Non-Probabilistic Decision Rules: Lexicographic Ordering, Satisficing, Maxmax Payoff, Slides of Human-Computer Interaction Design

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Non-probability

decision rules

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Types of Decision Making Environment

 Non-Probability Decision Making

 Decision maker knows with certainty the consequences of every alternative or decision choice

 Decision Making under Risk

 Decision maker can assign the probabilities of the various outcomes

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Values

Alternatives Attribute 1 Attribute 2 …

A

B

C

Decision Table

Outcomes Alternatives Outcome 1 Outcome 2 … A

B

C

Payoff Table

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Desirable Properties of Decision Rules

 Transitivity

 If alternative A is preferred to alternative B and alternative B is preferred to alternative C, then alternative A is preferred to alternative C

 Column Linearity

 The preference relation between two alternatives is unchanged if a constant is added to all entries of a column of the decision table or payoff table

 Addition/Deletion of Alternatives

 The preference relation between two alternatives is unchanged if another alternative is added/deleted from the decision table or payoff table

 Addition/Deletion of Identical Columns

 The preference relation between two alternatives is unchanged if a column with the same value in all alternatives is added/deleted to the decision table or payoff table

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Satisficing/Minimum Aspiration Level

Select any alternative which satisfies the minimum aspiration levels

(the minimum acceptable criteria) of all values

Values

Alternatives Safety ≥Medium

Price ≤13k

Reliability ≥Medium A High $15k High

B Medium $11k Medium

C High $13k Medium

May not be optimal because not all alternatives will be considered

as long as one satisfactory alternative is found

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Maxmax Payoff

Select the alternative which results in the maximum of maximum

payoffs; an optimistic criterion

Outcomes

Alternatives O1 O2 O

A $1,000 $1,000 $1, B $10,000 -$7,000 $ C $5,000 $0 $ D $8,000 -$2,000 $

Maximum Payoff

$1, $10,

Payoff Table

B > D > C > A

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Outcomes

Alternatives O1 O2 O3 O

A $1,000 $1,000 $1,000 $8, B $10,000 -$7,000 $500 $8, C $5,000 $0 $800 $8, D $8,000 -$2,000 $700 $8,

Payoff Table

Maximum Payoff $8, $10, $8, $8,

B > A = C = D

Maxmax payoff violates addition/deletion of identical columns

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Maxmin Payoff

Select the alternative which results in the maximum of minimum

payoffs; a pessimistic criterion

Outcomes

Alternatives O1 O2 O

A $1,000 $1,000 $1, B $10,000 -$7,000 $ C $5,000 $0 $ D $8,000 -$2,000 $

Minimum Payoff

$1, -$7,

Payoff Table

A > C > D > B

Maxmin payoff violates column linearity and addition/deletion of

identical columns Docsity.com

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Outcomes

Alternatives O1 O2 O

A $1,000 $1,000 $1, B $10,000 -$7,000 $ C $5,000 $0 $ D $8,000 -$2,000 $ E -$1,000 $4,000 $

Payoff Table

Outcomes O1 O2 O $9,000 $3,000 $ $0 $11,000 $ $5,000 $4,000 $ $2,000 $6,000 $ $11,000 $0 $1,

Regret Table

Maximum Regret $9, $11, $5, $6, $11,

C > D > A > B

Minmax regret violates addition/deletion of alternatives

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Laplace

Calculate the average of each alternative by assuming that the

outcomes are equally likely to occur, and select the alternative with the

largest average

Average

$1, $1,166.

Outcomes

Alternatives O1 O2 O

A $1,000 $1,000 $1, B $10,000 -$7,000 $ C $5,000 $0 $ D $8,000 -$2,000 $

Payoff Table

D > C > B > A

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Hurwicz score = Max. payoff ∙α + Min. payoff ∙(1-α)

α

Alternative A B C D 0 1000 -7000 0 - 0.1 1000 -5300 500 - 0.2 1000 -3600 1000 0 0.3 1000 -1900 1500 1000 0.4 1000 -200 2000 2000 0.5 1000 1500 2500 3000 0.6 1000 3200 3000 4000 0.7 1000 4900 3500 5000 0.8 1000 6600 4000 6000 0.9 1000 8300 4500 7000 1 1000 10000 5000 8000

Hurwicz Scores of Alternatives with Respect to α

A: Hurwicz score = 1000

B: Hurwicz score = 10000∙α + (-7000)∙(1-α) = 17000α- 7000

C: Hurwicz score = 5000∙α + 0∙(1-α) = 5000α

D: Hurwicz score = 8000∙α + (-2000) ∙(1-α) = 10000α- 2000

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α=0.2 α=0.4 α=5/ ≈0. When 0≤α<0.2, A is the best alternative When 0.2≤α≤0.4, C is the best alternative When 0.4≤α≤5/7, D is the best alternative When α>5/7, B is the best alternative Docsity.com