Subjective Inputs in MCDM David L. Olson University of Nebraska INFORMS – Miami, November 2001.

Subjective Inputs in MCDM

David L. OlsonUniversity of Nebraska

INFORMS – Miami, November 2001

Basic Preference Model

Can use multiplicative model for interactions

ijs

iw

K

j

i

swValue

ij

i

K

iijij

criterion on ealternativ of score

criterion ofweight

criteria ofnumber

index ealternativ

indexcriterion 1

James G. March

Bell Journal of Economics [1978]

• Rational choice involves guesses:– About future consequences of current actions– About future preferences of those consequences

Administrative Science Quarterly [1996]

• Alternatives & their consequences aren’t given, but need to be discovered & estimated

• Bases of action aren’t reality, but perceptions of reality• Supplemental exchange theories emphasize the role of

institutions in defining terms of rationality

Overview

• Inputs to preference models involve subjectivity– Weights are function of individual

– Scores also valued from perspective of individual

• Subjective assessment MAY be more accurate• Purpose of analysis should be to design better

alternatives

Objective Measures

• Objective preferred– can measure

• past profit, after tax

• Subjective– know conceptually, but can’t accurately

measure• response to advertising

How Subjective Might be More Accurate

• Want to buy house

• Criteria: monthly payment

location

age

• Alternatives: six among hundreds

House Payment Location Age

A 1500 20th & A 40 years

B 1600 30th & B 35 years

C 1700 40th & G 20 years

D 1700 50th & U 30 years

E 1800 51st & V 10 years

F 2000 62th & Y 20 years

Objective: Payment

• Might be able to fit function (could be nonlinear)– Less is always better than more– Continuous

Payment: $1800/mo=0.5

• U(x)=1.096-0.0024730.003047x

Distance: linear

• U(x)=1-0.01667x

Age: 30 years=0.5

• U(x)=1.784-0.78410.01644x

Single-Attribute Utilitiesanchor points given in red

Alt Pay SUF Blocks SUF Age SUF

A 1500 0.857 9 0.850 40 0.271

B 1600 0.772 8 0.867 35 0.390

C 1700 0.656 17 0.717 20 0.695

D 1700 0.656 41 0.317 30 0.500

E 1800 0.500 43 0.283 10 0.860

F 2000 0.000 57 0.050 20 0.695

Weight Tradeoffs

• Location > Pay[0,2000]>[60,1200] [0,2000]=[20,1200]• Age > Pay[0,2000]>[50,1200] [0,2000]=[30,1200]• Weights:

– Pay 0.167– Location 0.500– Age 0.333

Preference Model Result

Caveats

• There could be preferential dependence– System allows for nonlinear interaction

• Location not as simple as objectively measured– Could improve by splitting

• Minimize distance from work• Comfort zone – want at least 5 blocks from work• Close to school – but not across the street• Pleasantness of the area not a function of distance

• Age could be non-monotonic– Prefer 5 years old to new– Between 5 and 30, prefer newer– Over 30 gains in value

Subjective Assessment more flexible - Location

Not simply a function of distance (A & B)

Even if it were, too close & too far both bad

Alt Blocks Objective Subjective

A 9 0.857 0.3

B 8 0.867 0.5

C 17 0.717 0.6

D 41 0.317 0.7

E 43 0.283 0.6

F 57 0.050 0.4

Subjective Assessment - Age

• New good (but broken in a little better); Very old is good too

Alt Age Objective Subjective

A 40 0.271 0.7

B 35 0.390 0.6

C 20 0.695 0.7

D 30 0.500 0.5

E 10 0.860 0.8

F 20 0.695 0.7

Mixed Assessmentobjective in blue; subjective in red

• Alt Pay SUF Blocks SUF Age SUF

• A 1500 0.857 9 0.3 40 0.7

• B 1600 0.772 8 0.5 35 0.6

• C 1700 0.656 17 0.6 20 0.7

• D 1700 0.656 41 0.7 30 0.5

• E 1800 0.500 43 0.6 10 0.8

• F 2000 0.000 57 0.4 20 0.7

ResultantPay would yield A; Location & Age yield E

wgt 0.167 0.5 0.333 Sum

Alt Pay Loc Age Prod Rank

A 0.857 0.3 0.7 0.526 5

B 0.772 0.5 0.6 0.579 4

C 0.656 0.6 0.7 0.643 2

D 0.656 0.7 0.5 0.626 3

E 0.500 0.6 0.8 0.650 1

F 0.000 0.4 0.7 0.433 6

Ilya Prigogine, The End of Certainty, The Free Press, 1996

• Arrow of Time: past & future play different roles– We can see the past (with measurement error)

– The future is unknown• The issue of debate is whether it is knowable

• Decartes & Leibniz sought certainty– Led to Newton & Einstein

• Einstein: physics as triumph of reason over violent world – separate objective from uncertain & subjective

• Science seeks the power of reason

Prigogine

• Conflict: determinism & freedom

• Entropy: some things irreversible

• Natural instability captured in distributions

• Probability is the narrow path between the deterministic world and the arbitrary world of pure chance

Parallels: Probability & Preference

Donald Gillies, Philosophical Theories of Probability, London: Routledge, 2000

• Four interpretations of probability– LOGICAL

• Given same evidence, all rational humans have same belief

– SUBJECTIVE• Differences of opinion are allowed

– FREQUENCY• Probability the limiting frequency of outcome in long series

– PROPENSITY• Inherent propensity: frequency for large number of repetitions

Gillies, cont.

• OBJECTIVE: independent of humans– An ideal, Platonic

– The point, however, is to help humans decide

• SUBJECTIVE:– Preferences inherently subjective

– Utilities of alternatives over criteria also ultimately subjective

• Can measure objectively

• Value to decision maker still subjective

Herbert Simon: Reason in Human Affairs, Stanford University Press, 1983

• Facts usually gathered in with instruments permeated with theoretical assumptions– Impossible to generate unassailable general

propositions from particular facts– None of the rules of inference currently

accepted are capable of generating normative outputs

Simon, cont.

• Subjective Expected Utility– Conceptually deserving a prominent place in Plato’s

heaven of ideas• Impossible to employ

– Assumes human understands the range of alternative choices available, their joint probability distribution

– Never has been applied and never can be• Humans have neither the facts nor consistent structure of

values nor the reasoning power required to apply SEU

Simon, cont.

Instead of SEU, Simon suggested

• Rational adaptation

• Mental models

• Satisficing as a way to cope

March, redux

March & Olsen, Institutional Perspectives on Political Institutions, Governance 9, 1996, 246-264

• Supplemental exchange theories emphasize the role of institutions in defining terms of rational exchange

• Rational action depends on:– subjective perceptions of alternatives– their consequences– and their evaluations

Conclusions-I

• Prigogine: The world involves high levels of uncertainty

• Gillies: Variety of probabilities, including subjective

• Simon: Subjective Expected Utility impossible to employ

• March: Rationality is flexible

Conclusion

• Measures of alternative future performance, preference for that performance both subjective

• Objective measures not always better

• Focus should be on:– Learning (changing preference)– Design of better alternatives