iraq even earlier, citing "international support".


-- 
G. Branden Robinson|
Debian GNU/Linux   |   If ignorance is bliss,
[EMAIL PROTECTED] |   is omniscience hell?
http://people.debian.org/~branden/ |


pgpz9NxnnqSZW.pgp
Description: PGP signature

Re: Request for comments [voting amendment]

[Branden Robinson]

On Wed, Nov 13, 2002 at 03:42:37PM -0500, Aaron M. Ucko wrote:
> AFAICT, your version only gives one level of transitivity, which does
> not necessarily suffice. 

I have retracted it.

> An explicitly iterative version would have to read along the lines of
> 
>   Definition: An option F is in the beat path of option G if option G
>   defeats option F, or if there is a sequence of other options H_1,
>   ..., H_n (where n may be 1) such that H_1 defeats F, G defeats H_n,
>   AND for every i from 1 to n-1, H_{i+1} defeats H_i.
> 
> which I'm not convinced is better.

I don't know.  It's pretty close to Anthony's, which I support, except I
think I see away to avoid the term "beat" altogether (and "dominate",
too).

A minimum of jargon is, I think, a feature.

-- 
G. Branden Robinson| One man's "magic" is another man's
Debian GNU/Linux   | engineering.  "Supernatural" is a
[EMAIL PROTECTED] | null word.
http://people.debian.org/~branden/ | -- Robert Heinlein


pgpG2Unm2TeuO.pgp
Description: PGP signature

Re: Request for comments [voting amendment]

[Anthony Towns]

On Wed, Nov 13, 2002 at 06:13:14PM -0500, Buddha Buck wrote:
> The Schultz Set = { A | A>>>A }
> Note:  Because A==A, it isn't the case that A>>A,

This is clever, but wrong. Consider an election with people voting:

30 x ABCD
40 x ACDB
50 x ADBC

A wins unanimously and is the only member of the *Schwartz* set. However,
B beats C beats D beats B, so { x | x >>> x } = {B, C, D}.

Alternately, consider something like:

40 x AB CDE
30 x AB DEC
20 x BA DEC
50 x BA ECD

A and B are equal (70 votes each), and C > D > E > C, but A,B both beat
each of C,D,E, but { x | x >>> x } = {A,B,C,D,E}.

The correct restatement is something more like:

{ x | forall y: y >> x --> x >>> 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.''


pgptaGmNv7A3V.pgp
Description: PGP signature

Re: Request for comments [voting amendment]

[Branden Robinson]

On Tue, Nov 12, 2002 at 06:03:54PM -0500, Raul Miller wrote:
> This is not a full draft.  In this post, I'm only including
> text for replacing A.6 of the constitution.  I wanted to
> also rewrite the changes to A.3, but I've got to run some
> errands tonight and I'm not going to have time to write up
> a full draft.

It's just as well that we review the changes separately, IMO.

I concur with all of Anthony's revisions from Message-ID:
<[EMAIL PROTECTED]>, except that I would say
"among" instead of "amongst"[1].

>   Definition: An option F is in the beat path of option G if
>   option G defeats option F or if there is some other option
>   H where option H is in the beat path of G AND option F is in
>   the beat path of H.

I'm not crazy about recursive definitions.

  Definition: An option F is in the beat path of option G if option G
  defeats option F, or if there is another option H which defeats G, AND
  option F defeats H.

With this definition you can mentally "build up" a beat path, applying
F, G, and H to different options as you iterate.  Your definition does
have the advantage of functioning better as pseudocode, though.  :)

I suggest this because, being American and thus unaccustomed to
preferential voting mechanisms, I was unfamiliar with the concept of
"beat path" when I was first exposed to it.

>  The more votes in favor of a defeated option, the weaker
>  the defeat.  Where two pairs of options have the same number
>  of votes in favor of the defeated option, the fewer votes in
>  favor of the defeating option, the weaker the defeat.

I find the second sentence awkward even if it is grammatical.

I suggest:

  Where two pairs of options have the same number of votes in favor of
  the defeated option, the pair with fewer number of votes in favor of
  the defeating option is the weaker defeat.

I have made these suggestions because I think it is important that
people have a firm understanding of how the proposed new voting
procedure works.  We will require a lot of votes to successfully pass
this GR, and while those who have taken the time to educate themselves
on election methods seem unanimously convinced that this GR is a good
idea, we need to able to rely on more than faith in authority figures to
persuade the developers.

