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Robonson wins; Debian v monotonicity (was Re: Some analysis of DPL 2003 results

This is a lengthy argument against the current Debian problem of
wrongly rejecting Mr Branden Robinson who would almost certainly be
the winner if the method of the last election was maximally proportional
(and passing P2) and monotonic. I.e. the method then is almost the
smallest adjustment that 'debugs' the unfair Alternative Vote method.

Below I suggest a replacement for the Debian Condorcet voting system,

In this election a monotonic method passing my P2 would make the winners
be one of these sets: {}, {A}, {A,B}, {A,B,C}

>3 ABC
>2 CAB
>2 BCA

For the 1 case, B and C lose since under the 1/3 quota. then 

At 2003\04\20 02:29 -0700 Sunday, Rob Lanphier wrote:
>Hi all,
>Being the election methods geek that I am, I decided to do some analysis 
>of the last DPL election.  I've posted the results of this here:
>I ran through a few scenarios using Instant Runoff Voting to tally the 

Both Robs use the same noun phrase.

>votes instead of using Condorcet.  The result depended on whether tied 
>ballots are allowed.  Allowing for tied ballots (and improvising a way 
>to deal with them), Martin Michlmayr still wins the election.  However, 
>strictly following the rules that were just enacted in San Francisco for 
>future mayorial elections, Branden Robinson would have won.
>At any rate, I'm not trying to kick up any dust or call the legitimate 
>results into question.  My take is that the analysis seem to further 
>legitimize the results.

Well, that is a big error: the winner was incorrect.
The San Francisco method is not the best.

(I agree that the Alternative Vote finds Mr Martin Michlmayr to be the

At 03\04\20 13:27 -0400 Sunday, David Z Maze wrote:
>David Weinehall <tao@acc.umu.se> writes:
>> On Sun, Apr 20, 2003 at 02:29:16AM -0700, Rob Lanphier wrote:
>>> http://electorama.com/modules.php?op=modload&name=News&file=article&sid=32
>> Interesting reading, although I don't know what I should make out of
>> this sentence:
>> "What complicates this is that the ballot allows for multiple first
>> choices. Relatively few Debian developers did this though (453 of the
>> 488 total votes)."
>I think you missed a sentence; my reading of the relevant paragraph is
>"relatively few developers had multiple first-choice votes; thus,
>Table 1 has the 453/488 votes with only one first-choice vote."

The ties can be easily dealt with by smudging the weight of the paper out
over the permutations that would eliminate a tie of the preferences.


  Candidate: ABCDE
  Rank.....: 1222-

  Paper = (1/4)( (ABCD)+(ABDC)+(ACBD)+(ACDB)+(ADBC)+(ADCB) )

It seems to make no difference if plain Condorcet is used even but it
could have an effect when a patched in part of the whichever
pairwisingish algorithm being run:

 | Counts after using permuting.
 | . . 2.  3.  4. The figures here : 3-->2-->4<--3
 | 2. .  250 238
 | 3 233. .  235
 | 4 242 246
 | The official results, taken from
 | . http://www.debian.org/vote/2003/vote_0001
 | . . 2.  3.  4. Official : Official 3-->2-->4<--3
 | 2. .  238 224
 | 3 221. .  226
 | 4 228 237

The fraction of votes affected by the smudging resolution of ties on
preferences was a lot greater (in the last Debian election) than the
percentage needed to undo a victory of the winner.

Somehow the methods are insensitive to whether that permuting was 
done or not.

It may have to do with passing P2.
P2 saying things including this:
  the winners are unaffected by the change 2(A)-(AB)-(AC) results in
  an implausible preferential voting method):

   From:   Craig Carey <research@ijs.co.nz> 
   Date:  Fri Apr 4, 2003  9:41 am
   Subject:  P2 Linearity, an essential axiom in 3W1 preferential voting

Maybe Condorcet passes P2. 
Likers of Condorcet maybe would  not mention that pass.

