Hurwitz score related decision making methods
Skorkovský
Department of business economy

Uncertainty-Risk
•Although the possible returns of the investment are beyond the control of the decision maker, the
decision maker might or might not be able or willing to assign probabilities to them.
•
•If no probabilities are assigned to the possible consequences, then the decision situation is
called "decision under uncertainty".
•
•If probabilities are assigned then the situation is called "decision under risk".
•
•This is a basic distinction in decision theory, and different analyses are in order.
•
2

First approach
Decision
(what to do ?)
Alternative 1
Alternative 2
Alternative i
 A/O
 O1
O2
O3
 O4
O5
 A1
po11
po12
po13
po14
 po15
 A2
 po21
 po22
po23
 po24
 po25
A3
po31
po32
po33
 po34
 po35
A4
 po41
 po42
 po43
po44
 po45
Where : A=alternative(action); O=Outcome, po=payoff (benefits), (přínosy, prospěch)
A=(A1,A2,…Ai) = inventory of viable options=vector, O=(O1,O2,…Ok)= outcome vector
Decision
Table
(payoff table)
10000000 USD
500000 EUR
8000000 EUR
Shares in diamond mines
Bonds
Antiquities
Outcomes

Chosen criteria I
•MaxiMax
–MaxiMax is the rule for the optimist. A slogan for MaxiMax might be "best of the best" - a
decision maker considers the best possible outcome for each course of action, and chooses the
course of action that corresponds to the best of the best possible outcomes
–
•
4
Choices
Profit
Strong market
Fair market
Poor market
invest $8000
$800
$200
-$400
invest $4000
$400
$100
-$200
invest $2000
$200
$50
-$100
invest $1000
$100
$25
-$50
Example of the decision table   I (best of the vector {800,400,200,100} is 800 !!
Example  II

MaxiMax Payoff
•Select the alternative which results in the maximum of maximum payoffs; an optimistic criterion
Outcomes
Alternatives
 O1
O2
O3
A
$1,000
$1,000
$1,000
B
$10,000
-$7,000
$500
C
$5,000
$0
$800
D
$8,000
-$2,000
$700
Maximum Payoff
$1,000
$10,000
Payoff  Table
$5,000
$8,000
B > D > C > A
Alternatives (invested amount, expectant spouse inheritance, type of the car,..)

Chosen criteria II
• MaxiMin
–The MaxiMin decision rule is used by a pessimistic decision maker who wants to make a conservative
decision. Basically, the decision rule is to consider the worst consequence of each possible course
of action and chooses the one that has the least worst consequence (in our case= -50). So it is
better to invest nothing !!!!
•
6
Choices
Profit
Strong market
Fair market
Poor market
invest $8000
$800
$200
-$400
invest $4000
$400
$100
-$200
invest $2000
$200
$50
-$100
invest $1000
$100
$25
-$50
Example  II

MaxiMin Payoff
•Select the alternative which results in the maximum of minimum payoffs; a pessimistic criterion
Outcomes
Alternatives
 O1
O2
O3
A
$1,000
$1,000
$1,000
B
$10,000
-$7,000
$500
C
$5,000
$0
$800
D
$8,000
-$2,000
$700
Minimum Payoff
$1,000
-$7,000
Payoff  Table
$0
-$2,000
A > C > D > B

8
 A/O
 O1
O2
O3
 O4
O5
 A1
po11
po12
po13
po14
 po15
 A2
 po21
 po22
po23
 po24
 po25
A3
po31
po32
po33
 po34
 po35
A4
 po41
 po42
 po43
po44
 po45
Decision Strategy I
(Hurwitz criterion allows to choose strategies depending on propensity (inclination, tendency) to
risk,
Example on the next slide

Decision Strategy II
9
 A/O
 O1
O2
O3
 a=max
b=min
 A1
 1
5
7
7
1
 A2
 3
2
6
6
 2
A3
5
4
3
5
 3






Where ai = max (pi,Ok) and  bi=
  min(pi,Ok)
Where 5,8=7*0,8+(1-0,8)*1=5,6+0,2; 5,2=6*0,8+(1-0,8)*2,…….
First line
Second line

Thanks for Your attention
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