This document discusses different approaches to decision making under uncertainty, including maximin, expected monetary value, and multi-attribute utility analysis. It explains that maximin is inherently pessimistic by only considering the worst possible outcome for each option. Expected monetary value focuses only on monetary attributes and assumes a linear value function for money. Multi-attribute utility analysis derives single-attribute utility functions and combines them to evaluate options based on multiple attributes like time, cost, and risk preferences. It can incorporate non-monetary attributes if preferences conform to specific axioms.

1. Decision Making Christian Hamonangan – 29113025-YP49B
The simplest method involves the use of words such as unlikely, almost impossible,
probable, doubtful and expected. It has been found that different people attach very different
meanings to these expressions, and even individuals are not consistent over time in their use of
them. Numbers offer a much more precise way of measuring uncertainty, and most people will
be familiar with the use of odds. While many decision makers may be happy to use expressions
such as 100 to 1 against or evens, odds do have the disadvantage that they are awkward to handle
arithmetically when, for example, we want to determine the chances that a number of different
outcomes will occur.
Probability are measured on a scale which runs from 0 to 1, then if probability of an
outcome occurring is zero then this implies that the outcome is impossible. At the opposite
extreme, it considered that an outcome is certain to occur then this will be represented by a
probability of 1 and the greater the chances of the event occurring, the closer its probability will
be to 1.
The list from the probability itself is shown below:
 Both products fail.
 Product A succeeds but B fails.
 Product A fail but B succeeds.
 Both products succeed.
Each of the four possible things that can happen is called an outcome. An event consists
of one or more possible outcomes. For example, the event ‘just one product succeeds’ consists of
the two outcomes: ‘A succeeds but B fails’ and ‘A fails but B succeeds’. The event ‘at least one
product succeeds’ consists of the last three outcomes in the list. However, the event ‘both
products fail’ clearly consists of only one outcome.
There are three different approaches to deriving probabilities: the classical approach, the
relative frequency approach and the subjective approach. The first two methods lead to what are
often referred to as objective probabilities because, if they have access to the same information,
different people using either of these approaches should arrive at exactly the same probabilities.
In contrast, if the subjective approach is adopted it is likely that people will differ in the

2. Decision Making Christian Hamonangan – 29113025-YP49B
probabilities which they put forward. The classical approach to probability involves the
application of the following formula:
The probability of an event occurring
= Number of outcomes which represent the occurrence of the event
Total number of possible outcomes
In the relative frequency approach the probability of an event occurring is regarded as the
proportion of times that the event occurs in the long run if stable conditions apply. This
probability can be estimated by repeating an experiment a large number of times or by gathering
relevant data and determining the frequency with which the event of interest has occurred in the
past.
The subjective approach contained the situation that uniqueness, the past data required by
the relative frequency approach will not be available. When looked at the three approaches, then
it needed to consider the concepts and rules which are used in probability calculations. These
calculations apply equally well to classical, relative frequency or subjective probabilities. Two
events, A and B, are said to be independent if the probability of event A occurring is unaffected
by the occurrence or non-occurrence of event B:
(AB) = (A)
The fact that B has occurred does not change the probability of A occurring. In other
words, the conditional probability is the same as the marginal probability. One device which can
prove to be particularly useful when awkward problems need to be solved is the probabilit y tree.
If use the subjective probabilities to express degree of belief that events will occur then the
thinking must conform to the axioms of probability theory. These axioms have been implied by
the preceding discussion, but formally state them below.
 Axiom 1: Positiveness. The probability of an event occurring must be non-negative.
 Axiom 2: Certainty. The probability of an event which is certain to occur is 1. Thus
axioms 1 and 2 imply that the probability of an event occurring must be at least zero and
no greater than 1.
 Axiom 3: Unions. If events A and B are mutually exclusive then:
p(A or B) = p(A) + p(B)
It can be shown that all the laws of probability that have considered in this chapter can be
derived from these three axioms. Note that they are generally referred to as Kolmogoroff’s