[1] How small a nit can I pick?  Only Ian Jackson knows for sure...

-- 
G. Branden Robinson|I just wanted to see what it looked
Debian GNU/Linux   |like in a spotlight.
[EMAIL PROTECTED] |-- Jim Morrison
http://people.debian.org/~branden/ |



msg01896/pgp0.pgp
Description: PGP signature

Re: Proposal - non-free software removal

[John Goerzen]

I accept Branden's amendment.

On Tue, Nov 12, 2002 at 04:48:04AM -0500, Branden Robinson wrote:
> I would like to a very minor amendment to this proposal.  I will not
> withdraw my second if you elect not to accept it.
> 
> > D. That the maintainer of the Debian Policy Manual, or an appointee of
> > the Debian Project Leader, be directed to update that manual
> [...]
> > E. That the maintainers of the Debian archives and website, or an
> > appointee of the Debian Project Leader, be directed to implement the
> 
> s/appointee/delegate/
> 
> I think it is preferable that we employ in this resolution the term used
> by the Constitution for such people.
> 
> -- 
> G. Branden Robinson|People are equally horrified at
> Debian GNU/Linux   |hearing the Christian religion
> [EMAIL PROTECTED] |doubted, and at seeing it
> http://people.debian.org/~branden/ |practiced. -- Samuel Butler





msg01897/pgp0.pgp
Description: PGP signature

Re: Request for comments [voting amendment]

[Aaron M. Ucko]

Branden Robinson <[EMAIL PROTECTED]> writes:

> On Tue, Nov 12, 2002 at 06:03:54PM -0500, Raul Miller wrote:
[...]
> >   Definition: An option F is in the beat path of option G if
> >   option G defeats option F or if there is some other option
> >   H where option H is in the beat path of G AND option F is in
> >   the beat path of H.
> 
> I'm not crazy about recursive definitions.
> 
>   Definition: An option F is in the beat path of option G if option G
>   defeats option F, or if there is another option H which defeats G, AND
>   option F defeats H.
> 
> With this definition you can mentally "build up" a beat path, applying
> F, G, and H to different options as you iterate.  Your definition does
> have the advantage of functioning better as pseudocode, though.  :)

AFAICT, your version only gives one level of transitivity, which does
not necessarily suffice.  An explicitly iterative version would have
to read along the lines of

  Definition: An option F is in the beat path of option G if option G
  defeats option F, or if there is a sequence of other options H_1,
  ..., H_n (where n may be 1) such that H_1 defeats F, G defeats H_n,
  AND for every i from 1 to n-1, H_{i+1} defeats H_i.

which I'm not convinced is better.

-- 
Aaron M. Ucko, KB1CJC (amu at alum.mit.edu, ucko at debian.org)
Finger [EMAIL PROTECTED] (NOT a valid e-mail address) for more info.


-- 
To UNSUBSCRIBE, email to [EMAIL PROTECTED]
with a subject of "unsubscribe". Trouble? Contact [EMAIL PROTECTED]

Re: Request for comments [voting amendment]

[Anthony Towns]

On Wed, Nov 13, 2002 at 12:54:59PM -0500, Branden Robinson wrote:
> >   Definition: An option F is in the beat path of option G if
> >   option G defeats option F or if there is some other option
> >   H where option H is in the beat path of G AND option F is in
> >   the beat path of H.
> I'm not crazy about recursive definitions.
>   Definition: An option F is in the beat path of option G if option G
>   defeats option F, or if there is another option H which defeats G, AND
>   option F defeats H.

This isn't equivalent.

First, it's wrong: G defeats H and H defeats F, for F to be in the beat
path of G. I really dislike the phrase "in the beat path of", since it
makes exactly this sort of mistake easy to make. Please let us switch
to "transitively beats" or "dominates" or something with a similarly
intuitive meaning.

