Hello, a Question, and an Idea

[Rob LeGrand]

Josh Narins wrote:
> Hello everybody. I'm Josh, I, as a hobby, am very interested in voting
> methods. 

Welcome to EM, Josh!

> Has everyone seen Episode 11 and 12 of the Annenberg/CPB math educational
> series "For All Practical Purposes" ? Episodes 11 through 15 are about
> "Social Choice" and 12, specifically, is about voting methods. It's a little
> too low budget for prime time, but, it's got a great presentation level for
> anyone who's at least finished high school and is willing to pay attention,
> and is not so dumbed down to be insulting to someone trained in the art. The
> main example of the show is about a 5 way primary race for an imaginary
> party. They use Plurality, Plurality with Runoff, Sequential Runoff Voting,
> Borda and Condorcet. They also hand pick an interesting result, in that a
> different of each of the 5 candidates wins with each different method. There
> are interview segments with Kenneth Arrow at the end of the tape, where he
> explains that his theorem does not say that there are no better methods,
> just that there is no perfect method. He compares this to engine efficiency.
> They've proved it's impossible to have 100% efficient engine, but not that
> you can't have a better engine.

I've never heard of that series, but I've seen similar examples that give
different results for those common methods.  One is in the introduction to
Hannu Nurmi's book Comparing Voting Systems (Reidel, 1987).  I believe Kenneth
Arrow himself recommended a system similar to minmax-elimination.  (Is that
correct, Markus?)

> My idea is we vote on the best election method. We first vote on what voting
> method we use to to count the results of our vote to choose the best
> election method. To find out which method we use to count the resulsts of
> our vote to find the best method of counting the votes for our vote to find
> the best voting method, we hold a vote. We can continue like this for hours,
> but, I'm sure we all have better things to do.

About a year ago we had two polls on EM.  The first poll was to decide the
topic for the second; the winner was single-winner voting systems.  The second
poll was really two polls, as there were seperate ballots to choose the best
voting system for public proposal and the best voting system on pure merit. 
Both were won convincingly by Approval Voting, which seems to be pretty much
the only thing this list can agree on (except maybe that plurality and IRV are
bad).  EM would never be able to agree on a single Condorcet method as best,
although every margins method in the second poll defeated every winning-votes
method pairwise according to both sets of ranked ballots.

If we ever had another similar poll, I think it would be fun to have a series
of approval polls.  One of us could decide on a random number, maybe on the
order of 5 to 10 or 20, and accept approval ballots for a series of that many
polls.  No one voting would know when he was voting in the last one, so he
would be unlikely to vote insincerely for the purpose of manipulating other
votes in the subsequent polls.  For each poll after the first the voters would
know the results of the previous poll and vote accordingly.  I'd be interested
to see how fast a stable outcome would be reached, or even whether there would
be one.  We could even use Forest's cumulative repeated approval idea and keep
a running total, in which case I predict that it will take longer to reach a
stable outcome, but it would jump around less in the absence of a sincere
Condorcet winner.


=====
Rob LeGrand
honky98 at aggies.org
http://www.aggies.org/honky98/

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