THE ART OF DECISION MAKING: EXPLORING THE DECISION THEORY

PICTURE CREDIT: PINTEREST

INTRODUCTION TO DECISION THEORY

Have you ever stood in a supermarket aisle for a proper ten minutes mulling over which cereal box to buy? Well, if you have, you know how intense those ten minutes can be. You have so many considerations to take in, and come to a final decision. This is an example of a small decision that we make in everyday life. There are numerous others we take that are of far greater consequence. Such a decision may take longer than ten minutes to make, not only because of its importance, but also because of the different things one will need to consider while making such a decision. This is where the Decision theory comes in.

The Decision Theory, otherwise known as the theory of choice, refers to the study of how an individual, who is generally referred to as an ‘agent’, makes choices. It explores how agents make choices under varying circumstances. While everyone on this planet is constantly making decisions, not the same number of people know the Decision Theory, textually. This theory is, therefore, more of a discovery than an academic invention, as everyone unknowingly uses the decision theory to go about making their everyday decisions.

The decision theory gets applied in a situation where norms are already established. This means that while a decision theorist may be able to advise an entrepreneur on how to grow her business, the question of whether it is necessary for the entrepreneur to grow the business at all does not come under the purview of the decision theory.

The theory comprises two branches: descriptive and normative theory. The distinction between normative and descriptive decision theories is, in principle, very simple. A normative decision theory is a theory about how decisions should be made, and a descriptive theory is a theory about how decisions are actually made.

In this project, we will be looking closely at this fascination theory, focusing mainly on the normative decision theory.

DECISION PROCESS

Most decisions are made over a period of time, or the rationing out takes place in phases. One of the earliest theories regarding the stages of decision-making was given by Conderset, the french philosopher and mathematician. He proposed the following stages:

1. “discusses the principles that will serve as the basis for decision in a general issue; one examines the various aspects of this issue and the consequences of different ways to make the decision.”

2. This is followed by the second discussion in which “the question is clarified, opinions approach and combine with each other to a small number of more general opinions.”

3. The third stage consists of the actual choice between these alternatives. (Condorcet, 1793)

While this is one of the earliest recorded distinctions made in the various stages of decision-making, Condorset’s theory does not feature in the modern decision theory. Instead, the starting-point of the modern discussion is generally taken to be John Dewey's exposition of the stages of problem-solving. According to Dewey, problem-solving consists of five consecutive stages:

1. a felt difficulty,

2. the definition of the character of that difficulty,

3. suggestion of possible solutions,

4. evaluation of the suggestion, and

5. further observation and experiment leading to acceptance or rejection of the suggestion.

Herbert Simon (1960) modified Dewey's list of five stages to make it suitable for the context of decisions in organisation According to Herbert Simon, who modified Dewey’s list of five stages to the context of decisions in organisations, decision-making consists of three principal phases: "finding occasions for making a decision; finding possible courses of action; and choosing among courses of action." The first of these phases he called intelligence, "borrowing the military meaning of intelligence", the second design, and the third choice.

Several economists have argued against the idea that the decision process consists of consecutive stages. Rather, it is argued that it is a lateral process. As Whitte (1972) had written

"We believe that human beings cannot gather information without in some way simultaneously developing alternatives. They cannot avoid evaluating these alternatives immediately, and in doing this they are forced to make a decision. This is a package of operations and the succession of these packages over time constitutes the total decision making process." (Whitte 1972, p. 180.)

One of the most influential models that satisfy the above criterion was proposed by Mintzberg, Raisinghani, and Théorêt (1976). In the view of these authors, the decision process consists of distinct phases, but these phases do not have a simple sequential relationship. They used the same three major phases as Simon, but gave them new names: identification, development and selection. The identification phase (Simon's "intelligence") consists of two routines. The first of these is decision recognition, in which "problems and opportunities" are identified, after which the second routine in this phase comes into play, which is diagnosis. The development phase (Simon's "design") serves to define and clarify the options. This phase, too, consists of two routines. The search routine aims at finding ready-made solutions, and the design routine at developing new solutions or modifying ready-made ones. The last phase, the selection phase (Simon's "choice") consists of three routines. The first of these, the screen routine, is only evoked "when search is expected to generate more ready-made alternatives than can be intensively evaluated" (p. 257). In the screen routine, alternatives that are below par are removed. The second routine, the evaluation-choice routine, is the actual choice between the alternatives. It may include the use of one or more of three "modes", namely judgement, bargaining and analysis. In the third and last routine, authorisation, the choice highest in the hierarchy is approved.

