Multiattribute Utility Theory - Human Decision Making - Lecture Slides, Slides of Human-Computer Interaction Design

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Multi-Attribute Utility

Theory (MAUT)

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Introduction

 Conflicting Objectives and Tradeoffs in Decision Problems

 e.g. higher returns vs. lower risks in investment, better performance vs. lower

price of computer

 Objectives with Incomparable Attribute Scales

 “Attribute” refers to the quantity used to measure the accomplishment of an

objective

 e.g. maximize profits vs. minimize impacts on environments

 Multi-Attribute Decision Making (MADM)

 A study of methods and procedures that handle multiple attributes

 Usages

 Identify a single most preferred alternative  Rank alternatives  Shortlist a limited number of alternatives for subsequent detailed appraisal  Distinguish acceptable from unacceptable possibilities

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You want to buy a car with a long expected life span and a low price. You have

narrowed down your choices to three alternatives: the Portalo (a relatively expensive

sedan with a reputation for longevity) , the Norushi (renowned for its reliability),

and the Standard Motors car (a relatively inexpensive domestic automobile). You

have done some research and evaluated these three cars on both attributes, as

follows.

Alternatives

Attributes Portalo Norushi

Standard

Motors

Price ($k) 17 10 8

Life Spans

(Years)

Worst (^) Best

Best Worst

Automobile Example

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None of the cars dominates

How much are you willing to pay to increase the life span of your car? (subjective judgment)

Start with the Standard Motor, the cheapest among the three alternatives Prefer Norushi to Standard if you are willing to pay $2k or more to increase the life span of your car by 3 years  Prefer Portalo to Norushi if you are willing to pay extra $7k or more for an additional 3 years

Portalo

Norushi

Standard

Life Span

Price

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Additive Utility Function

 A Simplified Utility Model

 Ignores interactions among attributes

 For a consequence set that has values x 1 , x 2 , …, xm on the attributes

of m objectives, its overall utility is computed as



m

i

i i i

m m m m

k x

x x x k x k x k x

1

1 2 1 1 1 2 2 2

U ( )

U( , , , ) U ( ) U ( ) U ( )

Ui( x i) – the utility function of the ith attribute

( k 1  k 2  km  1 )

0  U( x 1 , x 2 ,, xm ) 1

0  U i ( xi ) 1

k i – the weight of the ith attribute

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UPrice(Norushi) = UPrice(10000) = (10000 – 17000) / (8000 – 17000) = 0.

Set UPrice(Portalo) =UPrice(8000) = 1,

Utility Functions

UPrice(Standard) = UPrice(17000) = 0

ULife(Norushi) = ULife(9) = (9 – 6) / (12 – 6) = 0.

Alternatives

Utilities Portalo Norushi

Standard

Motors

UPrice 0 0.78 1

ULife 1 0.5 0

U( x )  



i i

i

x x

x x 

x i : the worst value of attribute X i ; : the best value of X i



x i

ULife(Standard) = ULife(12) = 1, ULife(Portalo) = ULife(6) = 0

Automobile Example (Cont’d)

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• Indirectly specify the tradeoffs between objectives

e.g. You are willing to pay up to $600 for an extra year of life span

U(Norushi) = 0.714•UPrice(Norushi) + 0.286•ULife(Norushi) = 0.

U(Standard) = 0.714•UPrice(Standard) + 0.286•ULife(Standard) = 0.

U(Portalo) = 0.714•UPrice(Portalo) + 0.286•ULife(Portalo) = 0.

Suppose taking the Standard Motors as the base case. You are indifferent

between paying $8000 for 6 years of life span and paying $8,600 for 7 years of

life span

U($8,000, 6 Years) = U($8,600, 7 Years)

kPrice•UPrice(8000) + kLife•ULife(6) = kPrice•UPrice(8600) + KLife•ULife(7)

UPrice(8600) = (8600-17000)/(8000-17000)= 0.933, ULife(7) = (7-6)/(12-6)=0.

kPrice•1 + kLife•0 = kPrice•0.933 + kLife•0.167  0.067kPrice= 0.167kLife (Eq. 1)

Weight Assessment (Cont’d)

Solve Eqs (1) and (2)  kPrice= 0.714, kLife = 0.

kPrice + kLife = 1 (Eq. 2)

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Indifference Curve

• Alternatives falling on the same indifference curve have the same utility
• The decision maker is indifferent among these alternatives

Indifference Curves of the Automobile Example (Trade $600 for an additional year of life span)

Portalo

Norushi

Standard

Price($K)

Life Span(Year) (^) 0.714 0.7 (^) 0.

