[EM] Re: completing Condorcet using ratings information

[James Green-Armytage]

Chris,
	I greatly appreciate your feedback about my proposal; I find it very
constructive. Some replies follow.

>CB: I should have written "maximised and scaled".  Yes,  the
>highest-rated  Schwartz-set member  is changed  to the maximum,
>the lowest-rated member is changed to the minimum, and the middle-ranked
>are changed so as to keep their relative spots in the 
>range between those two extremes. For example if there are three
>Schwartz-set members then (assuming a rating scale of 0-100)
>100, 99, 98  becomes  100, 50, 0; and  0, 1, 4  becomes  0, 25, 100; and
> 80, 20, 2 becomes 100, 23.684, 0.
>In your example, the voters have thoughtfully done this themselves.
>If this is not done, then I think there would remain some incentive to
>exaggerate ratings among the likelt top-tier contenders.

	Yes, you make a very good point here. Let's say that my sincere ratings
were Nader 100 > Dean 20 > Kerry 19 > Bush 0. That is, let's imagine that
I care much more about Nader winning then I would about any of the
Democrats beating Bush, but I care more about the Democrats beating Bush
than I do about which Democrat wins. (In real life I'm not sure that I
still prefer Nader to the Democrats, but let's imagine...)
	If I thought that the likelihood of Nader being in the Schwartz set was
not very strong, and a cycle between the other three was less likely, then
I would be tempted to vote Nader 100 > Dean 99.9 > Kerry 99.8 > Bush 0. If
such a cycle indeed happened, I'd be feeling pretty smart. However, if the
result was a Nader-->Dean-->Kerry-->Nader cycle, then I'd be kicking
myself.
	So yeah, this is the problem you want to address, right?
	It seems like a good idea, I have to say. With a maximization in scale
provision, I could vote sincerely and feel reasonably confident that my
vote would reinforce the most important part of a cycle if one happened to
arise. Of course, there is a chance that this will not be the case, but
anyway I think that chance is reduced from the original version of the
method.
	The only objection I have to this provision is rather a weak one, simply
the desire to keep the method as simple as possible. In general I trust
relatively simple and parsimonious methods more than I do very complex
ones. However, I haven't been able to imagine a case where this provision
causes any undue harm, so provisionally speaking I think that it's a good
idea. Thank you for suggesting it.

>CB: On reflection, better still would be to derive simple approval scores
>from the ballots by each ballot approving the 
>Schwartz-set member they rate above average (of  the members), and
>half-approving those they rate exactly average.
>Then in step 3, the  "strength of the defeats" are the scores derived
>thus : on those ballots that rank the pairwise-winner 
>above the pairwise- loser, simple approvals for the winner minus simple
>approvals for the loser.
>(Another good alternative  would be to simply eliminate the candidate
>with the lowest  approval score, and then  start again.)
>One advantage of this version is that it should get rid of any need or
>demand for separate ranked-ballots. Voters would 
>have no disincentive to rate favoured candidates slightly differently, so
>the rankings can be simply inferred from the ratings.
>What do you think?  

	I don't know... I proposed a version of the method that uses approval
cutoffs instead of ratings, but I prefer the ratings version. 
	It seems like your variation would simplify the ratings information more
than I want it to. As I understand it, if A, B, and C are all part of the
Schwartz set, the variation effectively transforms a ballot marked A 100 >
B 90 > C 0 into a ballot marked A 100 > B 100 > C 0, and then the rest of
the procedure is more or less the same as what I proposed. Is that right?
I say, if people want to indicate that ten point differential, I'd like to
let them do so. Why not, really, you know? As David pointed out, I'm
barely using the ratings info as it is. And I want to make the ratings as
significant as possible while keeping the integrity of the pairwise
comparisons. I don't want to undermine the value of the ratings more than
I already have... 'Cause you know, I think ratings are cool. In that they
allow for more detailed expression than rankings.
	I am more inclined to agree with your earlier amendment, that is to
maximize and scale the ratings with regard to the Schwartz set. That way,
you are keeping the differentials that people indicated, but just
maximizing their power.
	As for inferring the rankings from the ratings, I don't consider that to
be something that needs to be worried about too intensely right now. First
I want to know how sound the method is... perhaps if it proves to be worth
implementing I will start worrying more about the ballot interface.
However, once again if there was only a ratings ballot, and you wanted a
rankings differential without a significant ratings differential, you
could vote A 100, B 99.999, C 0, and then the computer could infer that
your rankings are A>B>C. 

>
>My old idea of completing Condorcet by compressing ranks also picks Kerry
>here, so I'm interested in  seeing how the two methods compare in future
>examples.

	Yes, I'm interested in that too. I haven't really been looking into the
question myself, but I agree that it is a natural and important one to ask
at this juncture. Didn't you produce some sort of failure example for the
compressing ranks method a while ago? I'd be interested in seeing that
again if there is one. I remember reading the compressing ranks proposal
and assuming that it wouldn't work, as I was setting off on my quest to
devise a ratings-rankings method. But to be honest I never really backed
that intuition up with a lot of evidence; maybe I was wrong after all. So
yes, I'd be happy to think about and discuss that method some more.

my best,
James Green-Armytage