The relation between these phases and routines is circular rather than linear. Typically, if no solution is found to be acceptable, he will cycle back to the development phase.

RELATING AND VALUING

When making decisions, we try to obtain as good an outcome as possible, according to some standard of what is good or bad. The value standard set to choices while making decisions is usually subject to the agent’s moral philosophy.

Let us consider a common example in an attempt to see how this can be done: you have to choose between various cans of pasta sauce at the supermarket. It is likely that your value level is linked to price, taste, or some combination thereof. Suppose you like soup A better than soup B or soup C, soup B better than soup C and soup B better than soup C. You would then take soup A.

One way to express the value pattern is as a relation between the three soups, the relation "better than". We have:

A is better than B;

B is better than C;

A is better than C

Clearly, since A is better than all the other alternatives, A should be chosen.

Another way to express this value pattern is to assign integer values to each of the three alternatives. In this case , we can assign the value 15 to A, the value 13 to B and the value 7 to C. This is a numerical representation or representation of the value pattern in terms of numbers. Since A has a higher value than either B or C, A should be picked.

Relational representation of value is very normal in colloquial speech and is often used in discussions that plan for decision-making. To compare alternatives, we use phrases such as "better than," "worse than," "equally good," "at least as good," etc. These are all binary relationships, i.e. they relate two objects ('arguments') to each other. Betterness and worseness are not exactly symmetrical in ordinary usage. To claim that A is better than B is not quite the same as saying that B is worse than A.

For convenience, we sometimes use the logical notation "A > B" instead of the common-language expression "A is better than B." A > B is taken to represent "B is worse than A" and "A is better than B." Another significant comparative value concept is "equal value to" or "equal value." We may use the ≡ to denote it, hence A≡B indicates that A and B have the same value (according to the norm that we have chosen). Another word that is sometimes used in value comparisons is "at least as good as." We denote it "A≥B".

The three comparative terms "better than" (>), "equal in value to" (≡) and "at least as good as" (≥) are important components of the formal language of preference rationale. > is said to reflect preference or strong preference, ≥ weak preference, and (≡) indifference.

Preference relations are used in decision-making to find a suitable choice. For this purpose, the following simple principle can be used:

“an alternative is (uniquely) best if and only if it is better than all other alternatives. If there is a uniquely best choice, choose it.”

DECISION MAKING UNDER VARIOUS CONDITIONS

Under Uncertainty:-

The area of choice under uncertainty represents the heart of decision theory. Known from the 17th century, the idea is that, when faced with a number of choices, each of which could give rise to more than one possible outcome with different probabilities, the rational procedure is to identify all possible outcomes, determine their values and the probabilities that will result from each course of action, and multiply the two to give an "expected value", or the average expectation for an outcome; the action to be chosen should be the one that gives rise to the highest total expected value.

In 1738, Daniel Bernoulli published an influential paper entitled Exposition of a New Theory on the Measurement of Risk, in which he uses the St. Petersburg paradox to show that expected value theory must be normatively wrong. It is based on a particular (theoretical) lottery game that leads to a random variable with infinite expected value (i.e., infinite expected payoff) but nevertheless seems to be worth only a very small amount to the participants. The St. Petersburg paradox is a situation where a naive decision criterion which takes only the expected value into account predicts a course of action that presumably no actual person would be willing to take.In his solution, he defines a utility function and computes expected utility rather than expected financial value.

Expected utility could, more precisely, be called "probability-weighted utility theory". In expected utility theory, each alternative is assigned a weighted average of its utility values under different states of nature, and the probabilities of these states are used as weights.

This can also be stated in a more general fashion: Let there be n outcomes, to each of which is associated a utility and a probability. The outcomes are numbered, so that the first outcome has utility u1 and probability p1, the second has utility u2 and probability p2, etc. Then the expected utility is defined as follows:

p1⋅u1 + p2⋅u2 + ... + pn⋅un

Several decision criteria have been proposed for decision-making under uncertainty.

1. Maximin expected utility: According to the maximin EU rule, we should choose the alternative such that its lowest possible expected utility is as high as possible (maximise the minimal expected utility). For each alternative, a set of expected values can be calculated that corresponds to the set of potential probability distributions derived for the binary measure. The lowest level of utility given to an alternative by any of the possible distributions of probability is called the "minimal expected utility" of that choice. The alternative with the largest minimum estimated utility should be selected.

