[EM] James: counting time

[James Green-Armytage]

>
>No, pairwise counting takes longer than Approval, nearly always., whether 
>done by ballot or show of hands. 

	Oh, I wasn't trying to argue that a rough pairwise count is quicker than
approval. I was just saying that the extra time it takes is trivial unless
there is less than a few minutes to make the decision, in which case it's
likely to be an executive decision rather than a committee decision anyway.

>Pairwise count time increases quadratically 
>with the number of candidates. Approval counting time increases linearly 
>with the number of candidates.

	Here's what I'm suggesting for a quick pairwise count within a committee.
First of all, you don't have to count all of the pairwise contests. Let's
say that there are six options, A through F, and you want to make a quick
majority decision between these options.

Step 1: Have everyone jot down their preference order on a sheet of paper
in front of them. However, they keep the piece of paper, rather than
handing it over to someone else.

Step 2: Start with two options that seem relatively likely to be Condorcet
winners. Let's say that this is A and B. The chairperson (or whatever you
call the person managing the process) asks for a show of hands for A>B,
and then a show of hands for B>A. Let's say that B wins. The chairperson
makes a note of the pairwise victory, preferably on a chalkboard or
something everyone can see, drawing an arrow from the winner to the loser,
with the arrow marked by the defeat strength.

Step 3: Since B is unbeaten, try comparing other options to B, starting
with the options that seem most viable. If B is a Condorcet winner, then
you can have the whole thing over with in 5 counts. There's no need to do
the other 10. 
	Or maybe candidate D beats candidate B. Then you want to do the
comparisons with D to see if D is a Condorcet winner. It's possible that
you'll uncover a cycle, in which case the process will take a bit longer,
but there should still be pairwise comparisons that you can safely avoid
without even compromising GeTChA-efficient methods like beatpath and
ranked pairs. If you're using minimax (PC), you can get away with doing
even fewer comparisons.

For example, let's say that the process goes like this, in a 15-member
council (I don't know if these exact numbers are possible, but it doesn't
matter):
Count 1: A vs. B. B>A, 9-6 
	B is unbeaten
Count 2: B vs. C. B>C, 11-4
	B is unbeaten
Count 3: B vs. D. D>B, 10-5
	D is unbeaten
Count 4: D vs. A. A>D, 8-7
	D has the weakest defeat against it
Count 5: D vs. C. D>C, 10-5
	D has the weakest defeat against it
Count 6: D vs. E. D>E, 12-3
	D has the weakest defeat against it
Count 7: D vs. F. D>F, 11-4
	D has the weakest defeat against it. All pairwise comparisons with D have
been explored. D is certainly the minimax winner; no more comparisons are
necessary.

	So, we've resolved a 3 candidate cycle in 7 counts, rather than doing the
full 15 counts. Obviously more time-consuming than an approval election,
but it can probably be done within 5 minutes, if the council members are
on the ball. But anyway, I think that proving a CW in 5 or 6 counts is the
most likely scenario, which makes things easier.
>
>You're talking about when there are only very few candidates or 
>alternatives. Maybe then handcounted Condorcert would work in a hurry.

	Yeah, maybe I'm not thinking about a very large number of options. I
don't think that semi-formal quick decision committee scenarios with more
than 7 or 8 viable options are very common, but I'm not sure. Can you
think of some good examples of this?
>
>In a group voting on what movie to go to, I'd suggest Condorcet (PC) if 
>there were only a few movies. If it were necessary to vote among many 
>movies, and there weren't much time, or much pre-existing interest in
>voting 
>systems, and no already-programmed computer, I'd use Approval instead of 
>Condorcet.

	Hmm, actually I'd rather be in a movie group that uses a proportional
representation system of some kind. That is, even if we only get one movie
per night, doing proportional representation for the movies chosen over a
longer period of time.
	But if it was just a one-time thing, I don't know. I don't think the
group should get a movie that isn't approved of by everyone; I'd like to
think that it would be choosing between multiple movies that are
acceptable to everyone. So, what if more than one movie gets a perfect
approval score?

Sincerely,
James
fc.antioch.edu/~james_green-armytage/voting.htm