Comments on: Arrow Theorem and Ultrafilters
https://agtb.wordpress.com/2010/04/01/arrow-theorem-and-ultrafilters/
Computation, Economics, and Game TheorySun, 04 Apr 2010 20:23:53 +0000
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By: Jonathan Weinstein
https://agtb.wordpress.com/2010/04/01/arrow-theorem-and-ultrafilters/#comment-1183
Sun, 04 Apr 2010 20:23:53 +0000http://agtb.wordpress.com/?p=771#comment-1183I wouldn’t call it a corollary, since showing that the set of decisive coalitions must be an ultrafilter is to me the most substantial step of the proof (requires replicating the Condorcet paradox.) I would say that familiarity with ultrafilters is useful for organizing the steps in the Arrow proof into 1) Decisive coalitions form an ultrafilter, 2) Ultrafilters on finite sets are principal.
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