2. Reliability-weighted expected utility: Under reliability-weighted probability weighted average can be used to calculate a definite expected value for each alternative. Reliability-weighted expected utility was used by Howard (1988) in an analysis of the safety of nuclear reactors. However, it is possible that a lot of people would consider this to be an unduly optimistic decision rule. Several of the most discussed decision criteria for uncertainty can be seen as attempts at compromises between the pessimism of maximin expected utility and the optimism of reliability-weighted expected utility.

Under Ignorance:-

By decision-making under ignorance is commonly meant decision-making when it is known what the possible states of affairs are, but no information about their probabilities is available.

To better understand this concept, let us make use of an example. You have won a radio contest, the price of which is a one-week vacation in a secret location. You do not have the slightest idea where this secret location is. Therefore, you do not know if you will need to carry an umbrella or not, i.e, the probability of rain is anywhere between 0 and 1. The following will be the decision matrix for the example:

It RainsIt doesn’t rainUmbrella carriedDry clothes; Heavy suitcaseDry Clothes; Heavy suitcaseUmbrella not carriedWet clothes; light suitcaseDry clothes; light suitcase

Now, let us try and attach preferences to each of these situations:

Dry clothes; light suitcase > Dry clothes; heavy suitcase > wet clothes; light suitcase

In such a case, the following maximin rule is applied:

“For each alternative, we define its security level as the worst possible outcome with that alternative.”

Therefore, according to the maximin rule above, we prioritise security, and go for the ‘dry clothes; heavy suitcase’, as the ‘dry clothes, light suitcase’ option is risky, and the ‘wet clothes; light suitcase’ option is least suitable. The maximin rule was first proposed by John von Neumann, the renowned Hungarian mathematician.

There are two kinds of decision making under ignorance. In decision-making under unknown non-zero probabilities, we know what the possible outcomes are of the various options, but all we know about their probabilities is that they are non-zero. A still higher level of uncertainty is that which results from ignorance of what the possible consequences are, i.e., decision-making under unknown possibilities. This is the case when there is some consequence for which we do not know whether its probability, given some option, is zero or non-zero.

Unknown possibilities are impossible to predict. It ranges from trying to predict natural phenomena, to trying to understand the consequence of human action. A historical example is the dilemma faced by those who made the atomic bomb. While few argue that the scientists were well aware that it would lead to casualties, one could argue that any invention in the wrong hands can be catastrophic. The other unpredictable aspect of creation of the atomic bombs used in Hiroshima and Nagasaki is that while the scientists knew that it was a potent weapon, nobody really knew what its actual effects were. In a sense, any decision may have a catastrophic consequence. That is why, while the above discussed maximin, among other tactics, are used to make decisions under such difficult circumstances, no strategy can completely mitigate the possibility of an unpleasant consequence.

CONCLUSION

We make millions of decisions in our lifetimes, as we go from making decisions of very little consequence as little children, to decisions with more seriousness as we age, when we are responsible to make decisions that could affect your loved ones and any others in your life. With each and every one of these decisions, there is a certain level of uncertainty looming around its expected outcome, so we try and find ourselves taking decisions that will mitigate the risk element of our decision. Even when we decide to be reckless, it comes from a certain expected level of happiness we are sure to derive from it, only to become aware of a possible negative long-term outcome, however big or small.

If we were to stop for a minute and analyse how we are making decisions, we would find a lot of aspects that are concurrent with the theory we have discussed. The importance of this theory is that it exists for us to observe around us. And while it may exist in our thought process without our conscious knowledge of it, a greater deal of understanding of the complexity of every decision making process will render us far more proficient with decision making. The ten minutes spent in the supermarket aisle for cereal can be considerably cut down. However, it will allow us to be better risk takers. Understanding the theory gives us the tools to be adventurous enough to be conscious risk takers, rather than being reckless in the name of being adventurous.

There is an art to making decisions.

BIBLIOGRAPHY

1. Steele, Katie and H. Orri Stefánsson, "Decision Theory", The Stanford Encyclopedia of Philosophy (Winter 2020 Edition), Edward N. Zalta (ed.),

2. Decision Theory: A Brief Introduction, by Sven Ove Hansson.

3. Wikipedia ( St. Petersburg Paradox; decision theory)