Re: CHAT (POLITICS!!!): Putting the duh in Florida

On Fri, 1 Dec 2000, Adrian Morgan wrote:

> Nik Taylor wrote, quoting Mangiat:
>
> This may sound a little harsh, but I find it unbelievable that a
> reasonably literate nation should still use a FPTP voting system (i.e.
> where everyone marks just one candidate). I think FPTP is suitable
> for developing nations with very low literacy, but I don't see why it's
> accepted elsewhere, because in the end it says nothing about which
> candidate really carries most favour with the community. I'd like to see
> Americans adopt a preferential voting system, or an equally sophisticated
> equivalent.
If I understand you correctly, does this mean that you would advocate a
system where everyone, say, marks candidates in order of preference?

If you aren't, well, the below is probably irrelevant to you politically,
but might be of mild interest mathematically.

(I'm jumping into this topic on a mathematical note, not a political
one.  I can't remember details, so I may have gotten some wrong.  If
anyone's more familiar with this branch of math, do jump in!  Or if
anyone's curious and no one jumps in, I can probably snag a local math
prof and ask.  I think this might be somewhere in statistics or discrete
systems or something.)

Apparently someone (more likely several someones) out there has done a
mathematical study of voting systems where you rank multiple candidates
in order of preference, e.g. 1 for your favourite, 2 for your next
favourite, etc.

Then you might (using the simplest weighting system) add up the number of
ranks that every candidate has gotten, so if Mr. Very Unpopular had just
5 votes ranking him 1st, 2nd, 3rd, 4th and 5th he'd get a total ranking
of 15.  The person with the lowest ranking wins, presumably.

However, mathematically speaking, you can end up with indeterminate
results, i.e. lots of ties.  You can also end up with circular
preferences (probably not *too* likely in politics, but...).  Someone
might prefer Nader to Gore, Bush to Nader, and Gore to Bush.  (Okay,
politically very unlikely, but this could be seen happening with, say,
apple vs. blueberry vs. cherry pie.  Er, if such a thing as cherry pie
exists.)  In which case a ranking system with 1, 2, 3 etc. still doesn't
accurately reflect the voter's preferences, and (if I remember this
correctly) and even if you did allow circular preferences you can still
end up with annoying indeterminate results.

According to the book where I read it <banging head trying to
remember--probably one of Ivars Peterson's books on math for
non-mathematicians>, a ranking system of one of the two kinds described
above has been historically favored by political thinkers, but
mathematically-minded people looked at it and began seeing problems with it.

<Shrug>  Just some half-remembrances of math.  I'm sure someone here has
done much more extensive study of/reading about the mathematics of
voting systems than I have, though!

YHL