[EM] The Economist: "Democratic Symmetry"

[Craig Carey]

At 15:44 06.03.00 , Rob Lanphier wrote:
>This week's Economist (Mar 4-10, 2000 edition) has an article titled
>"Democratic Symmetry; The mathematics of voting".  Unfortunately, it is
>not one of the articles they decided to put online.  It goes on to explain
>Donald Saari's theories on democratic symmetry, and gave an uncritical
>look at Borda's method. 
>
>What's the best online critique of Donald Saari's work?  It would be nice
>if the Economist received a large number of articulate letters from people
>who disagree with Dr. Saari on this matter (especially from other Dr.s)... 
>:) 
>
>Let me quote a chunk of the article (The Economist, Mar 4 2000, p. 83):
>   The fairest voting system, says Dr Saari, would respect both
>   symmetries.  The only system that fits the bill is the Borda count,
>   proposed by Jean-Charles de Borda in 1770 to elect members to the
>   Academy of Sciences in Paris. [...] Admittedly, this is more complex
>   than plurality voting and cannot be used with current American voting
>   machines (though it is used in Australia).  Also if voters are not
>   familiar with all candidates, and do not rank them all, the unassigned
>   points must be divided up evenly between the unranked candiates.  But
>   for small elections, the system is ideal. 
>

---

I accessed the Economist website and found that the article could not
 be accessed. Eventually it will appear in the archives.

How would people rule out Borda?. Others may be reluctant to answer. My
 main objection would be that it has too much disrespect for preferences,
 especially the 1st preference (SPC truncation resistance)
   * On the "EM FAQ/Dictionary", I doubt agreement is obtainable and the
     permitteduse of synonyms makes it seem unnecessary. Often the
     definitions are bad or missing: What would Demorep1 put for the word
     fairness?, which may be summing without weights but with an
     undefined idea of optimal truncating of contributions from
     preferences distant from the first. Or is that named by another
     name?.

What does "fairest" mean(?), or at least, what does Mr Saari have that
 word mean? (I am not going to write asking).

Maybe by fairness, Mr D. Saari means summing of votes that is done about
 correctly with weights near to 1, unless they need to be near 0.
 He wrote:
   "The unfairness of this method is obvious; it ranks a student with
    3 A's and failures in all other classes above the student with
    2 A's and the rest B's."
 That was in Scientific American's ask the expert:
      http://www.sciam.com/askexpert/math/math2.html

 Applying my recently stated power equation
  Min(Sum(Xi-Min(X)),Sum(Max(X)-Xi)), Standard Borda would be fair (or
  getting there). But the Borda method said to be of Saari, which had
 trailing zeroes, is not (Bart Ingles, approx 3 March 2000, "Points for
  truncator in Saari's version: A = 1, B = 0, C = 0").

"Democratic Symmetry" sounds like it could pass a lot methods...

I was unable to find, using AltaVista, a use of of Borda in Australian
 government. There is the Cape Borda Lighthouse, and some online
 Borda method results neatly presented by Bob Such (Liberal), on the
 topic of cycling in Australia, http://www.bisa.asn.au/survey_full.html .



Donald G. Saari's page:
http://www.math.nwu.edu/~d_saari/


--------------------
Correction: 

This ought to have been "Blake C.", here:

At 14:17 06.03.00 , Craig Carey wrote:
...
>Bart was commenting on my use of axioms and then failing methods
 i.e. Blake
...