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7/29/2019 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