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Olsson’s account includes the following measure (where
is any information set):
is a straightforward measure of the relative overlap amongst the
propositions in an
-membered information set (recall that “relative overlap” refers to the amount of the total probability mass assigned to
propositions that lies in their intersection).
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is any information set):
is a straightforward measure of the relative overlap amongst the
propositions in an
As such,
is a generalization of logical equivalence;
takes its maximal value 1 whenever
is made up entirely of logically equivalent propositions:
and