[EM] Re: IIA Theory

[Craig Carey]

Dear Demorep

(From Craig Carey)

I don't understand what the numbers inside the table are.
I thought I might write about the Borda method (i.e. 
 fail, perhaps with a 'vote for A and A loses' example.

I can't understand the numbers in your tables (below).

People don't respond to you (your give not well commented
 numbers the would be suspected of illustrating some of
 the worst methods areound). You may be a Borda expert.

If there are 3 candidates, are the weights 3, 2, and 1?.
Having the last weight being other than 0 is sure to
 permit existence of some dumb Borda examples. It is so
 flawed people won' spend time on it. 

I ask you to start using those ">" or ":" characters into the
 left hand side (please). Such a request would appear bad I presume,
 if found in the list.

If Mr Saari is a proponent of Borda, then he's at about where
 I was in the 1st week of my researches. So he is protected
 because people won't spend time on him. What is done about
 the missing preferences. I suppose the final decider is 
 what US schools do or whatever.


At 12:58 08.10.99 , you wrote:
>Mr. Schulze wrote in part-
>
>Saari's geometric terminology makes sense only if you have
>already agreed with him that the Borda method is best.
>
>Borda and Saari implicitely presume that there is an even
>distribution of the candidates. But if there is an even
>distribution of the candidates then of course the Borda
>method is best because then every pairwise comparison has
>the same independent importance.
>---
>D- The reality is that some candidates are more or less clones of other 
>candidates - such as 2 or more similar liberals or conservatives.

What are the mathematical expressions that represent
 "reality"?. Reality is a matter tha can effect the outcome
 along with all the paper counts, yet it is lacks a place
 in the formula?.

>
>35 ABC
>34 BCA
>31 CAB

Borda: A:B:C = (3*35+34+2*31):(2*35+3*34+31):(35+2*34+3*31)

>
>    A    B    C
>A   --  66   35    101
>B  34   --   69    103   [Borda winner]
>C  65   31   --     96
>                   300

The primary method is in the table and the text comment to
 the right is additional

>
>D who is clone of C is added.
>
>35 ABCD
>34 BCDA
>31 CDAB
>
>
>    A    B    C   D
>A   --  66   35  35   136
>B  34   --   69  69   172   
>C  65   31   -- 100   196  [Borda winner]
>D  65   31    0  --    96
>                      600
>
>C becomes the Borda winner by having a clone of itself.
>Obviously, Borda is totally defective (as pointed out by Condorcet some 215 
>years ago).
He pointed it out without providing a proof?. 


I suspected you were onto something briefly but I can now
 not see nothing in your message except two tables of a
 lot of arithmetic mistakes. I downloaded a program from
 Arizona and gave different numbers for Borda counts.
So you must have two methods there, or that really is Borda
 but some theorem was applied to change the numbers.

Inserting D before winner B, to give this

     31 CDAB

 can be done but it is not that obvious that it is bad
 for B to start losing. I suppose it should.

I can't imagine I would be writing in response to your messages
 and the others that write to the list don't also. Every
 good rule I make up, it seems to be sure Borda will fail.
 I use a computer tryig losts of integers to get the examples
 that show up problems with methods. Can you put your "legal"
 into a mathematical format for me und die millionen der bürger.

Mr G. A. Craig Carey              E-mail: research at ijs.co.nz
Auckland, Nth Island, New Zealand
Pages: Snooz Metasearch: http://www.ijs.co.nz/info/snooz.htm
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