Slightly more subtly, though, it's not equivalent: if you've got A
defeats B, B defeats C, C defeats D, (and C defeats A, D defeats A,
and D defeats B), then D is still in the beat path of A, even though
neither of the following are true:

B defeats D and A defeats B   (F=D, G=A, H=B -- B doesn't defeat D)
C defeats D and A defeats C   (F=D, G=A, H=C -- C doesn't defeat D)

This is possible in an election where people vote as follows:

50 DABC
40 BCDA
30 CDAB

A defeats B, 80 to 40
B defeats C, 90 to 30
C defeats D, 70 to 50
C defeats A, 70 to 50
D defeats A, 120 to 0
D defeats B, 80 to 40

> With this definition you can mentally "build up" a beat path,

If you want to avoid recursion, you need explicit iteration, something
like:

Option F is said to transitively beat option G if F beats G, or if
there are a sequence of options, H_1, H_2, ..., H_n, such that F
beats H_1, H_i beats H_i+1, and H_n beats G.

> I suggest this because, being American and thus unaccustomed to
> preferential voting mechanisms, I was unfamiliar with the concept of
> "beat path" when I was first exposed to it.

"beat paths" are exclusive to Condorcet style voting, and Debian's still
the sole group to actually use one of those, outside of election-method
geeks. So it ain't just yankees who aren't familiar with it.

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.''


-- 
To UNSUBSCRIBE, email to [EMAIL PROTECTED]
with a subject of "unsubscribe". Trouble? Contact [EMAIL PROTECTED]

Re: Request for comments [voting amendment]

[Buddha Buck]

Raul Miller wrote:

This is not a full draft.  In this post, I'm only including
text for replacing A.6 of the constitution.  I wanted to
also rewrite the changes to A.3, but I've got to run some
errands tonight and I'm not going to have time to write up
a full draft.

Please let me know of any flaws in the following partial draft:


I'd like some clarifications...



  A.6 Vote Counting

1. Each ballot orders the options being voted on in the order
   specified by the voter.  Any options unranked by the voter are
   treated as being equal to any other unranked options and below
   all options ranked by the voter.


Definition:  A "ballot" consists of a ranking A>B>C>D>... of options 
submitted by a voter.  It defines a total ordering of options for a 
particular voter (i.e., for any pair of options A and B, we can claim 
that a particular voter feels either A>B, AB, then 
B

Let |A>B| be the number of voters who voted A>B.
Similarly, for |A

(Obviously, |A>B| + |A=B| + |A

2. Options which do not defeat the default option are eliminated.

   Definition: Option A defeats option B if more voters prefer optio
   A over option B than prefer option B over option A.


Let A>>B ("A defeats B")if |A>B| > |B>A|
Let A==B ("A ties B")   if |A>B| = |B>A|
Let AA|
(Note: A==A, for all options A)

Eliminate all options A if Default>>A.

Clarification:  What if Default==A?


3. If an option has a quorum requirement, that option must defeat
   the default option by the number of votes specified in the quorum
   requirement or the option is eliminated.


Does is mean:

Eliminate A if |A>Default| < Quorum

or

Eliminate A if |A>Default| - |Default>A| < Quorum

Again, how do we deal with that |A=Default| case?



4. If an option has a supermajority requirement, that option must
   defeat the default option by the ratio of votes specified in the
   quorum requirement or the option is eliminated.


(?) Eliminate A if |A>Default| / |A

5. If one remaining option defeats any other remaining options,
   that option wins.


s/any/all/

"Condorcet Winner"

If there is a remaining option A, such that for all remaining options B, 
either A=B, or A>>B.

6. If more than one option remains after the above steps, we use
   Cloneproof Schultz Sequential Dropping to eliminate any cyclic
   ambiguities and then pick the winner.  These represent a procedure
   and must be carried out in the specified order:

   i. All options not in the Schultz set are eliminated.

  Definition: An option C is in the Schultz set if there is no
  other option D such that C is in the beat path of D AND D is
  not in the beat path of C.


Let A>>>B mean there is a possibly empty sequence C, D, ..., E, F of 
remaining options such that A>>C, C>>D, ..., E>>F, F>>B

Then B is on the beat path of A.

The Schultz Set = { A | A>>>A }

Note:  Because A==A, it isn't the case that A>>A, so if the Schultz set 
includes A, then there must be a B!=A such that A>>B>>...>>A.  Since 
A>>B, we then have B>>...>>A>>B, so B is also in the Schultz set. 
Therefore, the Schultz Set can't be a Singleton Set.

  Definition: An option F is in the beat path of option G if
  option G defeats option F or if there is some other option
  H where option H is in the beat path of G AND option F is in
  the beat path of H.

   ii. Unless this would eliminate all options in the Schultz set,
	   the options which have the weakest defeat are eliminated.

