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Ken Johnson | 1 Mar 2004 02:49
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There's nothing wrong with Average Rating.


>...
>Date: Sun, 29 Feb 2004 13:02:20 +0100
>From: Markus Schulze <markus.schulze <at> alumni.tu-berlin.de>
>...
>my favorite formulation of Arrow's Theorem is Pattanaik and Peleg's
>formulation ... In their formulation, this theorem says that
>there is no rank method that is non-dictatorial and satisfies Pareto
>and regularity. ...
>
But is there any such non-rank method? (I presume "rank" means a 
ranked-preference method, which CR is not.)

>...
>
> Arrow restricts his considerations to paretian
>non-dictatorial rank methods because he considers other election
>methods to be quite unacceptable. ...
>
>  
>
So is it correct to say that Arrow did not prove that "there is no 
perfect voting system"; he only proved that the methods he deems to be 
acceptable are imperfect?

Ken Johnson

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Markus Schulze | 1 Mar 2004 12:37
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Re: There's nothing wrong with Average Rating.

Dear Ken,

I wrote (29 Feb 2004):
> My favorite formulation of Arrow's Theorem is Pattanaik and Peleg's
> formulation (Prasanta K. Pattanaik, Bezalel Peleg, "Distribution of
> Power Under Stochastic Social Choice Rules," Econometrica, vol. 54,
> p. 909-921, 1986). In their formulation, this theorem says that
> there is no rank method that is non-dictatorial and satisfies Pareto
> and regularity. "Regularity" says that adding candidate Z should
> not increase the probability that candidate A (with A <> Z) is
> elected.

You wrote (29 Feb 2004):
> But is there any such non-rank method? (I presume "rank"
> means a ranked-preference method, which CR is not.)

Arrow proved that there is no single-winner election method with
the following four properties:

   1) It is a rank method (= a ranked-preference method).
   2) It satisfies Pareto.
   3) It is non-dictatorial.
   4) It satisfies IIA.

All four properties are needed to get an incompatibility.
For example, RandomDictatorship is a paretian rank method that
satisfies IIA, RandomCandidate is a non-dictatorial rank method
that satisfies IIA, Approval Voting is a paretian non-dictatorial
method that satisfies IIA, my beatpath method is a paretian
non-dictatorial rank method.
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James Green-Armytage | 1 Mar 2004 16:17

my ballot

Approval cutoff: between rank 1 and rank 2

candidates		ranks		approval		CR

Howard  Dean	5					83

Edwards    		10					70

Kerry           	7					79

Kucinich       	1		yes			95

Nader         		1		yes			95

Sharpton 		6					80

Jim Hightower       10					70

Amy Goodman      4					84

Ron Daniels           10					70

Medea Benjamin     6					80

Winona LaDuke      6					80

Bill Moyers             2					90

Peter Camejo          10					70
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Eric Gorr | 1 Mar 2004 21:22
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Survey Results

A few weeks ago I mentioned that I was going to run an Oscar Vote for 
a local movie group that I am involved in in the Washington DC area.

Had a total of 17 voters.
Everyone did not vote in each category.
I have include the complete ballots.
There were no ties, when votes were submitted, and only a single 
cycle was generated.

This poll has an interesting property that not all voters would have 
been familiar with each of the options, electing to rank only those 
options they were  familiar with...a property that would likely be 
shared with any real election with many candidates.

I enjoyed introducing Condorcet methods to nearly 800 people in the DC Area...

Anyone know of a web-based IRV voting calculator into which I can 
past these ballots? Did a brief google search and couldn't find 
anything. Would be interested in comparing results.

Anyone else have any interesting analysis to add?

ACTOR IN A LEADING ROLE
>  ACTOR IN A LEADING ROLE
>  A. Johnny Depp - PIRATES OF THE CARIBBEAN: THE CURSE OF THE BLACK PEARL
>  B. Ben Kingsley - HOUSE OF SAND AND FOG
>  C. Jude Law - COLD MOUNTAIN
>  D. Bill Murray - LOST IN TRANSLATION
>  E. Sean Penn - MYSTIC RIVER
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Richard Moore | 2 Mar 2004 03:36
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Re: There's nothing wrong with Average Rating.

Ken Johnson wrote:
> So is it correct to say that Arrow did not prove that "there is no 
> perfect voting system"; he only proved that the methods he deems to be 
> acceptable are imperfect?
>  
> Ken Johnson

I would think that "perfect" and "imperfect" (in this context) are 
value judgements.

Theorems are facts, not judgements, so it is incorrect to state that 
Arrow proved anything about a value judgement.

  -- Richard

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Ma Anguo | 2 Mar 2004 04:50
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better, easier condorcet voting

Hello,

those of you who were put off from voting given the size and 
the generally clumsy layout of the Condorcet poll, can now 
take part in the vote.
As mentionned in the news section of the home page 
www.masquilier.org and in the changelog, the layout is much 
more user friendly now.

