Transcript Slajd 1 - Supernat

Decision-making
Techniques
dr. hab. Jerzy Supernat
Institute of Administrative Studies
University of Wrocław
Decision-making Techniques
Elements of decision problem

The decision body.

The decision options (courses of action).

The uncontrollable factors.

The consequences.
dr. hab. Jerzy Supernat
Decision-making Techniques
The decision body

single decision maker

multi decision-maker decision body
There are very few decisions which can be reached by a
single decision maker with total disregard for others’ views.
Even when the formal procedures of an organizations dictate
that an individual has the responsibility for making the
decision, the views of interested parties will usually need to
be sought and the tacit agreement or acquiescence of other
individuals and groups obtained. Clearly the implication is
that all members of the decision body do not have the same
degree of influence on a decision.
dr. hab. Jerzy Supernat
Decision-making Techniques
Where collective decisions over matters of common concern
have to be taken, the collegium system is traditionally adopted.
The system requires that the individual's judgments should be
pooled in such a way as to make sure that:

the group always bears in mind its (agreed) objectives

every member of the group participates
all relevant information is made available to every member of
the group


a majority vote determines the ultimate choice
The approach is designed to ensure that factors other than those contained
within the immediate decision situation do not impinge on the choice process.
It is not, however, uncommon for historical residues to produce coalitions or
antagonisms within decision bodies, leading to choices being made other than
on the strict merits of the case.
dr. hab. Jerzy Supernat
Decision-making Techniques
Groupthink
Groupthink occurs when a group makes faulty
decisions because group pressures lead to a
deterioration of „mental efficiency, reality testing,
and moral judgment” (Irving L. Janis)
dr. hab. Jerzy Supernat
Decision-making Techniques
Symptoms of groupthink according to Irving L. Janis:








Illusion of invulnerability – Creates excessive optimism that encourages
taking extreme risks.
Collective rationalization – Members discount warnings and do not
reconsider their assumptions.
Belief in inherent morality – Members believe in the rightness of their
cause and therefore ignore the ethical or moral consequences of their
decisions.
Stereotyped views of out-groups – Negative views of ‘enemy’ make
effective responses to conflict seem unneces-sary.
Direct pressure on dissenters – Members are under pressure not to
express arguments against any of the group’s views.
Self-censorship – Doubts and deviations from the perceived group
consensus are not expressed.
Illusion of unanimity – The majority view and judg-ments are assumed to
be unanimous.
Self-appointed ‘mindguards’ – Members protect the group and the leader
from information that is problematic or contradictory to the group’s
cohesiveness, view, and/or decisions.
dr. hab. Jerzy Supernat
Decision-making Techniques
The decision options
Decision options are the alternative courses of action between
which the decision body must choose. Options lie at the heart of
decision-making because, unless there is more than one way to
proceed, then there is no choice to be made and therefore no
decision.
The number of options in a decisional problem can be anything
between two and infinity (one type of decision where the
options are always infinite is the case where the decision
variable is continuous).
dr. hab. Jerzy Supernat
Decision-making Techniques
Where to elect there is but one, ‘tis Hobson's choice:
take that or none.
Thomas Ward (1652-1708)
dr. hab. Jerzy Supernat
Decision-making Techniques
The Hobson behind Hobson's Choice lived in Cambridge, England during the late 16th and early 17th centuries. Licensed to carry passengers, parcels, and mail
between Cambridge and London, Thomas Hobson kept a
stable of about forty high quality horses. As a sideline, he
also rented out his horses to university students.
After students began requesting particular horses again
and again, the liveryman realized certain horses were
being overworked. That inspired Hobson to come up with
a new system of rotating the horses for hire. Hobson gave
customers looking for horses the choice of taking the one
nearest the stable door or taking none at all.
dr. hab. Jerzy Supernat
Decision-making Techniques
The other major characteristic of decision options concerns how
discernible they are at the start of the decision process. Some decision
problems have options which are obvious when the problem is defined.
In other decision problems, the precise nature of the options is not
immediately apparent. In fact, the options within a decision problem
can turn out to be a mixture taken from a continuum which goes
between totally defined at the beginning of the decision process and
completely novel and developed specifically for the decision in
question. Henry Mintzberg classifies decision options by whether they
are:
•
given – fully developed at the start of the decision process
found ready made – fully developed in the environment of the
decision and discovered during the decision process
•
•
modified – ready-made options with some customized features
•
custom made – developed especially for the decision in question
dr. hab. Jerzy Supernat
Decision-making Techniques
The uncontrollable factors
Uncontrollable factors are those parts of the decision problem
which, although having an influence on the final outcome,
cannot be controlled directly by the decision body. They may be
treated as alternative states of nature (or scenarios), i.e. states
which the environment takes after, and independent of, the
decision itself.
When there is only one uncontrollable factor, the total possible
states of nature will correspond to all states which that particular
uncontrollable factor can take.
When more than one uncontrollable factor is involved there
could be a state of nature corresponding to every possible
combination of the levels which the uncontrollable factors can
take.
dr. hab. Jerzy Supernat
Decision-making Techniques
When considering the uncontrollable factors within a
decision problem, it is useful to take the three following
steps:
identify the factors which will influence the final
consequence of a decision

