  We study the geometrical properties of the utility space (the space of
expected utilities over a finite set of options), which is commonly used to
model the preferences of an agent in a situation of uncertainty. We focus on
the case where the model is neutral with respect to the available options, i.e.
treats them, a priori, as being symmetrical from one another. Specifically, we
prove that the only Riemannian metric that respects the geometrical properties
and the natural symmetries of the utility space is the round metric. This
canonical metric allows to define a uniform probability over the utility space
and to naturally generalize the Impartial Culture to a model with expected
utilities.
