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**Unformatted text preview: **B , c W ∈ C such that for any p ∈ P , c B º p º c W . (4) [Hint: use completeness and transitivity to ﬁ nd c B , c W ∈ C with c B W for º c º c all c ∈ C ; then use induction on the number of consequences and the Independence Axiom.] 3. Let P be the set of probability distributions on C = { x, y, z } . Find a continuous preference relation º on P , such that the indi f erence sets are all straight lines, but º does not have a von Neumann-Morgenstern utility representation. 4. Let º ˙ be the "at least as likely as" relation de ﬁ ned between events in Lecture 3. Show that º ˙ is a qualitative probability. 2...

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- Spring '10
- Yildiz
- Utility, Morgenstern, preference relation, px − py