Subjective Inputs in MCDM

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

2. Basic Preference Model Can use multiplicative model for interactions

3. 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

4. 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

5. Objective Measures • Objective preferred • can measure • past profit, after tax • Subjective • know conceptually, but can’t accurately measure • response to advertising

6. How Subjective Might be More Accurate • Want to buy house • Criteria: monthly payment location age • Alternatives: six among hundreds

8. Objective: Payment • Might be able to fit function (could be nonlinear) • Less is always better than more • Continuous

9. Payment: $1800/mo=0.5 • U(x)=1.096-0.0024730.003047x

10. Distance: linear • U(x)=1-0.01667x

11. Age: 30 years=0.5 • U(x)=1.784-0.78410.01644x

12. Single-Attribute Utilitiesanchor points given in red

13. Weight Tradeoffs • Location > Pay [0,2000]>[60,1200] [0,2000]=[20,1200] • Age > Pay [0,2000]>[50,1200] [0,2000]=[30,1200] • Weights: • Pay0.167 • Location 0.500 • Age 0.333

14. Preference Model Result

15. 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

16. Subjective Assessment more flexible - Location Not simply a function of distance (A & B) Even if it were, too close & too far both bad

17. Subjective Assessment - Age • New good (but broken in a little better); Very old is good too

18. Mixed Assessmentobjective in blue; subjective in red • Alt Pay SUF Blocks SUFAge SUF • A 1500 0.857 9 0.340 0.7 • B 1600 0.772 8 0.535 0.6 • C 1700 0.656 17 0.620 0.7 • D 1700 0.656 41 0.7300.5 • E 1800 0.50043 0.610 0.8 • F 2000 0.000 57 0.420 0.7

19. ResultantPay would yield A; Location & Age yield E

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. Simon, cont. Instead of SEU, Simon suggested • Rational adaptation • Mental models • Satisficing as a way to cope

27. March, redux March & Olsen, Institutional Perspectives on Political Institutions, Governance9, 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

28. 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

29. 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