Arthur Pedersen (Max Planck Institute/MCMP) gives a talk at the MCMP Colloquium (5 November, 2015) titled "Admissibility Decisions, Permissible Previsions". Abstract: In this talk I shall consider the problem of designing a theory of judgment and decision making that adequately addresses outstanding challenges to the normative adequacy of strict “Bayesian” theories inspired by the pioneering developments of Ramsey, de Finetti, and Savage. The questions I shall ask are basic ones: how are personal opinions expressed in situations of uncertainty, especially those where information is conflicting or scarce; what bearing do they have upon decisions taken to promote personal objectives; and what norms—in particular, what decision-making criteria—set appropriate standards against which to evaluate interrelated states of attitudinal judgments such as these? I shall propose a theory of judgement and decision making that advances constitutional reform along two dimensions: (a) it repeals gratuitous requirements the strict Bayesian canon imposes on states of attitudinal judgment (e.g., complete comparability of personal opinions), and (b) it enacts mandatory requirements the strict Bayesian canon fails to impose on such states (e.g., admissibility—rejection of weakly dominated courses of action). Unlike alternative proposals, the theory I advance (i) specifies the function of an agent’s judgments in inquiry and decision making, (ii) does not capitulate to the mathematical convenience of weakened Archimedean restrictions (or other regularity conditions, e.g., measurability, topological, or subsidiary cardinality restrictions), and (iii) subsumes existing proposals (admitting numerical representations in terms of formal power series fields in a single infinitesimal).