Also I derive a fair 1/3 quota for losers here:

PS. Mr Voss suggests that Condorcet is good (which is false) and that
Debian has ... a good method and incorrectly Mr Voss says that Condorcet
is monotonic which is really untrue:


>                    The Debian Voting System
>Good properties of Condorcet voting (summarised from
>Monotonicity Criterion (MC) 
>With the relative order or rating of the other candidates
>unchanged, voting a candidate higher should never cause the
>candidate to lose, nor should voting a candidate lower ever cause
>the candidate to win. 

"voting a candidate higher" means shifting the single preference towards
the 1st preference or putting it there.

The rule is one that fails Condorcet variants and the plain Condorcet
method samples the method in a Condorcet paradox region. Rather than
decide over 3 valued Booleans, either the rule or method could be
corrected. Anyway, I'd have plain Condorcet would fail the monotonicity
check. That is not what Mr Voss wrote.

The page concludes with some microbial sized comments on the need
for a tiny quota. The principle of equal suffrage (well interpreted
or defined) implies the rule of monotonicity and that (along with
P2 and the truncation resistance rule [a preference is unaffected
subsequent preferences] will lead to a large 1/3 quota that selects

A fair preferential voting method will election Mr Branden Robinson.

When the papers are smudged out to prevent discarding when preferences
are tied, then I found that the counts were:

Column #1: Moshe Zadka      : Sum =  258/24 =  10.75   =  2.20286%
Column #2: Bdale Garbee     : Sum = 3686/24 = 153.5833 = 31.47199%
Column #3: Branden Robinson : Sum = 4046/24 = 168.5833 = 34.54576%
Column #4: Martin Michlmayr : Sum = 3662/24 = 152.5833 = 31.26707%
Column #5: None Of The Above: Sum =   60/24 =   2.5    =  0.51229%

Next step:

Old:New : Name
#1: del : Moshe Zadka
#2: #1  : Bdale Garbee     : Sum = 3760 / 24 = 156.6666 = 32.2359%
#3: #2  : Branden Robinson : Sum = 4084 / 24 = 170.1666 = 35.0137%
#4: #3  : Martin Michlmayr : Sum = 3820 / 24 = 159.1666 = 32.7503%
#5: del : None Of The Above
Total = 11664/ 24 = 486

The next steps is to eliminate all candidates with less than 1/3
of the vote, leaving Mr Branden Robinson as the winner.

A 5 candidate problem was using a 3 candidate method.
It seems safe to me to do that given those numbers.

An easy derivation of the 1/3 quota is here:


Does anybody want to suggest any other quota.
I can't see any reason for using a small quota to find losers.

The qunatifier logic solver,
 REDLOG: http://www.fmi.uni-passau.de/~redlog/

Consideration of STV in England is around the idea that the method
must never fail a One Man One Vote test. Debian Condorcet readily
could. I have not checked it. I guess it could be that the negating
of votes is a bigger problem.

Here is an example of how a liker of a unfair Condorcet method
make over 50% of the details all be wrong: the REDLOG statement:

   Z := (if (0<c) then A else B);

is equivalent to ((0<c and A) or (c<=0 and B)). Typically polytopes
A and B fail to match up at cut created by (0<c).
Note that the cut (0=c) is then creating two faces with opposite
orientations. Typically one of the two faces would be immediately
failed by monotonicity if saying that if more (A) papers are added
then A should not change from a winner into a loser.

The constraints on  normal vectors might be a lot of N polytopes
that are convex and that contain the origin.

To convert the constraint into a shadow, then the constraints are
ANDed and then their duals are calculated:

    S(x) = (All y<>0)[N(y) impl (x*y <= 0)]

So when I write shadows are cast then that is precisely correct.

Here is an expression of when A wins:
  (b<=a)(c<=a)(d<=a) . (
    (2*c<=a+b)(2*d<=a+b) or
    (a+b<=2*c)(d<=c) or
    (a+b<=2*d)(c<=d) )

That simplifies to: b<a and c<a and d<a.

