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Topic:
Borda count
Replies:
9
Last Post:
Nov 17, 2000 3:13 PM




Re: Borda count
Posted:
Nov 17, 2000 1:40 AM


Guy Brandenburg wrote:
> Well, read it yourself. Here is the citation: > > http://www.colorado.edu/education/DMP/voting_b.html
I've given it a (very) quick scan, and I think that Saari doesn't claim to contradict Arrow. Instead, he has exploited the observation I made (that Arrow's result depends upon restrictive definitions, and, in consequence, reaches a restricted conclusion) to find ways around Arrow's Paradox. The real issue here is the common misstatement of Arrow's Paradox as "They ain't no fair way to make societal decisions". While I haven't gone deeply enough into the argument that Saari gives, I think that has picked up on a facet of Arrow's work that means that weighted voting can be fairor at least doesn't lead to the same paradox that other schemes do. I am not sure that Saari put his finger on the same thing that I did, but from my limited reading of Saari, he and Arrow both appear to be correct.
I presented my findings to members of my department about a year ago in a departmental colloquium talk entitled "The Slings and Misfortunes of Outrageous Arrow", in which I pointed out at the beginning of the talk that Arrow's Theorem seems at first blush to imply that there is no fair way to assign grades to students in a class, because, after all, the homework assignments, quizzes, exams, etc., can be viewed as "voting" on the relative rank of the students in the class. By the end of the talk, we had concluded that Arrow's Theorem does not apply because it requires a simple rankingthat is, function whose domain is the set of natural numbers {1, ..., n} (where n is the number of people in the class) and the members of the class. Most assessment instruments are much more than simple ranking tools.
Lou Talman



