Rationality and Dynamic Consistency Under Risk and Uncertainty
55
Theorem2.4Assume that
is an arbitrary binary preference relation on the set
L:=�(Y
)
of
simple roulette lotteries over consequences in the domain Y. The following two statements are equivalent:
(i) The preference relation
on
�(
Y
)
is represented by the expected value of each von
Neumann–Morgenstern utility function
Y
∋y�→v(y
)
in a cardinal equivalence class.
Moreover, this equivalence class is unique except in the trivial case where
induces at most two
indifference classes among the set δ
y
(y ∈ Y) of degenerate lotteries.
(ii) The preference relation
on
�(
Y)
satisfies ...
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