You may now cast your ballot.

On Tuesday 02 Mar 2004 4:22 am, Eric Gorr wrote:
> I enjoyed introducing Condorcet methods to nearly 800
> people in the DC Area...

thanks Eric for your contribution and for your survey 
results.
:-)

Blessings to all,

Augustin.

--

-- 
www.masquilier.org
Condorcet, Approval alternative voting.

In order to prevent people from receiving viruses
that would seem to originate from my email, 
if you use Microsoft Windows you do not have permission
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Ken Johnson | 2 Mar 2004 05:28
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There's nothing wrong with Average Rating.


>Date: Mon, 01 Mar 2004 12:37:08 +0100
>From: Markus Schulze <markus.schulze <at> alumni.tu-berlin.de>
>...
>Arrow proved that there is no single-winner election method with
>the following four properties:
>
>   1) It is a rank method (= a ranked-preference method).
>   2) It satisfies Pareto.
>   3) It is non-dictatorial.
>   4) It satisfies IIA.
>
>All four properties are needed to get an incompatibility.
>For example, RandomDictatorship is a paretian rank method that
>satisfies IIA, RandomCandidate is a non-dictatorial rank method
>that satisfies IIA, Approval Voting is a paretian non-dictatorial
>method that satisfies IIA, my beatpath method is a paretian
>non-dictatorial rank method.
>
But why did Arrow stipulate #1? If you remove this requirement, does the 
conclusion that "there is no perfect voting system" still follow, and is 
CR an example of a "perfect" system according to Arrow's remaining 
criteria?

(By the way, shouldn't the criteria also include transitivity, or does 
that follow from the other criteria?)

> ...
>
>Even though the presumption that the used single-winner
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wclark@xoom.org | 2 Mar 2004 05:51
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Re: There's nothing wrong with Average Rating.

Markus Schulze wrote:

>>Arrow proved that there is no single-winner election method with
>>the following four properties:

>>   1) It is a rank method (= a ranked-preference method).
>>   2) It satisfies Pareto.
>>   3) It is non-dictatorial.
>>   4) It satisfies IIA.

Ken Johnson wrote:

> But why did Arrow stipulate #1?

Because it was necessary for his method of proof.  Arrow demonstrated
that, given assumptions 1, 2, and 4, there was no method of resolving
disagreements between ballots, except to give one ballot priority over all
others (i.e. to be dictatorial.)

If you allow cardinal methods, then you can use the strength of
preferences to resolve such disagreements without letting the system
become dictatorial.  (This isn't to say that cardinal methods don't suffer
from their own problems -- just that they don't suffer from the particular
problems Arrow highlighted.)

Here's a rather straightforward graphical proof that might make it more
clear why restriction #1 plays such a crucial role:

http://www.indiana.edu/~econed/pdffiles/summer02/phansen.pdf
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Bart Ingles | 2 Mar 2004 08:41
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Re: There's nothing wrong with Average Rating.


Ken Johnson wrote:
> 
> >Date: Mon, 01 Mar 2004 12:37:08 +0100
> >From: Markus Schulze <markus.schulze <at> alumni.tu-berlin.de>
> >...
> >Arrow proved that there is no single-winner election method with
> >the following four properties:
> >
> >   1) It is a rank method (= a ranked-preference method).
> >   2) It satisfies Pareto.
> >   3) It is non-dictatorial.
> >   4) It satisfies IIA.
> >
> >All four properties are needed to get an incompatibility.
> >For example, RandomDictatorship is a paretian rank method that
> >satisfies IIA, RandomCandidate is a non-dictatorial rank method
> >that satisfies IIA, Approval Voting is a paretian non-dictatorial
> >method that satisfies IIA, my beatpath method is a paretian
> >non-dictatorial rank method.
> >
> But why did Arrow stipulate #1?

Because he was interested in ranked voting systems.  Also, the
combination of the other three conditions would have been unremarkable.

> If you remove this requirement, does the
> conclusion that "there is no perfect voting system" still follow, and is
> CR an example of a "perfect" system according to Arrow's remaining
> criteria?
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Eric Gorr | 2 Mar 2004 15:30
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Re: There's nothing wrong with Average Rating.

At 8:28 PM -0800 3/1/04, Ken Johnson wrote:
>So the ideal of the "perfect voting system" is unattainable in the 
>real world because people exaggerate and misrepresent their 
>preferences (i.e., they lie).

I just remembered this...

As an almost off-topic side note, there was a story by Asimov, I 
believe, in which statistical analysis had become so advanced that a 
computer was able to select a single citizen who simply would, 
whether they lied or not (for such things were taken into account), 
select the winner who would have won had everyone been allowed to 
vote.

I am blanking on the name of the story, but it was a rather good one.

Perhaps Asimov could be credited with the 'perfect' voting system.

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Gmane