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In the course of human decision making, we study the basic concept of the human computer interaction and the decision making:Making Choices, Expected Monetary Value, Risky Alternatives, Highest Expected Value, Monetary Values, Random Variable, Probability, Discrete Variable, Continuous Variable, Solving Decision Trees
Typology: Slides
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1
r i
n
i
=
(Discrete Variable)
ā āā
3
EMV(A1)=C1ā¢p 1 +C2ā¢(1-p 1 ) EMV(A2)=C3ā¢p 2 +C4ā¢ (1-p 2 )
(p 1 )
Payoff
(1-p 1 )
(p 2 )
(1-p 2 )
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Solving Decision Trees
Start at the endpoints of the branches on the far right-hand side and move to left When encountering a chance node, calculate its EV and replace the node with the EV When encountering a decision node, choose the branch with the highest EV Continue with the same procedures until a preferred alternative is selected for each decision node
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Donāt Perform
Perform Survey
Survey High
Old New
High $300,000 (0.3) Medium Low
Survey Low
Old (^) $130,
New Medium
Low
High $300,000 (0.6) $280,
$80, Old (^) $130,
New
Medium $100,000 (0.6) (^) $80,
-$120,
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Donāt Perform
Perform Survey
Survey High
Old New
-$100,
High $300,000 (0.3) Medium Low
Survey Low
Old (^) $130,
New Medium
Low
High $300,000 (0.6) $280,
Old $80, $130,
New
Medium $100,000 (0.6) (^) $80,
-$120,
EMV(U 3 ) =0.6ā¢280,000+0.4ā¢80,000=$200,
U 1
U 2
U 3
U 4 D 1
D 2
D 3
D 4
EMV(U 4 ) =0.6ā¢80,000+0.4ā¢(-120,000)=$
EMV= $
EMV= $200,
EMV(U 2 ) =0.3ā¢300,000+0.5ā¢(100,000)+0.2ā¢(-100,000)=$120,
EMV= $120,
EMV(U 1 ) =0.5ā¢200,000+0.5ā¢130,000=$165,
EMV= $165,
Conclusion: Perform survey. If survey shows high-level sales, then switch the new product ; otherwise, stay with the old product
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Decision Path and Strategy
Represents a possible future scenario, starting from the left-most node to the consequence at the end of a branch by selecting one alternative from a decision node and by following one outcome from a chance node.
Path 1 ( A 1 ) Path 2 ( A 2 O 1 ) Path 3 ( A 2 O 2 A 3 ) Path 4 ( A 2 O 2 A 4 )
D1 U 1 D 2
A 1
A 2
O 1
O 2
A 3
A 4
A 1
A 2 D 1 D 2
U 1
O 1
O 2
A 3 A 4
Decision Paths:
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Decision Path and Strategy (Contād)
The collection of decision paths connected to one branch of the immediate decision by selecting one alternative from each decision node along that path
Strategy 1 (A 1 ): Decision path A 1
Strategy 3 (A 2 A 4 ): Decision paths A 2 O 2 A 4 , A 2 O 1
Strategy 2 (A 2 A 3 ): Decision paths A 2 O 2 A 3 , A 2 O 1
A 1
A 2
D 1 D 2
U 1
O 1
O 2
A 3
A 4
Decision Strategies:
D1 (^) U 1 D 2
A 1
A 2
O 1
O 2
A 3
A 4
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Decision Strategies:
Decision Tree of the Product-Switching Example
Donāt Perform
Perform Survey
Survey High
Old New
-$100,
High (0.3) Medium Low
Survey Low
Old
New Medium
Low
High (0.6) $280,
Old $80,
New
Medium (0.6) (^) $80,
-$120,
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Strategy 1): Donāt perform survey and keep the old product Strategy 2): Donāt perform survey and switch to the new product
Donāt Perform
New (^) Medium
High
Low
Payoffs $300, $100, -$100,
**Probabilities
0.** Strategy 3): Perform survey and if survey high then keep the old product
Perform Survey
Survey High Survey Low
Old $130, $130,
$130,000 (100%)
Strategy 4): Perform survey and if survey high then switch to the new product
Perform Survey
Survey High Survey Low
New
$130,
Medium (0.4)
High(0.6) $280, $80,
Payoffs $280, $130, $80,
**Probabilities
0.**
$150,000 (100%)
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Payoff($)
Pr(Payoff)
Risk Profiles of the Product-Switch Example
Strategy 1 Strategy 2 Strategy 3 Strategy 4
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Cumulative Risk Profiles
Payoff($)
Pr(Payoffā¤x)
Trade Ticket Keep Ticket
Cumulative Risk Profiles of the Lottery Ticket Example
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Making Decisions with
Multiple Objectives
Sam has two job offers in hand. One job is to work as an assistant at a local small business. The job would pay a minimum wage ($5.25 per hour), require 30 to 40 hours per week, and have the weekends free. The job would last for three months, but the exact amount of work and hence the amount Sam could earn were uncertain. On the other hand, he could spend weekends with friends.