	   Definition: The strength of a defeat is represented by two
	   numbers: the number of votes for the defeated option and the
	   number of votes for the defeating option.

	   The more votes in favor of a defeated option, the weaker
	   the defeat.	Where two pairs of options have the same number
	   of votes in favor of the defeated option, the fewer votes in
	   favor of the defeating option, the weaker the defeat.


So if we have two defeats A>>B and C>>D, then we lexigraphically compare 
(|B>A|, -|A>B|) and (|D>C|, -|C>D|)

What do you mean by "options with the weakest defeat"?

My understanding was that we were removing defeats from consideration. 
If, for example, there were four options A, B, C, D in the Schultz Set, 
we'd initially be looking at the following set of defeats, in strongest 
to weakest order:

A>>B
A>>D
B>>C
C>>A
D>>C
B>>D

After eliminating the weakest defeat (in this case, B>>D, we no longer 
consider it when determining the Schultz Set, as if we had declared 
B==D, so that neither B>>D or D>>B held.

So what do we really want to eliminate here?

And...

What if we had |D>C| = |B>D|, |D=C| = |B=D|, |D>C nor B>>D was weaker than the other?  Do we eliminate both 
defeats?

   iii. If eliminating the weakest defeat would eliminate all options
	in the Schultz set, a tie exists and the person with the
	casting vote picks from among these options.


Hmmm

Re: Request for comments [voting amendment]

[Branden Robinson]

On Thu, Nov 14, 2002 at 06:24:14AM +1000, Anthony Towns wrote:
> On Wed, Nov 13, 2002 at 12:54:59PM -0500, Branden Robinson wrote:
> >   Definition: An option F is in the beat path of option G if option G
> >   defeats option F, or if there is another option H which defeats G, AND
> >   option F defeats H.
> 
> This isn't equivalent.
> 
> First, it's wrong: G defeats H and H defeats F, for F to be in the beat
> path of G. I really dislike the phrase "in the beat path of", since it
> makes exactly this sort of mistake easy to make. Please let us switch
> to "transitively beats" or "dominates" or something with a similarly
> intuitive meaning.

Sorry about that.  I retract my proposed amendment quoted above.

> Slightly more subtly, though, it's not equivalent: if you've got A
> defeats B, B defeats C, C defeats D, (and C defeats A, D defeats A,
> and D defeats B), then D is still in the beat path of A, even though
> neither of the following are true:
> 
>   B defeats D and A defeats B   (F=D, G=A, H=B -- B doesn't defeat D)
>   C defeats D and A defeats C   (F=D, G=A, H=C -- C doesn't defeat D)
> 
> This is possible in an election where people vote as follows:
> 
>   50 DABC
>   40 BCDA
>   30 CDAB
> 
> A defeats B, 80 to 40
> B defeats C, 90 to 30
> C defeats D, 70 to 50
> C defeats A, 70 to 50
> D defeats A, 120 to 0
> D defeats B, 80 to 40

I see.

> > With this definition you can mentally "build up" a beat path,
> 
> If you want to avoid recursion, you need explicit iteration, something
> like:
> 
> Option F is said to transitively beat option G if F beats G, or if
> there are a sequence of options, H_1, H_2, ..., H_n, such that F
> beats H_1, H_i beats H_i+1, and H_n beats G.

Can we use the term "transitively defeat", and thus leave the term
"beat" out of the proposal altogether.  This way no one will wonder what
an unqualified "beat" is.

While your definition smacks of mathematical notation (which scares some
people), it does seem the most clear way to express this.

> > I suggest this because, being American and thus unaccustomed to
> > preferential voting mechanisms, I was unfamiliar with the concept of
> > "beat path" when I was first exposed to it.
> 
> "beat paths" are exclusive to Condorcet style voting, and Debian's still
> the sole group to actually use one of those, outside of election-method
> geeks. So it ain't just yankees who aren't familiar with it.

Wow, be careful saying charitable things about Americans, it might tempt
W to start a war with Iraq even earlier, citing "international support".


-- 
G. Branden Robinson|
Debian GNU/Linux   |   If ignorance is bliss,
[EMAIL PROTECTED] |   is omniscience hell?
http://people.debian.org/~branden/ |



msg01901/pgp0.pgp
Description: PGP signature

Re: Request for comments [voting amendment]

[Branden Robinson]

On Wed, Nov 13, 2002 at 03:42:37PM -0500, Aaron M. Ucko wrote:
> AFAICT, your version only gives one level of transitivity, which does
> not necessarily suffice. 

