 where \(0 \lt q \lt 1.\) All such utility functions are guaranteed to satisfy Levi’s three principles. The parameter \(q\) is interepreted as a “degree of caution,” representing the premium  placed on truth as opposed to relief from agnosticism. When \(q=1\) the epistemic utility of suspending judgement, \(U(W)\), is equal to zero. This is the situation in which the premium placed on relief from doubt is the maximum. Levi proves that expected epistemic utility \(E(H)\) is maximal iff \(\Pr(H)&gt; q \cdot cont(\neg H).\) Therefore, Levi’s ultimate recommendation is that the agent believe all deductive consequences of \[\cap \{ \neg H_i \in {\bf Q} : \Pr(\neg H_i)&gt; 1 - q \cdot cont(\neg H_i) \}.\] From this formulation  it is possible to see Levi’s proposal as a question-dependent version of the Lockean thesis where the appropriate threshold is a function of content. However, Levi takes pains to make sure that the result of this operation is deductively cogent and therefore  avoids Lottery-type paradoxes.