identify the states or levels which each uncontrollable
factor could take

attempt to predict the likelihood of these states or levels
occurring for each of the uncontrollable factors

dr. hab. Jerzy Supernat
Decision-making Techniques
The consequences
For each combination of a course of action and the state of
nature, there will be a consequence.
Thus, if we have N alternative courses of action and M
mutually exclusive states of nature there will be N x M
possible consequences. Figure in the next slide illustrates
this as a matrix in which the two dimensions are the
courses of action and the alternative states of nature.
dr. hab. Jerzy Supernat
Decision-making Techniques
Decision matrix
p1
p2
...
pj
...
pm
F1
F2
...
Fj
...
Fm
D1
C11
C12
...
C1j
...
C1m
D2
C21
C22
...
C2j
...
C2m
...
...
...
...
...
...
...
Di
Ci1
Ci2
...
Cij
...
Cim
...
...
...
...
...
...
...
Dn
Cn1
Cn2
...
Cnj
...
Cnm
Probability
F
D
dr. hab. Jerzy Supernat
Decision-making Techniques
The decision rules (techniques)
1. The pessimistic decision rule.
2. The optimistic decision rule.
3. The regret decision rule.
4. The expected value decision rule.
5. The expected utility decision rule.
dr. hab. Jerzy Supernat
Decision-making Techniques
The pessimistic decision rule
In this case each course of action should be analyzed, and
the worst possible outcome for that course of action should
be identified. Next the decision-maker should select the
course of action providing the best of the worst possible
outcomes.
dr. hab. Jerzy Supernat
Decision-making Techniques
The pessimistic decision rule
F
The worst
outcome
F1
F2
F3
F4
F5
D1
80
80
80
80
80
80
D2
-20
160
160
160
160
-20
D3
-120
60
240
240
240
-120
D4
-220
- 40
140
320
320
-220
D5
-320
-140
40
220
400
-320
D
The best of
the worst
outcomes
80
dr. hab. Jerzy Supernat
Decision-making Techniques
The optimistic decision rule
In this case each course of action should be considered,
and the best possible outcome for that course of action
identified. Next the decision-maker should choose the
course of action yielding the best of the best possible
outcomes.
dr. hab. Jerzy Supernat
Decision-making Techniques
The optimistic decision rule
F
The best
outcome
F1
F2
F3
F4
F5
D1
80
80
80
80
80
80
D2
-20
160
160
160
160
160
D3
-120
60
240
240
240
240
D4
-220
-40
140
320
320
320
D5
-320
-140
40
220
400
400
D
The best of the
best outcomes
400
dr. hab. Jerzy Supernat
Decision-making Techniques
Should
a decision-maker always be
a total optimist?
Total optimism means taking into
account only the best outcome for
each course of action.
Decision-making Techniques
A decision-maker who behaves rationally should consider
two things:
 the best outcomes and
 the worst outcomes
modifying their weight (meaning) according to his/her
optimism (and pessimism).
He/she can do it applying the coefficient of optimism.
Decision-making Techniques
Calculations based on the coefficient of optimism of 0.6 (we often
accept 0.5, i.e. the half way point between total pessimism and total
optimism) are as follows:
D
The best The worst
outcome outcome
The expected value
(as understood by L. Hurwicz)
D1
80
80
80 x 0.6 + 80 x 0.4 = 80
D2
160
-20
160 x 0.6 + (-20) x 0.4 = 88
D3
240
-120
240 x 0.6 + (-120) x 0.4 = 96
D4
320
-220
320 x 0.6 + (-220) x 0.4 = 104
D5
400
-320
400 x 0.6 + (-320) x 0.4 = 112
dr. hab. Jerzy Supernat
Decision-making Techniques
the higher the coefficient of
optimism the higher the
decision-maker’s hope for
obtaining the best possible
outcome:
the coefficient of optimism of 1
leads to the behavior of a total
optimist

