[EM] FWD - How to Fix n Election

[David Catchpole]

Grrr... Physics student gets incredibly pissed off when people mention
"chaos theory" in any context, especially a patently wrong one... "Chaos
theory" is a tiny part of the study of dynamical systems. Actually, I
intuitively hold that you can't have folded manifolds in any model of
voting... invariably there's some equilibrium according to the system of
voting and your assumptions about the nature of voting, probabilistic
responses and voters' knowledge.

While we're on the subject of maths, I apologise for my stupidity in
saying "matlab" instead of "maple" in my last e-mail. I should at least
whinge about the right software...

Also, I don't like Saari at all. The only thing going for him is that he
knows how to get into pulp science magazines. His appraisal of Borda seems
a little biased (like that of most condorcetists only with less
justification). His contention that "if Borda goes wrong, every other
system does" is so patently false! (More about this when I actually get
around to finishing those EJETPR articles...)

> Saari used mathematical ideas from the study of dynamical
> systems, sometimes loosely called chaos theory, and algebraic
> geometry to identify situations in which different voting systems
> fail. The results indicate that, for more than two candidates, you
> can always find examples of voting procedures where the election
> results favor a specified outcome.
> 
> "You can get whatever result that you want," Saari says. Yet
> "nobody changes his or her mind."
> 
> It turns out that, despite some problems, the original Borda count
> is the best voting scheme. "It significantly reduces the number of
> paradoxes that might arise," Saari says. Moreover, "if something
> goes wrong in the Borda count, it will go wrong in every other
> procedure."
> 
> The worst scheme is the simple plurality vote. In elections in which
> voters must select candidates to fill two or more positions, giving
> the voters the option to choose any number of candidates up to the
> full allotment (approval voting) messes up the results even more.
> 
> That may explain the quirkiness often found in lists of the 100 best
> U.S. films or the top mathematicians of all time.
> 
> "Manipulating elections means taking advantage of voting
> paradoxes," Saari says. It's useful to be able to identify what can
> go right and what can go wrong.
> 
> In general, "who you elect reflects the procedures you use more
> than who you want," he adds. "Bad procedures can lead to lousy
> elections results."
> 
> 
> References:
> 
> Saari, D.G. 1995. Basic Geometry of Voting. New York: Springer-
> Verlag.
> 
> ______. 1995. A chaotic exploration of aggregation paradoxes.
> SIAM Review 37(March):37.
> 
> ______. 1992. Millions of election outcomes from a single profile.
> Social Choice and Welfare 9:277.
> 
> Saari, D.G., and F. Valognes. 1998. Geometry, voting, and
> paradoxes. Mathematics Magazine 71(October):243.
> 
> Additional information is available at Donald Saari's Web page at
> http://www.math.nwu.edu/~d_saari/.
> 
> Comments are welcome. Please send messages to Ivars Peterson
> at ip at sciserv.org.
> 
> Ivars Peterson is the mathematics/computers writer and online
> editor at Science News.
> 
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>  T H E   C O D E   O F   H O N O R   F O R   R E F O R M   A C T I V I S T S
> 
>      Any group of reform activists that are thinking about a petition drive
> to place a proposal on the ballot are to present their proposal beforehand
> to all other reform activists that they know of. The time for debate and
> negative comments is before the petition stage. Once the group makes its
> final proposal and enters the petition stage, the debates and negative
> comments by all reform activists is to cease.
>     At this time each activist is to make an honest evaluation. If the
> initiative will improve government then each activist is to find it in his
> heart to support the initiative, even if it is not exactly what the
> activist would like.
> 
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>    |                         Q U O T A T I O N                         |
>    |  "Democracy is a beautiful thing,                                 |
>    |       except that part about letting just any old yokel vote."    |
>    |                            - Age 10                               |
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> 
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