Agree. They want Borda. You want Condorcet.
Well, maybe. I want to give them something as intuitive as Borda in terms of showing a nice pretty set of scores that mere mortals can wrap their heads around, as well as being "correct" in terms of being non-strategic and non-sensentive to clone candidates as Condorcet, whether those same mortals understand this concept or not. I guess I want to have my cake and eat it too. So shoot me. :)
This is why I suggested you display the 1-d list of votes by ballot configuration. There is no ambiguity, and no information is lost. If you display this then you don't need to display the pairwise matrix that you're going to finally use to determine the winner, since anyone who cares can construct it for themselves.
I respectly note your suggestion, as well as your philosophical objection to my approach. Being as I am doing this for a client, ultimately I have to abide by their wishes, and I don't think I could sell them on displaying a matrix by default (I did mention it, and it wasn't received well). I suppose it comes down to a pragmatic marketing decision. I am *not* claiming, however, that I disagree with their preference.
If this puts me at odds with a more "pure" way of looking at election methods, well, so be it and I'll have to take comfort in knowing that the site will explain the formulas used so show the scores, and if people don't like the method of displying results, they are in no way forced to use the system.
This is really disturbing to me. What Arrow got his Nobel prize for was the proof that you CANNOT create a linear ranking from a pairwise matrix. Not only can it be linearized in "a reasonable way", it can be linearized in an infinite number of "reasonable" ways. But at the end of the day whatever linearization you chose has to match up with your election method, and I don't believe it is possible to do so for Condorcet-based methods. (That is not in itself a bad thing, it is just that that the requirement to display intermediate results is incompatible with an election method that only selects a winner after all results are in).
Well, if many others on this list can accept that Condorcet methods for determining a winner are reasonable to use -- even though Arrow has proven them to be imperfect -- I don't think I'll burn in hell for showing a set of scores which is equally discredited by Arrow.
The matrix is LESS information than the the counts per ballot combination, not more.
Agree, I don't think I implied otherwise, I said: "Full set of ballots -- all information Pairwise matrix -- lots of information"
"lots" is less than "all", no?
If "a simple ranking of candidates is to little." I am very confused, because as I understood it was the original request was for us to help come up with a simple ranking of candidates....
No, producing a simple ranking is easy, I would just pick a method such as ranked pairs or beatpath, apply it iteratively, and be done with it. If that was all I needed case I would not have needed to ask this question.
My original request was to suggest a way to produce a single scalar score per candidate which enhances, but does not conflict with, a simple ordered ranking. I apologize if I did not make that clear enough.
-rob
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