The initial expression seemed to be non-monotonic since the "a"
variables was not on the right hand side of these 4 half-space
terms: (a+b<=2*c), (d<=c), (a+b<=2*d), (c<=d)

But those terms are internal and not creating a surface.

A very rapid rejection of the Debian Condorcet method is possible
if that were posted up in a logic formulation.


                  Replacement For Condorcet

Here is a plan for what remains of the Debian voting

[1] Condorcet is rejected. Anything else is an adherence to
 the suspect idea interfering with the equal suffrage rights
 of members. A protest vote against the current leader could
 provide an incentive to the leader for sticking with the
 Condorcet method which probably has some anti-incumbent
 bias that is much less present in a monotonic method around
 the Alternative Vote and a 1/3 quota finding losers.

[2] Voters can change their mind during the vote. A voter
 can see all the other votes (though they'd not identify
 the persons except as authorized). The voter would use
 that knowledge when deciding on whether to change the vote.

[3] Each paper has only a single preference and the candidate
 with the least votes at each step, is eliminated.

[4] Each voter can optionally predict who they would be
 voting for.

[5] Item [4] allows voters to mislead other voters. That might
 be countered in a development that occurs later, by allowing
 voters to program the system to withhold predictions from
 persons who are unsympathetic.

The complete removal of the relentlessly faulty Condorcet
method would the voting part of the project. I would be stunned
if anything gets better. It is not that safe using Condorcet:
evey better method is passed up and reasoning might be missing.
(That's testable)


The Condorcet winner of a 2 candidate election is shown:

   (b0+ba<a0+ab) implies (A wins)
   (a0+ab<b0+ba) implies (B wins)

The Condorcet winner is defined by arroweads.

The winner is still the same candidate even when the method is
required to elect ZERO winnners.

Maybe a hack permitting reject of the whole method and the
new hack, could correct that.

So it got the wrong number of winners. Then a "variant" is created
to remove that problem.

Here it is: the Condorcet variant is built over this very principle:

 |  For the Condorcet method, a candidate that the winner must not be,
 |  is the Condorcet winner.

That axiom would be tossed in with another axiom requiring the
negation of the same principle. Roll calls are 0 winner elections
and Condorcet can't run a roll call.

But the word "Condorcet" may instead denote a variant. So there is
a chance that there is no problem with axioms almost be inconsistent.

Anyway, Condorcet is more like a thing plucked off the Ganges river
than abuilt to be fair.


An example of a simple case where equal suffrage considers
3 candidates all at once. It is providing a limitation and not
a 'right' the papers would prefer.

The "power<=1" equal suffrage rule can be worded to say this:
it requires that the base 2 satisfaction of the list (ABC) with
the winner set, will be sustained or improved upon for some
non-negatively weighted sum of the ballot paper fragments shown
in the sets. (There are 16 different rules in total.)

|   {(A),(BC)}
|   {(B),(AC)}
|   {(C),(AB)}
|   {(AB),(AC)}
|   {(AB),(BC)}
|   {(AC),(BC)}
|   {(A),(B),(C)}
|   {(A),(B),(AC)}
|   {(A),(B),(BC)}
|   {(A),(C),(AB)}
|   {(A),(C),(BC)}
|   {(B),(C),(AB)}
|   {(B),(C),(AC)}
|   {(A),(AB),(AC)}
|   {(B),(AB),(BC)}
|   {(C),(AC),(BC)}

There are rights for the paper (ABC).
There are no rights for the [disorded] set, {A,B,C}

For that sort of mistake I guess readers could study the Debian
project Condorcet voting system It 

The Condorcet variant could fail one of the tests and then found
to be gifing votes .


I note that Condorset has "pairs".
It is like marrying.
It is central to Condorcet that the candidates in the pairs do not
actually get awarded rights.

They seem to get Smith Set.

The satisfaction of a set with a winner-set is not defined by me.
So sets do not have rights.

