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VincentYu comments on Help with a (potentially Bayesian) statistics / set theory problem? - Less Wrong
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Comments (27)
If the aggregated preferences are transitive (i.e., 'not inconsistent' in your and Manfred's wording), then this preference relation defines a total order on the objects, and there is a unique object that is preferred to every other object (in aggregate). (Furthermore, this is isomorphic to the set {1,2,3,...,7} under the ≤ relation.)
As I understand things, you have no guarantee of transitivity in the aggregated preferences even if you do have transitivity in the individual preferences.
Yes, of course you are correct.
Very helpful - reading about this now. Starting here: http://en.wikipedia.org/wiki/Ranking