TY - JOUR
T1 - Savagés theorem with a finite number of states
AU - Gul, Faruk
N1 - Funding Information:
Ramsey \[17\] and Savage \[18\] have formulated the subjective or personalistic view of probability by imposing consistency or rationality requirements on preferences over bets on events and deducing utilities and probabilities as parameters of these preferences. While the concept of subjective probability is not the only conceivable nor the consensus view of probability, it is accepted to be the only coherent view in some and at least a useful alternative in many discussions of the foundations of probability. The Savage framework involves a set of states of the world /2, a set of consequences X, and the set of acts F, which are mappings from/2 to Z. The interpretation is that, since the true state of the world s e/2 is not known (possibly because it has not yet "occurred"), the individual's preferences over the acts depend on both the consequences of the acts (at each state) and how likely he considers the states to be. 1 Savage shows that, given a set of "rationality" assumptions on the preferences of the individual, there will exist a unique (finitely additive) probability measure p on the set of all subsets of/2 and a unique (up to positive affine transformations) utility function on consequences such that * I am grateful to Dilip Abreu, David Kreps, Mark Machina, Ennio Stacchetti, and Robert Wilson for their comments. Financial support from the Alfred P. Sloan Foundation is gratefully acknowledged. A detailed analysis and interpretation of the Savage postulates can be found in Savage \[18\].F ishburn \[8\]a nd Kreps \[13\]a lso provide comparisons with the other choice models discussed in this paper.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 1992/6
Y1 - 1992/6
N2 - Conditions which guarantee the existence of a (subjective) expected utility representation of preferences, when the state space is finite, are presented. The key assumptions are continuity and an analogue of the independence axiom.
AB - Conditions which guarantee the existence of a (subjective) expected utility representation of preferences, when the state space is finite, are presented. The key assumptions are continuity and an analogue of the independence axiom.
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U2 - 10.1016/S0022-0531(05)80042-0
DO - 10.1016/S0022-0531(05)80042-0
M3 - Article
AN - SCOPUS:0002730209
VL - 57
SP - 99
EP - 110
JO - Journal of Economic Theory
JF - Journal of Economic Theory
SN - 0022-0531
IS - 1
ER -