Behind equal suffrage can be placed proportionality. Proportionality
adds 3 to the candidates if the paper is this: 3(ABC).

Condorcet merges 2 rules so it is not respecting right counting.
That is completely bad, but the method really is unfair and yet
another mechnaism for getting the winners wrong might 
warrant further investigation.

It approximates a proportionality rule and it does not directly
use the rule.

The designers of the method might not have known how to separate
out the two principles.

Condorcet mishandles the right counting proportionality axiom that
would have made it a social method.


Attachment A:

How to resolve preference ties by smudging the weight equally over the
appropriately permuted-out papers:

 ---- New ----- Original
 Ranks   Weight  Ranks
 12345 ,  1/24 ; "11115"
 12435 ,  1/24 ; "11115"
 13245 ,  1/24 ; "11115"
 13425 ,  1/24 ; "11115"
 14235 ,  1/24 ; "11115"
 14325 ,  1/24 ; "11115"
 21345 ,  1/24 ; "11115"
 21435 ,  1/24 ; "11115"
 23145 ,  1/24 ; "11115"
 23415 ,  1/24 ; "11115"
 24135 ,  1/24 ; "11115"
 24315 ,  1/24 ; "11115"
 31245 ,  1/24 ; "11115"
 31425 ,  1/24 ; "11115"
 32145 ,  1/24 ; "11115"
 32415 ,  1/24 ; "11115"
 34125 ,  1/24 ; "11115"
 34215 ,  1/24 ; "11115"
 41235 ,  1/24 ; "11115"
 41325 ,  1/24 ; "11115"
 42135 ,  1/24 ; "11115"
 42315 ,  1/24 ; "11115"
 43125 ,  1/24 ; "11115"
 43215 ,  1/24 ; "11115"

 51234 ,  4/24 ; "51114"
 51324 ,  4/24 ; "51114"
 52134 ,  4/24 ; "51114"
 52314 ,  4/24 ; "51114"
 53124 ,  4/24 ; "51114"
 53214 ,  4/24 ; "51114"

 53124 , 12/24 ; "53114"
 53214 , 12/24 ; "53114"

Data came from: http://www.debian.org/vote/2003/vote_0001


Attachment B

The rule/principle of equal suffrage at the High Commissioner's website:


| International Covenant on Civil and Political Rights
| ...
| Article 25 General comment on its implementation
| Every citizen shall have the right and the opportunity, without any
| of the distinctions mentioned in article 2 and without unreasonable
| restrictions:
| (a) To take part in the conduct of public affairs, directly or
| through freely chosen representatives;
| (b) To vote and to be elected at genuine periodic elections which
| shall be by universal and equal suffrage and shall be held by
| secret ballot, guaranteeing the free expression of the will of the
| electors;
| (c) To have access, on general terms of equality, to public service
| in his country.


| Universal Declaration of Human Rights
| ...
| Article 21
| Everyone has the right to take part in the government of his
| country, directly or through freely chosen representatives.
| Everyone has the right to equal access to public service in his
| country.
| The will of the people shall be the basis of the authority of
| government; this will shall be expressed in periodic and genuine
| elections which shall be by universal and equal suffrage and shall
| be held by secret vote or by equivalent free voting procedures.

The UN wording above is notable in that there is no apparent mistake
over the trivial cases: when 0 or 2 winners, or when there is 1 candidate. 


I suppose that Condorcet can't solve all 1 winner 1 candidate
elections, since there are not enough candidates to permit a pair
to be formed. It could be quite difficult to spend a day or more
designing a method and then end up with Condorcet's failures under
extremely simple tests..

Condorcet selects the wrong winners. It raises candidate with too
few votes (sometimes) which easily makes it unused by governments.

Condorcet appears to have no desirable principles to it at all.

It would not be pulled out suddenly with no attention to the
consciousness of those who like the polytopes sequence.


Craig Carey
* Quantifier simplifier: http://www.ijs.co.nz/polytopes.htm

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