I have retracted it.

> An explicitly iterative version would have to read along the lines of
> 
>   Definition: An option F is in the beat path of option G if option G
>   defeats option F, or if there is a sequence of other options H_1,
>   ..., H_n (where n may be 1) such that H_1 defeats F, G defeats H_n,
>   AND for every i from 1 to n-1, H_{i+1} defeats H_i.
> 
> which I'm not convinced is better.

I don't know.  It's pretty close to Anthony's, which I support, except I
think I see away to avoid the term "beat" altogether (and "dominate",
too).

A minimum of jargon is, I think, a feature.

-- 
G. Branden Robinson| One man's "magic" is another man's
Debian GNU/Linux   | engineering.  "Supernatural" is a
[EMAIL PROTECTED] | null word.
http://people.debian.org/~branden/ | -- Robert Heinlein



msg01902/pgp0.pgp
Description: PGP signature

Re: Request for comments [voting amendment]

[Anthony Towns]

On Wed, Nov 13, 2002 at 06:13:14PM -0500, Buddha Buck wrote:
> The Schultz Set = { A | A>>>A }
> Note:  Because A==A, it isn't the case that A>>A,

This is clever, but wrong. Consider an election with people voting:

30 x ABCD
40 x ACDB
50 x ADBC

A wins unanimously and is the only member of the *Schwartz* set. However,
B beats C beats D beats B, so { x | x >>> x } = {B, C, D}.

Alternately, consider something like:

40 x AB CDE
30 x AB DEC
20 x BA DEC
50 x BA ECD

A and B are equal (70 votes each), and C > D > E > C, but A,B both beat
each of C,D,E, but { x | x >>> x } = {A,B,C,D,E}.

The correct restatement is something more like:

{ x | forall y: y >> x --> x >>> 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.''



msg01903/pgp0.pgp
Description: PGP signature

Re: Request for comments [voting amendment]

[Matthias Urlichs]

Hi,

So who did come up with the mistake "Schultz", and did they eat too many
peanuts? ;-)

Anthony Towns:

> The correct restatement is something more like:
> 
>   { x | forall y: y >> x --> x >>> y }
> 
Or, in understandable language: The Schwartz set is the innermost unbeaten
set, or the smallest set of candidates such that none are beaten by any
candidate outside the set.

As for resolution, I'd adopt the SSD method, which states
1- Determine the Schwartz set.
2- Drop the smallest defeat(s) within the set.
3- Repeat 1-3 until there's a winner.

See http://electionmethods.org/CondorcetEx.htm.
It explains all of this in reasonably easy-to-understand language.

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



msg01904/pgp0.pgp
Description: PGP signature

Re: Request for comments [voting amendment]

[Jochen Voss]

Hello,

On Tue, Nov 12, 2002 at 06:03:54PM -0500, Raul Miller wrote:
> 4. If an option has a supermajority requirement, that option must
>defeat the default option by the ratio of votes specified in the
>quorum requirement or the option is eliminated.
 ^^
   is this correct?

I guess the term "quorum" should be replaced by a second
"supermajority", shouldn't it?

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



msg01905/pgp0.pgp
Description: PGP signature

[mike ossipoff ] Cloneproof SSD program,with balloting

[Manoj Srivastava]

Hi,

Here is mail from Mike Ossipoff with code for SSD. I am also
 including aj's Perl code that was used in the last election.

manoj




cloneproof_ssd.pl
Description: clone proof ssd
--- Begin Message ---

Some time ago I sent to you a pasted copy of our
website's Python program, to implement Cloneproof SSD,
via the BeatpathWinner algorithm.

Cloneproof SSD is abbreviated "CSSD".

But that program doesn't include balloting. It has
as its input the pairwise vote totals array,
which in that program is called Pmat. That's the
array that records how many people ranked each i over
each j.

But I didn't write that program, though I suggested
the algorithm. Below, in this message, is a Python
Cloneproof SSD program that I myself _did_ write.
This way any errors in it are my own, and I can say
that I've not been able to find any errors in this
current version.

The other advantage of this program is that it
includes code that receives the rankings from the
keyboard, prompting, for example, for 
"enter your choice # 3 candidate:"

Of course this program also counts the rankings, to
make the pairwise vote totals array. The previous
program that I sent to you calls that array Pmat.
This program calls it V.

