Judgment and Decision Making in Information Systems Decision Making, Sensitivity Analysis, and the Value of Information. Yuval Shahar, M.D., Ph.D. Personal Decision Making: The Party Problem. Joseph K. invites his friends to a party, but needs to decide on the location:
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Yuval Shahar, M.D., Ph.D.
O-S (best)
P-S
I-R
I-S
P-R
O-R (worst)
B
W
1
0
O-S (best)
P-S
I-R
I-S
P-R
O-R (worst)
0.95
B
0.05
W
0.67
B
0.33
W
0.57
B
0.43
W
0.32
B
0.68
W
0
B
1
W
S 0.4
R 0.6
O
S 0.4
P
R 0.6
I
S 0.4
R 0.6
1
S 0.4
B
0
W
0
B
R 0.6
O
1
W
0.95
S 0.4
B
0.05
W
P
0.32
B
R 0.6
0.68
W
0.57
I
S 0.4
B
0.43
W
0.67
R 0.6
B
0.33
W
B
B
B
W
W
W
0.4
0.6
O
0.57
P
0.43
I
0.63
0.37
B
B
B
W
W
W
0.4
0.6
O
0.57
P
0.43
I
0.63
<=
0.37
Preference Probability
S 0.4
1
E-value =0.40
R 0.6
0
O
S 0.4
0.95
E-value= 0.57
P
R 0.6
0.32
I
S 0.4
E-value= 0.63
0.57
R 0.6
0.67
Prospect Preference Probability $ Value
O-S (best)1 100
P-S0.95 90
I-R0.67 50
I-S0.57 40
P-R 0.32 20
O-R (worst) 00
Utility
1
0.5
0
+
$0 $34 $50K $100K
Money
Note: Once we know JK’s utilility curve, we can compute his certain equivalent for ANY deal, e.g., a (<$100K, 50%; $0, 50%> deal, which happens to be $34, using graphical or other methods; or the $ certain equivalent of any outcome (e.g., Outdoor location)
O
P
I
$value U value
U= 0.40 $26
0.4 S
O
0.6 R
U= 0.57 $40
0.4 S
P
U= 0.63 $46
0.6 R
No clairvoyance
U=0.63 ( $46)
0.4 S
I
0.6 R
U= 0.63 $46
$value $value-$cost
1 S
$85
0 R
1 S
U= 0.92 $85
$75
“S”
0 R
1 S
$25
0.4
Buy clairvoyance for $15
U =0.67 ( $51)
0 R
$-15
“R”
0 S
O
1 R
$ 5
0.6
P
0 S
I
U= 0.50 $35
0 S
$35
1 R
0.8 “S”
0.32
0.4 S
0.2 “R”
0.08
0.2 “S”
0.12
0.6 R
0.8 “R”
0.48
0.727 S
0.32
0.44 “S”
0.273 R
0.08
0.143 S
0.12
0.56 “R”
0.857 R
0.48
$value U value
S p
100
1
R 1-p
0
0
O
S p
U = p
90
0.950
P
R 1-p
20
0.323
U = 0.323+0.627p
I
S p
40
0.568
U = 0.667-0.099p
R 1-p
50
0.667
The value of information
$
U
100
Free clairvoyance:
0.667+0.333p
1
90
0.8
I: 0.667+0.0.099p
0.6
40
0.4
20
P: 0.323+0.628p
0.2
O:p
0.2
0.4
0.47
0.6
0.8
P
X4
X12
X3
X5
X7
X8
- 0 +