Monotonicity: For all acts f, g, if the roulette lottery f(s) is weakly preferred to the
roulette lottery g(s) for every state s, then fg.
The expected utility representation of preferences over horse-roulette acts f= (…;P
j
if E
j
; …) = (…;(…;x
ij
,p
ij
; …),E
j
; …) implied by these axioms takes the form
where U(·) is a von Neumann-Morgenstern utility function and μ is a finitely additive
probability measure (“prior”), which is uniquely identified as in Savage’s axiomatiza-
tion. As seen in the above equation, the term U( f (s)) in the integral
S
U(f(s))dµ(s
)
is the expected utility of the roulette lottery f ...
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