summary book (decision analysis for management judgment)

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MM 5010 Strategic Decision Making & Negotiation MBA - ITB

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CHAPTER 6 (SIX)

Decision trees and influence diagrams can be extremely useful in helping people to gain

an understanding of the structure of the problems which confront them.Decision problems are

multi-stage in character when the choice of a given option may result in circumstances which

will require yet another decision to be made.

Decision trees can serve a number of purposes when complex multi-stage problems are

encountered. They can help a decision maker to develop a clear view of the structure of a

problem and make it easier to determine the possible scenarios which can result if a particular

course of action is chosen. This can lead to creative thinking and the generation of options which

were not previously being considered.Decision trees can also help a decision maker to judge the nature of the information

which needs to be gathered in order to tackle a problem and, because they are generally easy to

understand, they can be an excellent medium for communicating one persons perception of a

problem to other individuals.

Influence diagrams offer an alternative way of structuring a complex decision problem

and some analysts find that people relate to them much more easily.Influence diagrams can be

converted to decision trees and we will therefore regard them in this chapter as a method for

eliciting decision trees.

Constructing a decision tree

A square is used to represent a decision node and,because each branch emanating from

this node presents an option, the decision maker can choose which branch to follow. A circle, on

the other hand, is used to represent a chance node. The branches emanating from a circle are

therefore labeled with probabilities which represent the decision makers estimate of the

probability that a particular branch will be followed.


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Determining the optimal policy

It can be seen that our decision tree consists of a set of policies. A policy is a plan of

action stating which option is to be chosen at each decision node that might be reached under

that policy.The technique for determining the optimal policy in a decision tree is known as the

rollback method. To apply this method, we analyze the tree from right to left by considering the

later decisions first.It can be seen that the rollback method allows a complex decision problem to

be analyzed as a series of smaller decision problems.

Decision trees involving continuous probability distributions

The method is based on earlier work by Pearson and Tukey and requires three estimates

to be made by the decision maker:

(i) The value in the distribution which has a 95% chance of being exceeded. This value is

allocated a probability of 0.185.

(ii) The value in the distribution which has a 50% chance of being exceeded. This value is

allocated a probability of 0.63.

(iii) The value in the distribution which has only a 5% chance of being exceeded. This value is

also allocated a probability of 0.185.

Nevertheless, in general, there are clear advantages in using this approximation. Above

all, it is simple and each distribution requires only three estimates to be made which has the

obvious effect ofreducing the decision makers judgmental task.

Assessment of decision structure

It is really a matter of the decision analysts judgment as to whether the elicited tree is a

fair representation of the decision makers decision problem. Once a structure is agreed then the

computation of expected utility is fairly straightforward. The figure below presents a description


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of the typical phases in a decision analysis of a problem that the decision maker wishes to

resolve with help of the practitioner of decision analysisthe decision analyst.

Eliciting decision tree representations

What methods have been developed to help elicit decision tree representations from

decision makers? One major method, much favored by some decision analysts, is that of

influence diagrams which are designed to summarize the dependencies that are seen to exist

among events and acts within a decision.


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In addition, influence diagrams are more easily revised and altered as the decision maker

iterates with the decision analyst. Decision trees, because of their strict temporal ordering of acts

and events, need completely respecifying when additional acts and events are inserted into

preliminary representations.

One step-by-step procedure for turning an influence diagram into a decision tree is as

follows:

(1)Identify a node with no arrows pointing into it (since there can be no loops at least onenode will be such).

(2)If there is a choice between a decision node and an event node, choose the decision node.(3)Place the node at the beginning of the tree and remove the node from the influence

diagram.

(4)For the now-reduced diagram, choose another node with no arrows pointing into it. Ifthere is a choice a decision node should be chosen.

(5)Place this node next in the tree and remove it from the influence diagram.(6)Repeat the above procedure until all the nodes have been removed from the influence

diagram.

Finally, we analyzed the process of generating decision tree representation of decision

problems and advocated the influence diagram as a key technique to facilitate decision

structuring.


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CHAPTER 8 (EIGHT)

Bayes theorem

Bayes theorem will be used as a normative tool, telling us how we should revise our

probability assessments when new information becomes available. In Bayes theorem an initial

probability estimate is known as a prior probability.

The steps in the process are summarized below:

(1)Construct a tree with branches representing all the possible events which can occur andwrite the prior probabilities for these events on the branches.

(2)Extend the tree by attaching to each branch a new branch which represents the newinformation which you have obtained. On each branch write the conditional probability

of obtaining this information given the circumstance represented by the preceding branch.

(3)Obtain the joint probabilities by multiplying each prior probability by the conditionalprobability which follows it on the tree.

(4)Sum the joint probabilities.(5)Divide the appropriate joint probability by the sum of the joint probabilities to obtain

the required posterior probability.

