Quantitative judgment is the evaluation of cases on the basis of a set of cues (attributes, evidence) with respect to a set of criteria, or a single criterion. It differs from decision making in that the response represents a certain kind of value of each case, not, by itself, a choice. Some judgments involve assigning numbers: for example, assigning grades to students’ essays, salaries to employees, sentences to convicted criminals, ratings to figure skaters, or probabilities to future events.

The normative theory of decision making is closely related to several applied fields. These include decision analysis1 and cost-effectiveness analysis. This chapter and the next discuss the problem of measuring utility for such applied purposes. This chapter concerns basic comparisons of the utility of two outcomes.

Moral thinking is important for decision making as a whole, because most real decisions involve moral issues, at least because they affect other people. The choice of one’s work, for example, is often considered to be a purely personal decision, but we can do various amounts of good or harm to others by choosing different paths through our working lives.

Many of our beliefs concern the relation between one quantity and another. We may ask whether the speed at which galaxies move away from us is related to their distance from the earth or whether IQ is related to income. Often we are concerned with such relationships because we want to decide whether to manipulate one thing in order to affect another.

This chapter and the next concern two common kinds of moral decision problems that have been studied extensively, both normatively and descriptively. The next chapter concerns decisions made by several people, each facing a conflict between what is best for the self and what is best for others. The present chapter is about the allocation of rewards and punishments: who gets what.

The last chapter examined conflicts between self and others. This chapter looks at a different, but analogous, kind of conflict, that between the present and the future. Many of our decisions require us to choose between satisfying our goals for the immediate present and our goals for the future. Should I do the crossword puzzle or work on this book?

A nozzle is sometimes called the exhaust duct or tail pipe, and is the last component of a jet engine through which the air passes. Up to two parallel nozzles are present on an engine: primary and fan (or secondary). In this chapter, both converging and converging– diverging (CD) nozzle types are discussed, and the two nozzles can be any combination of the two types (i.e., converging and converging–diverging, converging and converging, etc.). Recall that the functions of the nozzles are to convert high-pressure, high-temperature energy (enthalpy) to kinetic energy and to straighten the flow so that it exits in the axial direction. It is from this conversion process that the thrust is derived. Because of the high temperatures that a nozzle experiences, materials used in nozzle construction are usually a nickel-based alloy, titanium alloy, or ceramic composite. In Chapter 2, the nonideal effects of nozzles are discussed. The reader is also encouraged to review Appendix C as many of the fundamentals are covered therein. In this chapter, these effects are covered in more detail along with other design considerations.

Although the normative principles of choice appear reasonable enough to most people, psychological research has shown that we violate these principles systematically when we make decisions. That is, the violations are not just a consequence of the random variation to be found in any difficult judgment; rather, they are usually in a particular direction.

A hypothesis is a proposition that we evaluate, or test, by gathering evidence concerning its truth or, more generally, its probability. A physician trying to explain a patient’s illness forms hypotheses about the patient’s disease and then tests these hypotheses by asking the patient questions and ordering various tests.

As discussed in Chapters 2 and 4, the basic operating principle of a compressor is to impart kinetic energy to the working fluid by the means of some rotating blades and then to convert the increase in energy to an increase in total pressure. Axial flow compressors are covered in Chapter 5. These compressors are used on large engines and gas turbines. However, for small engines – particularly turboshafts and turboprops – centrifugal (or radial) compressors are used.

This chapter begins the discussion of the normative theory of decision making: that is, the theory of how we should choose among possible actions under ideal conditions. The best decision, I assume, is the one that best helps us to achieve our goals. This idea follows directly from the definition of rationality introduced in Chapter 3.