[EM] Condorcet strategy and weighted pairwise method

[James Green-Armytage]

James Green-Armytage here, replying to Dave Ketchum.

>Is this method worth the pain?

	There is no pain involved. You are simply giving the voters the option of
supplementing their ranking info with ratings. If they don't feel like
doing that, it's fine. If voters fill out the rankings but not the
ratings, then the system can easily assign default ratings to the ballot,
by giving the highest candidate(s) 100, the lowest candidate(s) 0, and
evenly spacing the rest of the ratings gaps. 
	Voters can even bullet vote if they want to, just like they can in
regular Condorcet. That way, you would be voting your favorite in first
place with a rating of 100, with everyone else tied for last and with a
rating of 0.
	When you talk about "is this method worth X", I think the main thing is
just to spring for a computerized voting system / interface (that is
secure and leaves a paper trail, dammit!), and that supports both ratings
and rankings in a snazzy, non-baffling way. And my answer to the question
is, sure, it's a small price to pay.

>      Does not matter unless you have more than two candidates evenly 
>matched enough to produce cycles - often enough to justify the pain 
>(because cycles can happen they must be attended to - question is how
>much 
>complexity to build in).

	If you don't have more than two viable candidates, then your election is
not very exciting. For elections like that you can use IRV or two-round
runoff and things will turn out fine. But I'd much rather have elections
with more than two viable candidates. Keep in mind that in close
multicandidate elections you might get insincere cycles as well as sincere
cycles... so I'd be relatively cautious as to how evenly-matched
candidates have to be before I want this method instead of rankings-only
Condorcet.
>
>      Condorcet precinct results are an array, with the arrays summable 
>for the whole district or any subdistrict.  IRV is not so simple.

	I think it is summable, probably, but to be honest, the summability
criteria seems like a bit of a red herring to me. Whether you use IRV or
Condorcet, when people ask for the results, they are going to want the
full results, that is, not just the matrix, but how many people voted a
particular preference ranking. So why does it matter that you can produce
a summable matrix for Condorcet? Anyway, it seems like you are
underestimating the power of contemporary (and future, since this method
won't be implemented for awhile) information technology. I think that the
full rankings & ratings information for any given precinct is really not a
big deal when you put it in a digital format. For example, you could
probably fit it all on a DVD or something like that.
	I do admit that it's going to be pretty hard to report the full results
of a weighted pairwise election in any kind of succinct way. The full
results can and must be made available, but they would hardly make for
nice bedtime reading. Of course, just as with ranked ballot methods, you
could digest them in different ways to bring forward the kind of numbers
that people can look at without their heads exploding.
	Anyway, I haven't really answered your question. To be honest I'm not a
big computer science guy, so I'm not sure I know what I'm talking about,
but my best guess is that it is summable. You can have one summable array
for the pairwise comparisons, and then maybe a second summable array for
the ratings differentials. Then, if you put them together you can
determine the winner? 
	Hmm. I know that Brian Olson implemented a simple version of the weighted
pairwise method in his election calculator.
http://bolson.org:8080/v/vote_form.html Plug in some ratings, indicate
"ratings" in the box up above, and when you get to the results, scroll
down to where it says "Pairwise Rating Differential Summation". I don't
really know how he did the code, but the way he has it, it looks summable
to me.


my best,
James