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Unformatted text preview: p % q iff U ( p ) ≥ U ( q ) . We will use the above axioms to isolate a family of preference relations and to derive a more structured utility function. Theorem (vNM): Let % be a preference relation over L ( Z ) satisfying I and C . There are numbers ( v ( z )) z ∈ Z such that p % q iff U ( p ) = 6 z ∈ Z p ( z ) v ( z ) ≥ U ( q ) = 6 z ∈ Z q ( z ) v ( z ). Note the distinction between U ( p ) (the utility number of the lot-tery p ) and v ( z ) (called the Bernoulli numbers or the vNM utilities). The function v is a utility function representing the preferences on Z and is the building block for the construction of U ( p ) , a utility function representing the preferences on L ( Z ) . We will also often say that v is a vNM utility function representing the preferences % over L ( Z ) ....
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This note was uploaded on 12/29/2011 for the course ECO 443 taught by Professor Aswa during the Fall '10 term at SUNY Stony Brook.
- Fall '10