Subjective Inputs in MCDM
David L. Olson
University of Nebraska
INFORMS – Miami, November 2001
Basic Preference Model
K
Valuej   wi  sij
i 1
i  criterion index
j  alternativ e index
K  number of criteria
wi  weight of criterion i
sij  score of alternativ e j on criterion i
Can use multiplicative model for interactions
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
A
B
C
D
E
F
Payment
1500
1600
1700
1700
1800
2000
Location
20th & A
30th & B
40th & G
50th & U
51st & V
62th & Y
Age
40 years
35 years
20 years
30 years
10 years
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 Utilities
anchor 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]
• Age > Pay
[0,2000]>[50,1200]
• Weights:
– Pay
– Location
– Age
0.167
0.500
0.333
[0,2000]=[20,1200]
[0,2000]=[30,1200]
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
B
C
9
8
17
0.857
0.867
0.717
0.3
0.5
0.6
D
E
F
41
43
57
0.317
0.283
0.050
0.7
0.6
0.4
Subjective Assessment - Age
• New good (but broken in a little better); Very old is good too
Alt
Age Objective
Subjective
A
B
C
D
40
35
20
30
0.271
0.390
0.695
0.500
0.7
0.6
0.7
0.5
E
F
10
20
0.860
0.695
0.8
0.7
Mixed Assessment
objective in blue; subjective in red
•
•
•
•
•
•
•
Alt Pay SUF Blocks
A 1500 0.857
9
B 1600 0.772
8
C 1700 0.656
17
D 1700 0.656
41
E 1800 0.500
43
F 2000 0.000
57
SUF
0.3
0.5
0.6
0.7
0.6
0.4
Age
40
35
20
30
10
20
SUF
0.7
0.6
0.7
0.5
0.8
0.7
Resultant
Pay would yield A; Location & Age yield E
wgt
Alt
A
B
C
D
E
F
0.167
Pay
0.857
0.772
0.656
0.656
0.500
0.000
0.5
Loc
0.3
0.5
0.6
0.7
0.6
0.4
0.333
Age
0.7
0.6
0.7
0.5
0.8
0.7
Sum
Prod
0.526
0.579
0.643
0.626
0.650
0.433
Rank
5
4
2
3
1
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