Module 2: Theories Of Decision-making

Slides

Normative decision theory

Decision theory is about the procedures for making optimal decisions in the face of uncertainty. The basic situation describes a decision maker who must choose from a finite set of two or more possible future events. The list of possible states of nature includes everything that can happen, and are defined so that only one of them will occur. The outcome resulting from the combination of a chosen alternative and a particular state of nature is referred to as the payoff.

Since the occurrence of the states of nature may be uncertain, probabilistic criteria are often used to choose the best alternative, for instance by computing the expected value of each alternative, expressed as the sum of weighted payoffs. (The weight for a payoff is the probability of the associated state of nature and therefore the probability that the payoff occurs.) For a maximization problem, the alternative with the largest expected value will be chosen; for a minimization problem, the alternative with the smallest expected value will be chosen

Rationality

Behaviour is considered rational if it satisfies two conditions. The first is that behaviour (or choices) is consistent. The second is that the behaviour serves to fulfil certain aims.

The criterion of consistency can either be weak or strong. The weak criterion means that if the same circumstances occur, then the same actions will be taken or the same choices made. The weakness is due to the imprecision of the term “same”, i.e., it denotes a homomorphism rather than an isomorphism. The strong criterion involves the notion of transitivity, and can therefore be defined in terms of the assumptions about rational economic man, i.e., the ability to impose a weak ordering and that this ordering is transitive.

That the behaviour serves to fulfil certain aims is essentially the same as saying that there must be a preference among alternatives, hence in some ways similar to the second of the above. One position is that the choice of an alternative implies rationality, i.e., the fact that something was chosen means that it was preferred. This does not leave room for deviations in achieving the outcome, but assumes a flawless execution (no pun intended).

A central concept in normative decision theory is the ideal of the rational economic (hu)man - homo economicus.

Homo Economicus

Classical (normative) decision theory, and specifically the part of decision theory that has to do with economic behaviour, often refers to an ideal decision maker know as homo economicus or the rational economic (hu)man.

The origins of homo economicus can be traced far back, at least to Jeremy Bentham (1738 – 1832), but probably even further. It may be argued that the early attempts to calculate probabilities for games reflect the assumptions of homo economicus. A game is a situation where the players have to make decisions about the future outcomes, e.g., whether or not to accept a bet. In order to do so it is necessary to know all the alternatives, all the possible outcomes, and the value of each outcome. For games the value is relatively easy to determine, since it can be equated with the economic value of the win (or loss).

It is commonly acknowledged that probability theory began in 1654 and involved Antoine Combauld Chevalier de Méré and Blaise Pascal - and later Pierre de Fermat. The issue was whether or not to accept a bet for a specific outcome in a game of dice, i.e., whether one outcome was more likely than another. (The concrete problem involved the probability of hitting a double six within 24 throws of two dice. For n=24, p=0.4913 while for n=25, p=0.5054.)

The following are the main assumptions made for homo economicus:

• The rational decision-maker is completely informed. This means that he/she knows what all the possible alternatives are, and also knows what the outcome of any action will be. This implies that the decision-maker’s beliefs are based on logical, objective analysis of all the available evidence.

• The rational decision-maker is infinitely sensitive. It is a requirement that the characterisation of the alternatives is infinitely divisible. (This is in order to make the functions continuous and differentiable, although this is not an absolutely necessary requirement.) The decision-maker must obviously be able to perceive differences among alternatives and discriminate among them, hence must be – in principle – infinitely sensitive.

• The decision-maker is rational. This requirement has two parts. The first is that the decision-maker must be able to put the alternatives into a weak ordering, the second is that choices are made so as to maximise something.

The ability to put alternatives into a weak ordering has two parts. The first part is that given two alternative A and B, then the decision-maker must be able to state whether he/she prefers A to B, B to A, or is indifferent between them. This means that the decision-maker must be able to state his/her preferences. The second part is that all preferences must be transitive, i.e., that the decision maker must be consistent in his/her choices. This means that if A is preferred to B, and B to C, then A must also be preferred to C.

Choices should be made to maximise something. This is a peculiar criterion, since it is always possible to claim post hoc that something was maximised. I.e., the fact that a choice was made is perforce a definition that one alternative was considered superior to all the others, hence that something was maximised. The principle of maximisation is, however, applied in a stronger sense, namely that the decision-maker must use a recognisable criterion to choose among the alternatives. If that is not the case, then it becomes impossible to predict decisions – and this is after all what decision theory very much is about.

