Decision Theories and Methodologies

Abstract

This chapter introduces the extant decision theories. Whereas the literature segments the field into the Normative, Descriptive, and Prescriptive theories, we identify a fourth. That is the Declarative strand of decision-making. We discuss all four strands of research and praxis. We locate our prescriptive paradigm in the Prescriptive segment. We discuss the question of what is a good decision and a good process. We will close this question in Chap. 10 after we have had the opportunity to illustrate the use of the machinery of our prescriptive paradigm in the main body of the book.

Abstract

Scientific knowledge, engineering science, and their best practices are cumulative. Every new idea and improvement is necessarily the result of standing on the shoulders of others. New knowledge, novel and useful practice are all part of evolving and connected strands of understanding, expertise and proficiency. The progression is cumulative and advancing to more insightful understanding and more effective practice. The trajectory is not necessarily a smooth one. There are many false starts and punctuated by what Kuhn (2012) calls paradigm shifts. We think of our approach as opening a new window in a magnificent structure and a modest punctuation. A new way to think about executive-management decisions. In this chapter, we show its multidisciplinary heritage rooted in mathematics, cognitive psychology, social science and the practice. We want to show its punctuated continuity with, and its debt to, the achievements of the past. Our debt, notwithstanding, we also draw contrasts between our engineering decision-design methods and other traditional methods.

Appendices

Appendix 2.1 Axioms of Normative Decision Theory

A lottery, or gamble, is central to utility theory. It specifies an alternative for decision making.

Mathematically, a lottery is a list of ordered pairs {(x₁,p₁), (x₂,p₂), … , (x_n,p_n)} where x_i is an outcome, and p_i is the probability of occurrence for that event.

• Completeness. For any two lotteries g and g′, either g⩾g′ or g′⩾g. i.e. given any two gambles, one is always preferred over the other, or they are indifferent.

• Transitivity. For any 3 lotteries, g, g′, and g″, then if g⩾g′ and g′⩾g″, then g⩾g″. i.e. preferences are transitive.

• Continuity. If g ⩾ g′⩾ g″, then there exists α, β in (0,1) ∋: αg+(1−α)g″⩾g′⩾βg+(1−β)g″. i.e. the Archimedean property holds, a gamble can be represented as a weighted average of the extremes.

• Monotinicity. Given (x₁,p₁) and (x₁,p₂) with p₁>p₂, then (x₁,p₁) is preferred over (x₁,p₂). i.e. for a given outcome, the lottery that assigns higher probability will be preferred.

• Independence (substitution). If x and y are two indifferent outcomes, x~y, then xp+z(1-p) ~ yp+(1-p)z. i.e. indifference between two outcomes also means indifference between two lotteries with equal probabilities, if the lotteries are identical. i.e. two identical lotteries can be substituted for each other (Morgenstern and Neumann 1944).

Appendix 2.2 Desiderata of Normative Decision Theory

One of normative decision theory’s strongest evangelist is Howard from Stanford. He puts forward the canons of “old time religion” as principles for the practice of normative decision analysis. These are summarized by Wu and Eriksen (2013) as shown in Table 2.7 as direct quotes.

Table 2.7 Desiderata of Normative Decisions

Appendix 2.3 Keeney’s Axiomatic Foundations of Decision Analysis

Keeney articulates 4 sets of axioms of decision analysis. The following are direct quotes from (Keeney 1992a, b) except for our comments in italics.

Axiom 1

Generation of Alternatives. At least two alternatives can be specified.

Identification of Consequences. Possible consequences of each alternative can be identified.

Axiom 2

Quantification of Judgment. The relative likelihoods (i.e. probabilities) of each possible consequence that could result from each alternative can be specified.

Axiom 3

Quantification of Preferences . The relative desirability (i.e. utility) for all possible consequences of any alternative can be specified.

Axiom 4

Comparison of alternatives. If two alternatives would each result in the same two possible consequences, the alternative yielding the higher chance of the preferred consequence is preferred.

Transitivity of Preferences . If one alternative is preferred to a second alternative and if the second alternative is preferred to a third alternative, then the first alternative is preferred to the third alternative.

Substitution of consequences. If an alternative is modified by replacing one of its consequences with a set of consequences and associated probabilities (i.e. lottery) that is indifferent to the consequence being replaced, then the original and the modified alternatives should be indifferent.

Note: “People are sensitive to the manner in which an outcome has been obtained … decisions with identical outcomes are judged as worse when they result from acts of commission than acts of omission”. (Keren and de Bruin 2003 ).

Appendix 2.4 Foundations of Descriptive Theory

The following are direct quotes from Edwards (1992) except for our comments in parentheses and italics.

Assumptions

• 1. People do not maximize expected utility, but come close.

• 2. There is only one innate behavioral pattern: they prefer more of desirable outcomes and less of undesirable outcomes. These judgments are made as a result of present analysis and past learning.

• 3. It is better to make good decisions than bad ones. Not everyone makes good decisions.

• 4. In decision making, people will summon from memory principles distilled from precept, experience, and analysis.

Principles

Guidance from analysis

• 1. more of a good outcome is better than less

• 2. less of a bad outcome is better than more

• 3. anything that can happen will happen (we interpret this to mean that outcomes are uncertain.)

Guidance from Learning

• 4. good decisions require variation of behavior (e.g. be creative)

• 5. good decisions require stereotypical behavior (e.g. be thorough, don’t play around)

• 6. all values are fungible

• 7. good decisions are made by good decision makers based on good intuitions

• 8. risk aversion is wise. “look before your leap.”

Guidance from experience

• 9. good decisions frequently, but not always, lead to good outcomes

• 10. bad decisions never lead to good outcomes (we interpret this to mean that poorly formulated problem statements, ad-hoc decision analyses, poor data are unlikely to produce relatively good outcomes even in favorable conditions.)

• 11. the merit of a good decision is continuous in its inputs

• 12. it is far better to be lucky than wise” (we interpret this to mean that the stochastic nature of future events may surprise the decision maker with a favorable outcome. We are certain Edwards is not suggesting that we depend on luck as the basis for decision making .)

Appendix 2.5 Results, Outcomes and Decision Quality

A decision implies a commitment to a specification with allocated resources. Outcomes are the results of the execution of such action. They are separated by time. A good decision is a good choice given the alternatives at the time when a commitment and resources are pledged. A good outcome is one which was intended. The chronological separation, between commitment and outcomes, permits uncertainty to intervene, aleatory unpredictable conditions that can generate an unintended outcome.

This example is due to Hazelrigg (1996). Consider a two round bet on a fair coin toss (Fig. 2.8). Bet $2.00. Get $5.00 if bet heads and get heads. Get $3.00 if call tails and get tails. After betting either heads or tails, the outcome is either head or tails. If betting heads, at the outset, and get heads, the best payoff is a net of $3.00. But if betting tails, the best case, is only a payoff of $1.00. As a bet, betting heads is better since it has a better payoff even though there is possibility of a loss of $2.00. A good decision can lead to a bad outcome. Similarly a bad decision, betting tails, can lead to the possibility of a $1.00 gain.

Fig. 2.8

A good decision and good outcomes are independent

Note: In retrospect, what could have been anticipated (in foresight) is consistently overestimated (Fischhoff 1975). This is a form of hindsight bias and overconfidence. Moreover, people justify how the decision process and the outcome could have been better using hypothetical “only if”, “could have”, and counterfactuals (Roese and Olson 1995). Especially in situations that “almost” happened (Kahneman and Varey 1990).