Utility

Hypothetical car

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Drug Counseling Center Choice

The drug-free center is a private nonprofit contract center that provides counseling

for clients sent to it by the city courts as a condition of their parole. It has just lost

its lease and must relocate.

The director of the center has screened the spaces to which it might move. After

the prescreening, 6 sites are chosen for serious evaluation. The director must, of

course, satisfy the sponsor, the Probation Department, and the courts that the new

location is appropriate and must take the needs and wishes of both employees and

clients into account. But as a first cut, the director wishes simply to evaluate the

sites on the basis of values and judgments of importance that make sense

internally to the center.

After consulting the members of the center staff, the director constructs a

fundamental objective hierarchy that expresses the value-relevant objectives and

attributes for comparing alternative center locations. Since the purpose of the

evaluation to compare quality, cost is omitted.

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A: Good conditions for staff

B: Easy access for clients

C: Suitability of space for center’s function

D: Administrative convenience

Maximize Overall Satisfaction

Office size Convenience of commuting Office attractiveness Office privacy Parking space

Closeness to clients’ homes Access to public transportation

No. and suitability of counseling rooms

Suitability of reception and waiting area

No. and suitability of conference rooms

Adequacy of space Flexibility of space layout

(0.43) (0.24)^ (0.19) (0.14)

Fundamental Objectives Hierarchy

A 1

A 2

A 3

A 4

A 5

B 1

B 2

C 1

C 2

C 3

D 1

D 2

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Attributes Sites 1 2 3 4 5 6

A (0.43)

A1(0.39) 1 0.50 0 0.50 0 0.

A2 (0.21) 0.47 0.26 1 0.05 0 0.

A3 (0.14) 0.27 0.93 0.80 0 1 0.

A4 (0.14) 1 0.25 0.38 0 0.31 0.

A5 (0.12) 0 0.56 0.22 0 1 0.

B (0.24)

B1(0.50) 0.33 0.33 0 0.56 1 0.

B2 (0.50) 0.71 0.71 1 0.47 0 0.

C (0.19)

C1 (0.52) 0.06 0.88 0 0.53 1 0.

C2 (0.32) 0.63 0.50 0 0 1 0.

C3 (0.16) 0.47 0.35 0.47 0 1 0.

D (0.14)

D1 (0.64) 0 0.75 0.50 1 0.50 0.

D2 (0.36) 0 0.42 0.53 1 0.11 0.

Relative Weights of Attributes and Utilities of Six Sites In terms of Attributes

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 Calculate the overall utility using the additive utility function

U(site 1) = kA∙(kA1∙U1, A1+ kA2∙U1, A2+kA3∙U1, A3+kA4∙U1,,A4 + kA5∙U1, A5) +

KB∙(KB1∙U1, B1 +kB2∙U1,B2) + kC∙(kC1∙U1, C1+ kC2∙U1, C2+kC3∙U1, C3) +

kD∙(kD1∙U1, D1+ kD2∙U1, D2)

U(site 2) = kA∙(kA1∙U2, A1+ kA2∙U2, A2+kA3∙U2, A3+kA4∙U2,,A4 + kA5∙U2, A5) +

KB∙(KB1∙U2, B1 +kB2∙U2,B2) + kC∙(kC1∙U2, C1+ kC2∙U2, C2+kC3∙U2, C3) +

kD∙(kD1∙U2, D1+ kD2∙U2, D2)

Utility of site 1 w.r.t attribute A1 (^) Expected utility of site 1 w.r.t attribute A