Subjective Probability and Expected Utility without Additivity

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论文题目：Subjective Probability and Expected Utility without Additivity
作者： David Schmeidler

内容简介：An act maps states of naturet o outcomes;d eterministico utcomesa s well as random
outcomes are included. Two acts f and g are comonotonic, by definition, if it never
happens that f(s) >- f(t) and g(t) >- g(s) for some states of nature s and t. An axiom of
comonotonici ndependenceis introducedh ere. It weakenst he von Neumann-Morgenstern
axiom of independence as follows: If f >- g and if f, g, and h are comonotonic, then
cff +(l-a)h>-ag+(1 -ac)h.
If a nondegeneratec,o ntinuousa, nd monotonic( statei ndependentw) eako rdero vera cts
satisfies comonotonici ndependencet, hen it induces a unique non-(necessarily-)additive
probabilitya nd a von Neumann-Morgensterunti lity. Furthermoreo, ne can computet he
expected utility of an act with respectt o the nonadditivep robabilityu, sing the Choquet
integral.
This extension of the expected utility theory covers situations, as the Ellsberg paradox,
which are inconsistentw ith additivee xpectedu tility. The concept of uncertaintayv ersion
and interpretationo f comonotonicin dependencein the contexto f socialw elfaref unctions
are included.
KEYwoRDsC: omonotonicin dependenceu, ncertaintya version,e xpectedu tility,s ubjective
probability.

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关键词：Probability subjective Additivity Expected bability Probability Expected without Utility Additivity