The other job is to work for a conservation organization. This job would require 10 weeks of hard work and 40 hours weeks at $6.50 per hour in a national forest in a neighboring state. This job would involve extensive camping and backpacking. Members of the maintenance crew would come from a large geographic area and spend the entire 10 weeks together, including weekends. Sam has no doubts about the earnings of this job, but the nature of the crew and the leaders could make for 10 weeks of a wonderful time, 10 weeks of misery, or anything in between.
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Objectives (and Measures)
Having fun (measured using a constructed 5-point Likert scale; Table 4.5 at page 138 ) (5) Best: A large congenial group. Many new friendships made. Work is enjoyable, and time passes quickly. (4) Good: A small but congenial group of friends. The work is interesting, and time off work is spent with a few friends in enjoyable pursuits. (3) moderate: No new friends are made. Leisure hours are spent with a few friends doing typical activities. Pay is viewed as fair for the work done. (2) Bad: Work is difficult. Coworkers complain about the low pay and poor conditions. On some weekends it is possible to spend time with a few friends, but other weekends, are boring. (1) Worst: Work is extremely difficult, and working conditions are poor. Time off work is generally boring because outside activities are limited or no friends are available.
Earning money (measured in $)
Decision to Make Which job to take (In-town job or forest job) Uncertain Events Amount of fun Amount of work (# of hours per week)
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Job Decision
Overall Satisfaction
Fun
Salary
Amount of Fun
Amount of Work
Fun
Overall Satisfaction
Salary
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Cumulative Risk Profiles of the Fun
Conclusion: For the fun objective, the forest job has higher EV but is more risky
Risk Profiles: Strategies:
Analysis of the Fun Objective (Contād)
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Samās dilemma: Would he prefer a slightly higher salary for sure and take a risk on how much fun the summer will be? Or otherwise, would the in-town be better, playing it safe with the amount of fun and taking a risk on how much money will be earned? Therefore, Sam needs to make a trade-off between the objectives of maximizing fun and maximizing salary.
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Combine multiple objectives into one overall objective Steps First, multiple objectives must have comparable scales Next, assign weights to these objectives (the sum of all the weights should be equal to 1) Subjective judgment Paying attention to the range of the attributes (the variables to be measured in the objectives) is crucial; Attributes having a wide range of possible values are usually important (why?) Then, calculate the weighted average of consequences as an overall score Finally, compare the alternatives using the overall score
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Set $2730 (the highest salary) = 100, and $2047.50 (the lowest salary) = Then, Intermediate salary X is converted to: (X-2047.50)Ā·100/(2730-2047.50) (Proportion Scoring)
Sam thinks increasing salary from the lowest to the highest is 1.5 times more important than improving fun from the worst to best, hence Ks=1.5Kf , Because Ks+Kf=1 Ks=0.6, Kf=0.
Convert the salary scale to the same 0 to 100 scale used to measure fun
Assign weights to salary and fun (Ks and Kf)
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Exercise
D 1
D 2
A
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D 1
D 2
A
33
D 1
D 2
A
Decision Strategies:
Strategy 1: A - A 1
$4 (0.73) $8 (0.27)
Strategy 2: A ā A 2
D 1
D 2
A
Strategy 3: B
D 1 B
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0
1
0 2 4 6 8 10 12 14 16 18 20 Strategy A-A 1 Strategy A-A 2 Strategy B
Risk Profiles
0
1
0 2 4 6 8 10 12 14 16 18 20
Cumulative Risk Profiles
Conclusion: No stochastic dominance exists
