Encounters With Risk PPP (Perception,Policy and Practice) During a Career in Operations Research

1. Encounters With Risk PPP(Perception,Policy and Practice) During a Career in Operations Research Stephen Pollock University of Michigan

2. A PERSONAL VIEW OF RISK PPP • MY EXPERIENCES WITH RISK PPP WHILE DOING O.R. • CLEARLY A BIASED PERSPECTIVE • A NUMBER OF ANECDOTAL EXAMPLES THAT MIGHT SERVE TO FORESHADOW OR TIE TOGETHER THE DIVERSE ISSUES OF THIS WORKSHOP

3. O.R./I.E/ ENGINEERING? • OPERATIONAL PROBLEM SOLVING • MOSTLY MATHEMATICAL MODELS • ALSO A WAY OF THINKING: • WATER GLASS • GUILLOTINE • FORK • UNCERTAINTY ALWAYS PRESENT

4. CONSEQUENCE x1 d3 p1 d1 CONSEQUENCE x2 1-p1 d2 p2 CONSEQUENCE x3 d4 1- p2 CONSEQUENCE x4 DECISION CHANCE TYPICAL DECISION ANALYSTS VIEW

5. d f(x|d) CHANCE DECISION MORE GENERIC VIEW CONSEQUENCE x

6. d’(d,x) f(y|d’,x) d f(x|d) DECISION CHANCE* DECISION CHANCE *”UNCERTAINTY” CONSEQUENCE (X,Y) MORE GENERAL VIEW

7. d f(x|d) X DECISION CONSEQUENCE UNCERTAINTY WHERE DOES RISK POLICY AND PERCEPTION FIT THIS SCHEMA?

8. d f(x|d) X POLICY CONSEQUENCE UNCERTAINTY RISK WHERE DOES RISK POLICY AND PERCEPTION FIT THIS SCHEMA?

9. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY RISK • RISK HAS TWO NECESSARY ASPECTS: • UNCERTAINTY -- WHAT WILL HAPPEN? • CONSEQUENCES -- WHY DOES ONE CARE? • CONFOUNDING THESE ARE • CONCEPTION (WHAT ONE THINKS THE “RISK” ASPECTS ARE) • PERCEPTION (HOW ONE “SEES” THE RISK ASPECTS) • CODIFICATION (HOW ONE “TALKS” ABOUT -- OR SHOULD TALK ABOUT -- RISK ASPECTS)

10. d f(x|d) X POLICY CONSEQUENCE UNCERTAINTY • THE POLICY COMPONENT (DECISION/MITIGATION) -- WHAT SHOULD ONE DO? • THIS ALSO INVOLVES A MIXTURE OF • CONCEPTION (WHERE DO POSSIBLE DECISIONS/OPTIONS/POLICIES COME FROM?) • PERCEPTION (HOW ONE “SEES” OPTIONS) • CODIFICATION (HOW TO DESCRIBE OPTIONS)

11. ?? d f(x|d) X POLICY CONSEQUENCE UNCERTAINTY FINALLY (AND PERHAPS MOST IMPORTANT): PRACTICE (WHAT ACTUALLY GETS DONE)

12. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY RISK TO THE “PERSON IN THE STREET”, ARE THE FOLLOWING “RISKY”? • BUNGEE JUMPING • NOT BUCKLING UP • BUCKLING UP • PICKING UP A $20 BILL FROM THE STREET • INOCULATING A CHILD AGAINST MEASLES • NOT INOCULATING A CHILD AGAINST MEASLES • LIVING • “EVERYDAY” ANSWERS SHOW ALL SORTS OF COGNITIVE BIASES, BUT NEGATIVE FRAMING SEEMS TO BE PERVASIVE

13. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY RISK SOME “EVERYDAY”*CONCEPTION, PERCEPTION, AND CODIFICATION OFRISK: *NY TIMES, NEW YORKER, NPR, ETC.

14. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY RISK “EVERYDAY” CONCEPTION, PERCEPTION AND CODIFICATION OFRISK Souffle (NPR 7/23) David Denby’s review of “A Fine Romance”: (referring to romantic film comedies) “ …with a married couple, romance is like “…a duel with slingshots at close quarters –- exciting but a little risky” (New Yorker 7/23)

15. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY RISK • “EVERYDAY” CONCEPTION, PERCEPTION AND CODIFICATION OFRISK • “The Black Swan” popular book dealing with “The role of the unexpected” in financial trading (NYT B.R. 7/29) • ”What is “unexpected”? • {13 craps in a row} • {this particular person dies within the next five years} • {this levee fails} • {a levee fails}

16. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY RISK “EVERYDAY” CONCEPTION, PERCEPTION AND CODIFICATION OFRISK Louis Menan’s review of Caplan’s “The Myth of the Rational Voter: Why Democracies Choose Bad Politics” (New Yorker 7/19) “You can’t use futures markets for assessing probabilities like you can for guessing the number of jellybeans in a bowl, or odds in sports gambling.”

17. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY RISK “EVERYDAY” CONCEPTION, PERCEPTION AND CODIFICATION OFRISK Louis Menan’s (continued): “People exaggerate the risk of loss; they like the status quo and tend to regard it as a norm; they overreact to sensational but unrepresentative information (shark attack phenomenon) … Most people, even if you explained …the economically rational choice … would be reluctant to make it, because … in particular, they want to protect themselves from the downside of change. They would rather feel good about themselves than to maximize ... profit.”

18. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY RISK “EVERYDAY” CONCEPTION, PERCEPTION AND CODIFICATION OFRISK Levitt and Dubner’s article “The Jane Fonda Effect” “... in 1916 … the legendary economist Frank Knight made a distinction between two key factors in decision making: risk and uncertainty. The cardinal difference, he declared, is that risk — however great — can be measured, whereas uncertainty cannot.” (NYT Magazine 9/16)

19. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY RISK “EVERYDAY” CONCEPTION, PERCEPTION AND CODIFICATION OFRISK Levitt and Dubner’s* article “The Jane Fonda Effect” “… Has fear of a [nuclear] meltdown subsided, or has it merely been replaced by the fear of global warming? …. in 1916 … the legendary economist Frank Knight made a distinction between two key factors in decision making: risk and uncertainty. The cardinal difference, he declared, is that risk — however great — can be measured, whereas uncertainty cannot.” (NYT Magazine 9/16) * Authors of “Freakonomics”

20. d f(x|d) X POLICY CONSEQUENCE UNCERTAINTY RISK “EVERYDAY” CONCEPTION, PERCEPTION AND CODIFICATION OFRISK AND POLICY HELMET WEARING BY NHL PLAYERS (1979-80 SEASON REQUIREMENT)

21. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY (ANECDOTAL) CONCEPTION, PERCEPTION AND CODIFICATION OFUNCERTAINTY HOW MUCH TIME TO CARRY A GARBAGE CAN FROM A BACK YARD TO THE CURB? WHICH CUTTER HEADS WERE THE DEFECTIVE ONES? WILL A SUB PASS BY DURING AN ASWEX?

22. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY MOST PEOPLE PREFER A CONCEPTION, PERCEPTION AND CODIFICATION OFUNCERTAINTY ELLSBERG PARADOX BAG A HAS 500 RED BALLS AND 500 GREEN BALLS BAG B HAS 1000REDANDGREEN BALLS YOU CHOSE A BAG, DRAW A BALL AND WIN $100 IF IT IS RED. WHICH BAG DO YOU PREFER?

23. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY CONCEPTION, PERCEPTION AND CODIFICATION OFUNCERTAINTY ELLSBERG PARADOX DEMONSTRATES MANY PEOPLE’S PREFERENCE FOR “CRISP” PROBABILITIES VS. “AMBIGUOUS” ONES

24. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY CONCEPTION, PERCEPTION AND CODIFICATION OFUNCERTAINTY ELLSBERG PARADOX -- PREFERENCE FOR “CRISP” PROBABILITIES VS. “AMBIGUOUS” ONES BAG A HAS 450 RED BALLS AND 550 GREEN BALLS BAG B HAS 1000 RED AND GREEN BALLS YOU CHOSE A BAG, DRAW A BALL AND WIN $100 IF IT IS RED. NOW WHICH BAG DO YOU PREFER?

25. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY CONCEPTION, PERCEPTION AND CODIFICATION OFUNCERTAINTY ELLSBERG PARADOX -- PREFERENCE (?) FOR “CRISP” PROBABILITIES VS. “AMBIGUOUS” ONES BAG A HAS 200 RED BALLS AND 800 GREEN BALLS BAG B HAS 1000 RED AND GREEN BALLS YOU CHOSE A BAG, DRAW A BALL AND WIN $100 IF IT IS RED. NOW WHICH BAG DO YOU PREFER?