3. Decision Making Christian Hamonangan – 29113025-YP49B
axioms and, as stated above, they relate to situations where the number of possible outcomes is
finite.
In many decisions the consequences of the alternative courses of action cannot be
predicted with certainty. A company which is considering the launch of a new product will be
uncertain about how successful the product will be, while an investor in the stock market will
generally be unsure about the returns which will be generated if a particular investment is chosen.
First outline a method which assumes that the decision maker is unable, or unwilling, to
estimate probabilities for the outcomes of the decision and which, in consequence, makes
extremely pessimistic assumptions about these outcomes. Then, assuming that probabilities can
be assessed, we will consider an approach based on the expected value concept. Because an
expected value can be regarded as an average outcome if a process is repeated a large number of
times, this approach is arguably most relevant to situations where a decision is made repeatedly
over a long period. A daily decision by a retailer on how many items available for sale might be
an example of this sort of decision problems.
According to the maximin criterion the manufacturer should first identify the worst
possible outcome for each course of action and then choose the alternative yielding the best of
these worst outcomes. If the outcomes had been expressed in terms of costs, rather than profits,
we would have listed the highest possible costs of each option and selected the option for which
the highest possible costs were lowest. Because we would have been selecting the option with
the minimum of the maximum possible costs our decision criterion would have been referred to
as minimax.
The main problem with the maximin criterion is its inherent pessimism. Each option is
assessed only on its worst possible outcome so that all other possible outcomes are ignored. The
implicit assumption is that the worst is bound to happen while, in reality, the chances of this
outcome occurring may be extremely small. If the manufacturers are able, and willing, to
estimate probabilities for the two possible levels of demand, then it may be appropriate for him
to choose the alternative which will lead to the highest expected daily profit. If he makes the
decision on this basis then he is said to be using the expected monetary value or EMV criterion.
The EMV criterion may have been appropriate for the food manufacturer because he was
only concerned with monetary rewards, and his decision was repeated a large number of times so

4. Decision Making Christian Hamonangan – 29113025-YP49B
that a long-run average result would have been of relevance to him. Let us now consider a
different decision problem.
Imagine that you own a high-technology company which has been given the task of
developing a new component for a large engineering corporation. Two alternative, but untried,
designs are being considered, and because of time and resource constraints only one design can
be developed.
It should also be noted that the EMV criterion assumes that the decision maker has a
linear value function for money. A further limitation of the EMV criterion is that it focuses on
only one attribute: money. In choosing the design in the problem we considered above we may
also wish to consider attributes such as the effect on company image of successfully developing
a sophisticated new design, the spin-offs of enhanced skills and knowledge resulting from the
development and the time it would take to develop the designs. All these attributes, like the
monetary returns, would probably have some risk associated with them.
Utility functions having this concave shape provide evidence of risk aversion (which is
consistent with the business woman’s avoidance of the riskiest option). Utility functions can be
derived for attributes other than money. This relates to a drug company which is hoping to
develop a new product. It is also possible to derive utility functions for attributes which are not
easily measured in numerical terms.
This will be true if the decision maker’s preferences conform to the following axioms:
 Axiom 1: The complete ordering axiom
 Axiom 2: The transitivity axiom
 Axiom 3: The continuity axiom
 Axiom 4: The substitution axiom
 Axiom 5: Unequal probability axiom
 Axiom 6: Compound lottery axiom

5. Decision Making Christian Hamonangan – 29113025-YP49B
The summarized here arguments both for and against the application of utility and then
present our own views at the end of the section. Assuming that mutual utility independence does
exist, now it’s derived the multi-attribute utility function as follows.
 Stage 1: Derive single-attribute utility functions for overrun time and project cost.
 Stage 2: Combine the single-attribute functions to obtain a multi-attribute utility function
so that we can compare the alternative courses of action in terms of their performance
over both attributes.
 Stage 3: Perform consistency checks, to see if the multi-attribute utility function really
does represent the decision maker’s preferences, and sensitivity analysis to examine the
effect of changes in the figures supplied by the decision maker.