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Re: Condorcet Voting for Council Elections and Council Votes

2004-12-13 20:53:57


I'm not wearing my "SPF Council" hat, but my "math geek" hat here.


When the suggests for things like Condorcet voting first came up in
the election for council members, I immediately understood why it was
being suggested, and if it had gained a lot of support, I would have
happily gone along.

I've been interested in various voting methods ever since a college
professor of mine told me about Arrow's imposibility theorem of voting
systems[1].  Basically, Arrow proved that if you take a few simple,
obviously good properties of a voting system, you can prove that no
such voting system can exist that satisfies all thoses few good
properties.

As originally formulated, Arrow used just three requirements of a good
voting system:

* If you vote *for* the candidate that is currently winning, you
  shouldn't cause that candidate to lose.

* Any candidate should be able to win.

* If there is a candidate that no one much likes, whether that
  candidate chooses to run or not shouldn't change the outcome of the
  election.

This is one of those mathematical proofs that makes you say "Huh?
That *can't* be true!".  For math geeks, it causes them to get sucked
in and learn why it is true.


So, while Arrow's theorem says that there is no perfect voting system,
there are systems that are a heck of a lot better than others.

As it turns out, one of the very worst voting systems is "one man, one
vote, the majority rules", also known as plurality or first-past-post
voting.  The most obvious problem is the "third party spoiler",
where a candiate enters the race, splits the majority and someone who
almost 2/3rds of the people don't like gets elected.  There are,
however, a bunch of smaller problems with this voting method.


Ok, the next thing I learned is that no one really studied the
mathematics of voting systems until after the American and French
revolutions.  There wasn't much point in studying voting when you
couldn't vote.  Unfortunately, most democracies adopted plurality
voting and it became ingrained before better voting systems were well
known. 



My favorite voting system is approval voting.  Its rule is: vote for
all the candidates that you approve of.  This turns out to be,
mathematically, a pretty good system and it is also dead simple, there
are never any spoiled ballots, and the primary mathematical "defect"
is it tends to pick centralist candidates over candidates that are
approved of by a small vocal minority.

When we were doing council member elections, voting for up to 5
candidates was close enough to approval voting that if we had used
approval voting, the outcome probably wouldn't have changed.


In my opinion, the mathematically best voting system is the Cloneproof
Schwartz Sequential Dropping (CSSD) Condorcet voting method.  It
*sounds* a lot worse than it really is.  For the voter, you simply
rank your choices.  For the vote counters, things are a little more
complicated, but nothing that a simple program can't handle and there
are quite a few programs out there that let you do the calcuations on
your PDA and this voting method is being used in meetings and such.



Ok, now putting my SPF Council member hat on:

I would much rather see either approval voting or CSSD than pluarity
voting.  I mildly favor approval voting over CSSD because it is
simpler.

I have not sunk a lot of time into this subject because Julian posted
a bunch of links to spf-council.  I've sunk a lot of time into it
because I'm a math geek.


-wayne