26. d f(x|d) X UNCERTAINTY CONSEQUENCE POLICY (ANECDOTAL) CONCEPTION, PERCEPTION AND CODIFICATION OFUNCERTAINTY “CRISP” VS. “AMBIGUOUS” PROBABILITIES • TEST OF CONCEPT OF TOTAL RE-DESIGN OF A GLOBAL LOGISTIC CHAIN VIA M.C. SIMULATION • USED PREVIOUS YEAR’S DEMAND DISTRIBUTION FOR TO PROVE OUT RE-DESIGN CONCEPT • MASSIVE CORPORATE PRESSURE AGAINST USING DISTRIBUTION OVER SIMULATION MODEL’S PARAMETERS -- SINCE “WE WON’T KNOW WHAT THEY MIGHT BE”

27. d f(x|d) X UNCERTAINTY CONSEQUENCE POLICY (ANECDOTAL) CONCEPTION, PERCEPTION AND CODIFICATION OFUNCERTAINTY “CRISP” VS. “AMBIGUOUS” PROBABILITIES • ORDER SIZE FOR CRITICAL MATERIAL BASED ON PROJECTED PRODUCT SALES AND MATERIAL PRICE • SALES BASED UPON “TARGETS” • MATERIAL PRICE BASED ON SPECIALIST’S FORECASTS • MASSIVE CORPORATE PRESSURE AGAINST USING DISTRIBUTION OVER EITHER SALES OR PRICES “THESE ARE EXPERTS, THEY SHOULD KNOW THE ANSWER”

28. d f(x|d) X UNCERTAINTY CONSEQUENCE POLICY uncertainty in Probability uncertainty in Loss Probability {loss > v} 95% “mean” prob. 5% v ($) CONCEPTION, PERCEPTION AND CODIFICATION OFUNCERTAINTY AMBIGUITY EXPRESSED AS PROBABILITY DISTRIBUTIONS OVER PROBABILITIES (REF: H. KUNREUTHER)

29. d f(x|d) X UNCERTAINTY CONSEQUENCE POLICY (ANECDOTAL) CONCEPTION, PERCEPTION AND CODIFICATION OFUNCERTAINTY WHAT IF ADVERSARIES CHOOSE THE PROBABILITIES?

30. d’(x) f(y|x,d’(x)) d f(x|d) d f(x|d) X OFFENSE PLAYER PERSONNEL PLAY OUTCOME (y) DEFENSIVE ALIGNMENT AUDIBLE PLAY CALL UNCERTAINTY CONSEQUENCE POLICY ADVERSARIAL RISK ANALYSIS FOOTBALL ANALOGY [OFFENSE’S VIEW]

31. d f(x|d) X POLICY CONSEQUENCE UNCERTAINTY (ANECDOTAL) CONCEPTION, PERCEPTION AND CODIFICATION OFPOLICY WHAT IF THE DECISIONMAKER CHOOSES THE PROBABILITIES? CONSIDER THE MATHEMATICAL PROGRAMMING PROBLEM: min f(x) s.t. g(x, z) ≥ 0

32. d f(x|d) X POLICY CONSEQUENCE UNCERTAINTY (ANECDOTAL) CONCEPTION, PERCEPTION AND CODIFICATION OFPOLICY “CHANCE CONSTRAINED PROGRAMMING” min f(x) s.t. Prob. { g(x, Z) ≥ 0 } ≥ p WHERE Z IS NOW A RANDOM VARIABLE

33. d f(x|d) X POLICY CONSEQUENCE UNCERTAINTY .10 p(z) z x = 2M EXAMPLE: DETERMINE d = BANK’S CASH RESERVES BANK WANTS TO MINIMIZE d REGULATORS REQUIRE SMALL PROBABILITY OF RUNNING OUT OF CASH; Z = DEMAND FOR CASH (A R.V.) min d s.t. Prob. { Z ≥ d } ≥ .90

34. d .55 f(x|d) .01 X z POLICY CONSEQUENCE UNCERTAINTY x = .6M x = 2.1M Prob. = .2.8 HOW ABOUT A RANDOMIZED POLICY? min x s.t. Prob. {x ≥ Z} ≥ .90 Prob. { x > Z} = .2(.55) +.8(.99) = .901 (OK) E(X) = .2(.6M) + .8(2.1M) = 1.93 ( better than 2) BUT -- WOULD THE REGULATORS APPROVE??

