  Unitary quantum theory, having no Born Rule, is non-probabilistic. Hence the
notorious problem of reconciling it with the unpredictability and appearance of
stochasticity in quantum measurements. Generalising and improving upon the
so-called 'decision-theoretic approach' (Deutsch, 1999; Wallace, 2003, 2007,
2012), I shall recast that problem in the recently proposed constructor theory
of information - where quantum theory is represented as one of a class of
superinformation theories, which are local, non-probabilistic theories
conforming to certain constructor-theoretic conditions. I prove that the
unpredictability of measurement outcomes (to which I give an exact meaning via
constructor theory), necessarily arises in superinformation theories. Then I
explain how the appearance of stochasticity in (finitely many) repeated
measurements can arise under superinformation theories. And I establish
sufficient conditions for a superinformation theory to inform decisions (made
under it) as if it were probabilistic, via a Deutsch-Wallace-type argument -
thus defining a class of decision-supporting superinformation theories. This
broadens the domain of applicability of that argument to cover
constructor-theory compliant theories. In addition, in this version some of the
argument's assumptions, previously construed as merely decision-theoretic,
follow from physical properties expressed by constructor-theoretic principles.