Decision theory has tried several suggestions for what should be maximised. Examples are utility or “general happiness” (John Stuart Mill), subjective expected utility, risk avoidance loss aversion, safety, pleasure, etc.

Hidden Assumptions

The description of the rational economic decision-maker implies a number of hidden, but important assumptions.

• A requirement to transitivity is that the dimensions of description do not change between alternatives. In the case where A is preferred to B on account of value X, and B is preferred to C on account of value Y, it is impossible to conclude that A also will be preferred to C.

• The overall description of the decision-maker also implies that he/she works alone, and only need to consider his/her own preferences and needs.

• A very important assumption is that the environment is stable during the time it takes to make the decision. Formally this means that the alternatives continue to exist, and that their value does not change. The latter requires that the external conditions are the same (i.e., that an alternative does not change state), and also that the decision-maker is internally consistent, i.e., will evaluate an alternative in exactly the same way at any stage of making the decision. The evaluation of an alternative must be independent of the order in which alternatives are evaluated!

Literature:

Edwards, W., "The theory of decision making." Psychological Bulletin, vol. 51 (1954), pp. 380-417

For special interest, see also L. J. Savage (1954) The Foundations of Statistics. 1972 edition, New York: Dover (Chapter 4)

Descriptive decision theory

Despite the noble ambitions of normative decision theory, people usually behave quite differently. The ideal of the homo economicus is far removed from actual human behaviour. Whereas normative decision theory describes how people ought to make decisions, descriptive decision theory tries to account for how people actually make decisions. There are many varieties of descriptive decision theory, ranging from an account of the heuristics that people use to Naturalistic Decision Making.

An excellent account of the heuristics that people apply in judgment and decision making is given by the two people who were pioneers in this research: 

Tversky, A. & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185, 1124-1131.

(A more complete treatment can be found in the book by the same name: Kahneman, D., Slovic, P. & Tversky, A. (Eds.), (1982). Judgment under uncertainty: Heuristics and biases. New York: Cambridge University Press.)

An important example of a descriptive decision theory is Elimination-by-aspects (EBA), proposed and developed by Amos Tversky. The principle of EBA is that the decision maker has several criteria to consider when making decisions. It is assumed that criteria are or can be ordered in terms of importance, that each criterion has a threshold below which an alternative is rejected, and that criteria are looked at sequentially based on order of importance. The decision process according to EBA ends when only one choice is left or the choices are so limited that an exhaustive consideration of all criteria can be accomplished.

See: Tversky, A. (1972). Elimination by aspects: A theory of choice. Psychology Review, 79, 281-290.

Descriptive decision theory also distinguishes between sequential and dynamic decision making. Sequential decision tasks are concerned with the sequential search for information needed to make decisions (choices).  Dynamic decision tasks are primarily concerned with controlling dynamic systems over time. Dynamic decision making is defined by three common features: (1) a series of actions must be taken over time to achieve some overall goal; (2) the actions are interdependent so that later decisions depend on earlier actions; and (3) the environment changes both spontaneously and as a consequence of earlier actions.

See: Brehmer, B & Allard, R. (1991) Real-time dynamic decision making. Effects task complexity and feedback delays. In J. Rasmussen, B. Brehmer & J. Leplat (eds.), Distributed decision making: Cognitive models for cooperative work. Chichester: Wiley.

Other types of descriptive decision theories/models will be described in Module 3.

Naturalistic Decision Making (NDM)

Naturalistic Decision Making emerged in the late 1980s as a common interest among researchers who for one reason or the other had found traditional decision paradigms too constrained. NDM is loosely defined as "the way people use their experience to make decisions in field settings". The appearance coincided, more or less, with the change to study "situated cognition", i.e., the study of "cognition in the world" rather than "cognition in the mind". (Note, however, that this was mainly a change in the North American view. European researchers had followed a different tradition, and therefore did not experience a similarly strong need for a change.) As we shall see in Module 3, NDM in many ways resemble Simon's proposal for "satisficing" and Lindblom's descriptive decision principles know as "muddling through".

NDM is strongly represented by Gary Klein and his group, see for instance Zsambok, C. E. & Klein, G. (Ed.) (1997). Naturalistic decision making. Lawrence Erlbaum Associates.