35. d f(x|d) X POLICY CONSEQUENCE UNCERTAINTY (ANECDOTAL) CONCEPTION, PERCEPTION AND CODIFICATION OFPOLICY • CAMSHAFT HARDENING • SEWAGE TREATMENT IN *** • 1979 NHL HELMET REGULATION (REVISITED)

36. d f(x|d) X UNCERTAINTY CONSEQUENCE POLICY (ANECDOTAL) CONCEPTION, PERCEPTION AND CODIFICATION OFUNCERTAINTY A US FEDERAL DEPARTMENT REPORT USES, WITH LITTLE DIFFERENTIATION: PROBABILITY LIKELIHOOD CHANCE FREQUENCY RELATIVE PROBABILITY STOCHASTIC PROBABILITY

37. d f(x|d) X UNCERTAINTY CONSEQUENCE POLICY (ANECDOTAL) CONCEPTION, PERCEPTION AND CODIFICATION OFUNCERTAINTY A US FEDERAL DEPARTMENT, IN A PRA REPORT, USES, AS SYNONYMS: MEAN AVERAGE

38. d f(x|d) X UNCERTAINTY CONSEQUENCE POLICY (ANECDOTAL) CONCEPTION, PERCEPTION AND CODIFICATION OFUNCERTAINTY ANOTHER US FEDERAL DEPARTMENT USES, AS SYNONYMS: DISTRIBUTION FUNCTION DENSITY FUNCTION PROBABILITY FUNCTION PROBABILITY DISTRIBUTION DISTRIBUTION

39. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY RISK (ANECDOTAL) CONCEPTION, PERCEPTION AND CODIFICATION OFRISK (computation) FEDERAL DEPARTMENT REPORT: RISK = "the probability or frequency of an event multiplied by the consequences of the event”

40. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY RISK CONCEPTION, PERCEPTION AND CODIFICATION OFRISK Society for Risk Analysis (SRA) Glossary (http://sra.org/resources_glossary.php) RISK = “The potential for unwanted, adverse consequences to human life, health, property, or the environment; BUT THEN SRA GOES ON TO SAY: “estimation of risk is usually based on the expected value of the conditional probability of the event occurring times the consequence of the event given that it has occurred."

41. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY RISK CODIFICATION OFRISK IN A FORTHCOMING PROPOSEDLEXICON RISK = The potential for unwanted, adverse consequences. It is important to distinguish between the term "risk,” which involves uncertainties, consequences and conditioning statements, and "expected risk" [q.v.] which combines these factors using a linear additive operation. PROBABILITY = One of a set of numerical values between 0 and 1 assigned to a collection of random events (which are subsets of a sample space) in such a way that the assigned numbers obey axioms [ …]

42. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY MORE CODIFICATION FROM THE PROPOSEDLEXICON CONSEQUENCE (OUTCOME) = A description of a scenario, in terms of measurable factors, that a decision-maker may consider when assessing preferences over different scenarios; these factors are often random variables. EXPECTED RISK = A summary measure of risk for an event, scenario, etc., as expressed by the expected value of any one of the measurable consequences associated with the risk.

43. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY RISK • CODIFICATION OFUNCERTAINTY IN A FORTHCOMING PROPOSEDLEXICON • ALEATORY PROBABILITY = A measure of the uncertainty of an unknown event whose occurrence is governed by some random physical phenomena that are either: a) predictable, in principle, with sufficient information (e.g., tossing a die); or b) phenomena which are essentially unpredictable (radioactive decay). • EPISTEMIC PROBABILITY = A representation of uncertainty about propositions due to incomplete knowledge. Such propositions may be about either past or future events.

44. (ANECDOTE) “NEWSVENDOR” STADIUM HOTDOG DEMAND NORMAL SEASON CONTENDER

45. (ANECDOTE) “NEWSVENDOR” STADIUM HOTDOGS NORMAL SEASON PROBABILITY = ? CONTENDER PROB = 1-?

46. (ANECDOTE) “NEWSVENDOR” STADIUM HOTDOGS OVERALL SALES

47. (ANECDOTE) “NEWSVENDOR” STADIUM HOTDOGS WHICH PROBS ARE ALEATORY WHICH ARE EPISTEMIC? NORMAL SEASON, CONTENDER PROBABILITIES OR CONDITIONAL DEMAND DISTRIBUTIONS?

48. (ANECDOTE) “NEWSVENDOR” STADIUM HOTDOGS DIFFERENCE BETWEEN IGNORANCE AND APATHY?

49. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY (ANECDOTAL) CONCEPTION, PERCEPTION AND CODIFICATION OFCONSEQUENCES WE’RE REALLY TALKING ABOUT APPROPRIATE PERFORMANCE MEASURES THIS IS DIFFICULT ENOUGH TO DO IN DETERMINISTIC O.R. -- THE UNCERTAINTY ASPECT ONLY MAKES THINGS MORE “INTERESTING”

50. d f(x|d) X CONSEQUENCE UNCERTAINTY POLICY (ANECDOTAL) CONCEPTION, PERCEPTION AND CODIFICATION OFCONSEQUENCES SUBMARINE SEARCH: MINIMIZE EXPECTED TIME TO DETECT ? MAXIMIZE PROB. {DETECT TIME ≤ Tcritical} ?