The effect of new information on the revision of probability judgments

It is interesting to explore the relative influence which prior probabilities and new

information have on the resulting posterior probabilities.At the extreme, if your prior probability

of an event occurring is zero then the posterior probability will also be zero. Whatever new

information you receive, no matter how reliable it is, you will still refuse to accept that the event

is possible. In general, assigning prior probabilities of zero or one is unwise.

Ironically, if the new information has less than a 0.5 chance of being reliable its result is

of interest and the more unreliable it is, the greater the effect it will have on the prior probability.


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Applying Bayes theorem to a decision problem

This simply involves the use of the posterior probabilities, rather than the prior

probabilities, in the decision model.

Assessing the value of new information

New information can remove or reduce the uncertainty involved in a decision and thereby

increase the expected payoff. However, in many circumstances it may be expensive to obtain

information since it might involve, for example, the use of scientific tests, the engagement of the

services of a consultant or the need to carry out a market research survey.

The expected value of perfect information

In many decision situations it is not possible to obtain perfectly reliable information, but

nevertheless the concept of the expected value of perfect information (EVPI) can still be useful.

We emphasize that our calculations are based on the assumption that the decision maker is risk

neutral. If the manager is risk averse or risk seeking or if he also has non-monetary objectives

then it may be worth him paying more or less than this amount.

The expected value of imperfect information

As with the expected value of perfect information, we will need to consider the possible

indications the test will give, what the probabilities of these indications are and the decision the

manager should take in the light of a given indication.

A summary of the main stages is given below:

(1)Determine the course of action which would be chosen using only the prior probabilitiesand record the expected payoff of this course of action;

(2)Identify the possible indications which the new information can give;


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(3)For each indication:(a)Determine the probability that this indication will occur;(b)Use Bayes theorem to revise the probabilities in the light of this indication;(c)Determine the best course of action in the light of this indication (i.e. using the

posterior probabilities) and the expected payoff of this course of action;

(4)Multiply the probability of each indication occurring by the expected payoff of the courseof action which should be taken if that indication occurs and sum the resulting products.

This will give the expected payoff with imperfect information;

(5)The expected value of the imperfect information is equal to the expected payoff withimperfect information (derived in stage 4) less the expected payoff of the course of action

which would be selected using the prior probabilities

There is an alternative way of looking at the value of information. New information can be

regarded as being of no value if you would still make the same decision regardless of what the

information told you.

Practical considerations

Clearly, it is easier to identify the expected value of perfect as opposed to imperfect

information, and we recommend that, in general, calculating the EVPI should be the first step in

any information-evaluation exercise. The EVPI can act as a useful screen, since some sources of

information may prove to be too expensive, even if they were to offer perfectly reliable data,

which is unlikely.

In most cases, however, the assessment of the reliability of the information will

ultimately be based on the decision makers subjective judgment. The inputs required by the

decision maker are: (1) the maximum loss which will need to be incurred before the product isremoved from the market, (2) the probability of incurring this loss if the product is introduced,

(3) the probability that the product will be successful, if introduced and (4) the probability that

the market research will accurately predict the true state of the market.


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In decision analysis models, illusory correlation is of concern when conditional

probabilities.

The representativeness heuristic

If you use the representativeness heuristic you will answer questions by judging how

representative the object, person or event is of the category or process.

Biases associated with the representativeness heuristic

1. Ignoring base-rate frequencies2. Expecting sequences of events to appear random3. Expecting chance to be self-correcting4. Ignoring regression to the mean5. The conjunction fallacy

The anchoring and adjustment heuristic

Judgment is widely used to make estimates of values such as how long a job will take to

complete or what next months sales level will be. Often these estimates start with an initial

value which is then adjusted to obtain the final estimate. Typical initial values might be how long

the last job took to complete or this months level of sales. Unfortunately, the adjustment from

these initial values is often insufficient; a phenomenon known as anchoring.

Biases associated with anchoring and adjustment

1. Insufficient adjustmentIn decision making, anchoring can be a problem in the estimation of costs, payoffs and

probabilities. Forecasts that are used in the decision process may be biased by forecasters

anchoring on the current value and making insufficient adjustment for the effect of future

conditions.

2. Overestimating the probability of conjunctive events


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inexperienced decision makers carrying out artificial tasks in psychological laboratories, rather

than real-world decision makers making real decisions.

1. Subjects in studies may be unrepresentative of real decision makers2. Laboratory tasks may be untypical of real-world problems3. Tasks may be misunderstood by subjects4. Subjects may be poorly motivated5. Citation bias6. Real world studies suggest better performance7. People think in terms of frequencies not probabilities

A methodology for choosing how to develop a subjective probability assessment

summary book (decision analysis for management judgment)

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