**Teddy Seidenfeld, Mark J. Schervish, and Joseph B. Kadane**

We extend de Finetti's (1974) theory of coherence to apply also to
unbounded random variables. We show that for random variables with
mandated infinite prevision, such as for the St. Petersburg gamble,
coherence precludes indifference between equivalent random
quantities. That is, we demonstrate when the prevision of the
difference between two such equivalent random variables must be
positive. This result conflicts with the usual approach to theories
of Subjective Expected Utility, where preference is defined over
lotteries. In addition, we explore similar results for unbounded
variables when their previsions, though finite, exceed their
expected values, as is permitted within de Finetti's theory. In
such cases, the decision maker's coherent preferences over random
quantities is not even a function of probability and utility. One
upshot of these findings is to explain further the differences
between Savage's theory (1954), which requires bounded utility for
non-simple acts, and de Finetti's theory, which does not. And it
raises a question whether there is a theory that fits between these
two.

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