  The Scrooge distribution is a probability distribution over the set of pure
states of a quantum system. Specifically, it is the distribution that, upon
measurement, gives up the least information about the identity of the pure
state, compared with all other distributions having the same density matrix.
The Scrooge distribution has normally been regarded as a purely quantum
mechanical concept, with no natural classical interpretation. In this paper we
offer a classical interpretation of the Scrooge distribution viewed as a
probability distribution over the probability simplex. We begin by considering
a real-amplitude version of the Scrooge distribution, for which we find that
there is a non-trivial but natural classical interpretation. The transition to
the complex-amplitude case requires a step that is not particularly natural but
that may shed light on the relation between quantum mechanics and classical
probability theory.