the lower the coefficient of
optimism, the higher the fear
of the decision-maker of
receiving the worst possible
outcome:
the coefficient of optimism of 0
leads to behavior of a total
pessimist

dr. hab. Jerzy Supernat
Decision-making Techniques
The regret decision rule
The regret decision rule is based on a deceptively simple
but extremely useful question: If we choose one particular
course of action, then, in hindsight, how much we do
regret not having chosen what turned out to be the best
course of action given a particular set of circumstances?
dr. hab. Jerzy Supernat
Decision-making Techniques
Calculated values of regret are in brackets. It’s a matter of
convention that regret is presented in positive numbers.
F
F1
D
D1
80
F2
(0)
F3
80 (80)
160
(0)
F4
F5
80 (160)
80 (240)
80 (320)
160 (80)
160 (160)
160 (240)
240
240 (80)
240 (160)
D2
-20 (100)
D3
-120 (200)
60 (100)
D4
-220 (300)
-40 (200)
140 (100)
D5
-320 (400) -140 (300)
40 (200)
(0)
320
(0) 320
(80)
220 (100) 400
(0)
dr. hab. Jerzy Supernat
Decision-making Techniques
After calculating the values of regret we are left with the regret
table.
F
F1
D
F2
F3
F4
F5
D1
0
80
160
240
320
D2
100
0
80
160
240
D3
200
100
0
80
160
D4
300
200
100
0
80
D5
400
300
200
100
0
dr. hab. Jerzy Supernat
Decision-making Techniques
Now one has to choose the best course of action by applying the
pessimistic decision rule to the regret table and choosing the course
of action with minimum of maximum regrets.
F
F1
F2
F3
F4
F5
Maximum
regret
Minimum
of
maximum
regrets
D
D1
0
80
160
240
320
320
D2
100
0
80
160
240
240
D3
200
100
0
80
160
200
D4
300
200
100
0
80
300
D5
400
300
200
100
0
400
200
dr. hab. Jerzy Supernat
Decision-making Techniques
Inconsistency in the regret decision rule
The regret decision rule is a powerful and intuitively
attractive idea. It attempts to minimize the embarrassment
we might feel of making the wrong decision. It is closely
related to the economist’s traditional concept of the
opportunity cost of a decision: i.e. by choosing one
alternative course of action, what opportunity are we
forgoing by not choosing another course of action?
dr. hab. Jerzy Supernat
Decision-making Techniques
Unfortunately, as a decision rule
the concept has a major
disadvantage: if we are choosing
the course of action which will
give us the least cause for regret
when compared with another
option, then the degree of regret
will depend upon which other
options are considered. This can
bring about problems of logical
inconsistency.
In order to illustrate this
inconsistency let’s move to the
next slide.
dr. hab. Jerzy Supernat
Decision-making Techniques
The analysis of the problem below shows the best course
of action from a regret rule viewpoint is process A.
F
F1
F2
Maximum
regret
Minimum
of maximum
regrets
3
D
D1 - process A
7 (3)
25 (0)
3
D2 - process B
10 (0)
20 (5)
5
dr. hab. Jerzy Supernat
Decision-making Techniques
Now, let’s assume that an additional process (process C) has been
elaborated allowing us to obtain the same result. Analysis of the
problem, taking into account the new process, shows that D2, in this
case, is the better option – previously being the worst one!
F
F1
F2
Maximum
regret
D
D1 - process A
7 (7)
25 (0)
7
D2 - process B
10 (4)
20 (5)
5
D3 - process C
14 (0)
15 (10)
10
Minimum
of maximum
regrets
5
dr. hab. Jerzy Supernat
Decision-making Techniques
The expected value decision rule
This rule weighs each outcome by the probability (or likelihood)
of its occurrence. The expected value is the weighted average of
the possible results anticipated from a particular course of action
where the weights are the probabilities. After calculating the
expected value for each option, the decision-maker should
