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This chapter deals with the basics of converting qualitative decision reasoning into quantitative models according to the logically consistent rules or norms of applied decision theory (ADT). Normative statistical decision theory comprises a body of logical norms or rules that check whether some of students judgments of uncertainty and value, expressed as numerical probabilities and utilities, are coherent. A model quantifies students judgments of options, outcomes and preferences and draws inferences from them according to decision theory norms. ADT is a class of prescriptive decision analysis tools that obey decision theory norms. Any sound reasoned argument can be quantified by ADT. A major class of ADT reasoning is projection, whereby the possible outcomes of options are modeled and utility is attached, depending on some uncertain condition. The subjective expected utility of possible outcomes is calculated as the average of their utilities, and this is the resulting utility of the options.
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