| Summary: | Unitary quantum theory, having no Born Rule, is <em>non-probabilistic</em>. Hence the notorious problem of reconciling it with the <em>unpredictability</em> and <em>appearance of stochasticity</em> in quantum measurements. Generalising and improving upon the so-called ‘decision-theoretic approach’, I shall recast that problem in the recently proposed <em>constructor theory of information</em> – where quantum theory is represented as one of a class of <em>superinformation theories</em>, which are <em>local, non-probabilistic</em> theories conforming to certain constructor-theoretic conditions. I prove that the unpredictability of measurement outcomes (to which constructor theory gives an exact meaning), 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 <em>conditions</em> for a superinformation theory to inform decisions (made under it) <em>as if</em> it were probabilistic, via a Deutsch–Wallace-type argument – thus defining a class of <em>decision-supporting</em> 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 <em>physical properties</em> expressed by constructor-theoretic principles.
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