choose the course of action with the maximum expected value.
It should be emphasized that expected values are, in themselves
totally hypothetical figures. In reality, the calculated expected
values on slide 76 will never actually occur. The values will be
any of the figures illustrated in the table but never the expected
figure. The expected values are merely an indication of the value
of each option.
dr. hab. Jerzy Supernat
Decision-making Techniques
Decision matrix
Probability
F
D
D1
D2
D3
D4
D5
p1=0.1 p2=0.2 p3=0.5 p4=0.2
F1
F2
F3
F4
-10
10
0
5
14
-5
10
25
8
18
20
10
0
10
2
11
10
25.5
15
16
EVi
dr. hab. Jerzy Supernat
Decision-making Techniques
Probability
F
D
D1
D2
D3
D4
D5
p1=0.1 p2=0.2 p3=0.5 p4=0.2
F1
F2
F3
F4
-10
10
0
5
14
-5
10
25
8
18
20
10
0
10
2
11
10
25.5
15
16
EVi
10.2
10
10.1
10.1
9.2
dr. hab. Jerzy Supernat
Decision-making Techniques
Example
The decision maker is deciding whether or not to undertake one of two contracts (A or B) offered to him. Each
contract can lead only to three possible outcomes. The
probabilities and outcomes are as follows:
dr. hab. Jerzy Supernat
Decision-making Techniques
Contract A
Contract B
Outcome
(in thsd’s)
Probability
Outcome
(in thsd’s)
Probability
80
0.6
50
0.5
10
0.1
30
0.3
-30
0.3
-10
0.2
dr. hab. Jerzy Supernat
Decision-making Techniques
Our example using a decision tree.
dr. hab. Jerzy Supernat
Decision-making Techniques
In order to reach the optimal decision, one should analyze
the decision tree from right to left (the roll-back technique).
Fundamental rules:
 The expected value should be calculated for each
outcome branch.
 The branch with the higher expected value should be
chosen at each decision node (there is only one decision
node in our example).
dr. hab. Jerzy Supernat
Decision-making Techniques
Calculations for each outcome branch:
EV1 = 80 x 0.6 + 10 x 0.1 + (-30) x 0.3 = 40
EV2 = 50 x 0.5 + 30 x 0.3 + (-10) x 0.2 = 32
Calculated expected values can be placed above the
relevant outcome nodes.
dr. hab. Jerzy Supernat
Decision-making Techniques
Decision tree with the expected values.
dr. hab. Jerzy Supernat
Decision-making Techniques
Moving from right to left we reach the (starting) decision
node where the decision maker must choose one of three
courses of action with calculated expected values (for the
course of action D3 – signing neither of the contracts –
profit equals zero).
Replacing outcome branches with their equivalents in the
form of expected values leads to the reduction of the
decision tree.
dr. hab. Jerzy Supernat
Decision-making Techniques
Reduced decision tree.
dr. hab. Jerzy Supernat
Decision-making Techniques
Using the expected value decision rule, the decision
maker should choose D1, and cut off D2 and D3, as
presented below:
||
dr. hab. Jerzy Supernat
Decision-making Techniques
When the analyzed decision problem pops up repeatedly
in the static decisional situation choosing D1 (concluding
contract A) arises no doubts. Choosing D1 in each case
gives the decision maker – in the long term – the highest
outcome.
The expected value decision rule is fully justified when
the decision process can be repeated many times in the
same stable set of circumstances.
dr. hab. Jerzy Supernat
Decision-making Techniques
However, static decision situations are rare.
In practical terms dynamic situations are
prevalent and, therefore, one-off decisions
are not made twice or more times in
identical situations.
In our example the decision maker might
fear a loss of 30 (with probability of 0.3)
connected with contract A (choosing the
worse option – from the expected value
decision rule – contract B, he risks only 10
with probability of 0.2).
dr. hab. Jerzy Supernat
Decision-making Techniques