This is a little like "sending coals to Newcastle",
sending software to professional programmers, who
are incomparably more experienced than I am at
program-writing. Still, as an advocate of
Cloneproof SSD, it's my responsibility to offer
count software of some kind. So now I'm sending you
a complete count program written entirely by me, which
is also my responsibility, however amateur a
programmer I am.

Anyway, it's important that a program make the
completed pairwise vote totals array, because making
that array is nearly the entire computational task
of the pairwise-count methods such as CSSD.

Of course, if you already have software that makes
that pairwise vote totals array, you could put its
values into V[A(i,j)], and just use the part of my
program that uses that V array to determine the
CSSD winner(s).

In that case, find the line, near the bottom of the
program, that says: W=[1]*N   The block of lines
just before that line is the beginning of the
part of the program that you'd still use if you
already had the pairwise vote total array. So you'd
use that block and all that follows.

And, add certain definition lines to a place just
before that block: The definitions of the dictionary
"cands", the variable N, the lists V & B, and the
function A(i,j) should be moved to that position from
their present positions earlier in the program.

The reason why I write the pairwise vote totals array
as V[A(i,j)] is because, instead of using
2-dimensional
nested lists, I'm using 1-dimensional lists, with
a function, A(i,j), which converts 2-dimensional
array positions into 1-dimensional array positions.

My balloting program doesn't recognize any such thing
as a spoiled ballot. If the voter chooses to
contradict himself in his ranking, he should be
able to. It only reduces the effectiveness of his
ballot, and that's his doing and his problem.

In my 3-nested for loops that find the strongest
beatpath from each i to each j, I don't include
requirements that i not equal j or k, etc. That's
because leaving such requirements out has no effect
on the winner(s), and so I leave it out for
simplicity.

In case the program will be used with its balloting
part, let me say something about how that works:

The balloting has 2 parts. Part 1 asks for & receives
the names, abbreviations, or initials of the
candidates (or alternatives). Part 2 receives the
rankings.

In part 1, the user is asked for candidate names,
and enters each one when prompted for it. If you
want to correct an entry error, by redoing the
previous entry, enter 1. The program will then
receive the replacement for that incorrect name
that you want to replace. When done with the names,
enter 0 (the zero key).

In part 2, when asked, for instance, for "choice #3,
enter that ranking's 3rd choice. Then, when prompted
for "choice #4, and if you want to enter an
additional 3rd choice (because you can enter as
many choices at any rank position as you want to),
enter 1. The program will say "enter more choice #3".

If you want to redo the most recent entry, enter 2.
If you want to redo the entire current ranking, enter
3. When finished with the current ranking, enter 
0 (the zero key). When done entering all the rankings,
enter 9.

One more thing: I don't have a computer, and so
I haven't been able to test this program. But I've
checked it for errors, including typos. At first I
found a number of them. Then I couldn't find any.
So there's a good chance that there aren't any now.

But if it doesn't run as intended, maybe the error
will be some obvious typo or other obvious error that
you can fix. Otherswise, you could send to me the
error message, and I could fix the error. Of course
when I get a computer I can send a program that I've
tested and which I c

Re: Request for comments [voting amendment]

[Branden Robinson]

On Thu, Nov 14, 2002 at 08:16:40AM +0100, Jochen Voss wrote:
> On Tue, Nov 12, 2002 at 06:03:54PM -0500, Raul Miller wrote:
> > 4. If an option has a supermajority requirement, that option must
> >defeat the default option by the ratio of votes specified in the
> >quorum requirement or the option is eliminated.
>  ^^
>is this correct?
> 
> I guess the term "quorum" should be replaced by a second
> "supermajority", shouldn't it?

Probably.  (Raul?  Anthony?)

Must a supermajority-required option directly defeat the default option
by this margin?  What happens if the supermajority-required option only
transitively defeats the default option?  How do we numerically define
the margin of the defeat?

I am concerned about the introduction of supermajority requirements
introducing an opportunity for strategic voting into our system
that Cloneproof SSD/Concorcet doesn't otherwise possess.

-- 
G. Branden Robinson|The errors of great men are
Debian GNU/Linux   |venerable because they are more
[EMAIL PROTECTED] |fruitful than the truths of little
http://people.debian.org/~branden/ |men. -- Friedrich Nietzsche



msg01907/pgp0.pgp
Description: PGP signature