The expected utility decision rule
As the previous slides indicated in the case of oneoff decision the proper analysis should not be the
one using the expected value decision rule. Rather
the analysis taking into account the decision body’s
preferences, in other words, the analysis applying
the expected utility decision rule.
Utility is a relative value of possible
outcomes taking into account the
preferences of the decision-maker.
dr. hab. Jerzy Supernat
Decision-making Techniques
In descending order, there are seven possible outcomes in
our example: 80, 50, 30, 10, 0, -10, -30 (0 corresponds
to choosing neither contract).
Because the scale of a utility function is discretionary, we can define utilities (U) of extreme outcomes as
follows:
U (80) = 1
i
U (-30) = 0
Next it is necessary to determine the utility of the five
other possible outcomes.
dr. hab. Jerzy Supernat
Decision-making Techniques
In order to accomplish this, we can ask the decisionmaker to make a choice of two possibilities:
 the first, being the certain outcome (in sequence 50,
30, 10, 0, -10)
 the second: a gamble on outcomes 80 with probability
p and -30 with probability 1-p.
80 p
(a gamble on outcomes 80 with probability p and -30 with probability 1-p)
50 (certain)
-30 1-p
dr. hab. Jerzy Supernat
Decision-making Techniques
At p = 0 the decision maker will choose 50, but increasing
the probability of winning 80 we will reach a spread of
probability making both possibilities equally good for the
decision-maker. This could happen at probability of 0.9
winning 80 and probability of 0.1 of loosing 30.
80 p
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
-30 1-p
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
50 (certain)
dr. hab. Jerzy Supernat
Decision-making Techniques
Applying the already known utilities, corresponding with
the extreme outcomes of the game, and having established the spread of probability, we can now calculate a utility
of 50 (or utility of the game, being the expected value of
utilities of game outcomes at the established spread of
probability):
U (50) = U (80) x 0.9 + U (-30) x 0.1
U (50) = 1 x 0.9 + 0 x 0.1
U (50) = 0.9
dr. hab. Jerzy Supernat
Decision-making Techniques
Repeating the procedure for the remaining outcomes
could show that the probability that makes the decisionmaker indifferent is for 30 as high as 0.8:
80 p
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-30 1-p
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
30 (certain)
U (30) = U (80) x 0.8 + U (-30) x 0.2 = 1 x 0.8 + 0 x 0.2
U (30) = 0.8
for 10 as high as 0.5
for 0 as high as 0.3
for -10 as high as 0.15
dr. hab. Jerzy Supernat
Decision-making Techniques
Utilities of all outcomes:
Outcome
80
50
30
10
0
-10
-30
Utility
1
0.9
0.8
0.5
0.3
0.15
0
dr. hab. Jerzy Supernat
Decision-making Techniques
The expected value analysis used earlier can now be
repeated, only using utility values instead of monetary
outcomes. We calculate the expected utility for each
possible course of action (D1 – make contract A, D2 –
conclude contract B and D3 – undertake neither contract)
as follows:
U1 (contract A) = 1 x 0.6 + 0,5 x 0.1 + 0 x 0.3
U1= 0.65
U2 (contract B) = 0.9 x 0.5 + 0.8 x 0.3 + 0.15 x 0.2
U2 = 0.72
U3 (neither contract A, nor contract B) = 0.3 x 1
U3= 0.3
dr. hab. Jerzy Supernat
Decision-making Techniques
Analysis of the utility of outcomes points to contract B as
the optimal decision. Moving from values expressed in
money to their utilities (taking into account preferences of
the decision-maker) has brought the change of the
decision.
dr. hab. Jerzy Supernat
Concluding Remark
Once you make a decision, the universe conspires
to make it happen.
Ralph Waldo Emerson
dr. hab. Jerzy Supernat