Classic Decision Puzzlers 1. conjunction fallacy Tversky, A. & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90, 293-315. A health survey was conducted in a representative sample of adult males in Chicago of all ages and occupations. Mr. F was included in the sample. He was selected by chance from the list of participants. Please rank the following statements in terms of which is most likely to be true of Mr. F. (1=more likely to be true, 6=least likely) ____ Mr. F smokes more than 1 cigarette per day on average. ____ Mr. F has had one or more heart attacks. ____ Mr. F had a flu shot this year. ____ Mr. F eats red meat at least once per week. ____ Mr. F has had one or more heart attacks and he is over 55 years old. ____ Mr. F never flosses his teeth. (results: 58% conjunction fallacy) 2. conjunction fallacy (Tversky, A. & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90, 293-315.) A 55-year old woman had pulmonary embolism (obstruction of a blood vessel in the lungs) documented angiographically (radiological picture of blood vessels) 10 days after a cholecystectomy (removal of gall bladder). Please rank order the following in terms of the probability that they will be among the conditions experienced by the patient (use 1 for the most likely and 6 for the least likely). Naturally, the patient could experience more than one of these conditions. _____ dyspnea (shortness of breath) and hemiparesis (partial paralysis) _____ calf pain _____ pleuritic chest pain _____ syncope (temporary suspension of circulation and respiration) and tachycardia (rapid heart rate) _____ hemiparesis (partial paralysis) _____ hemoptysis (coughing up blood) (91% conjunction fallacy) 3. Omission bias, (Ritov, I. & Baron, J. (1990). Reluctance to vaccinate: Omission bias and ambiguity. Journal of Behavioral Decision Making, 3, 263-277.) In the state where you live, there have been several epidemics of a certain kind of flu, which can be fatal to children under 3. The probability of each child getting the flu is 1 in 10, but only 1 in 100 children who get the flu will die from it. This means 10 out of 10,000 children will die. A vaccine for this kind of flu has been developed and tested. The vaccine eliminates the probability of getting the flu. The vaccine, however, might cause side effects that are also sometimes fatal. The children who die from the side effects of the vaccination are not necessarily the same ones who would die from the flu. Imagine that you are married and have one child, a one-year old. You wonder whether you should vaccinate your child. Your child will have a 10 in 10,000 chance of dying from the flu without vaccination. Would you vaccinate your child if the overall death rate for vaccinated children were (check those in which you would vaccinate): _____ 0 in 10,000 _____ 1 in 10,000 _____ 2 in 10,000 _____ 3 in 10,000 _____ 4 in 10,000 _____ 5 in 10,000 _____ 6 in 10,000 _____ 7 in 10,000 _____ 8 in 10,000 _____ 9 in 10,000 _____ 10 in 10,000 (57% stop before 9) 4. Sunk Cost (adapted from Arkes, H.R. & Blumer, C. (1985). The psychology of sunk cost. OBHDP, 35, 124-140.) a. As the president of a large pharmaceutical company, you have invested 10 million dollars of the company's money into a research project. The purpose was to develop a vaccine that would prevent people from acquiring HIV. When the project is 90% completed, another firm begins marketing a vaccine that prevents HIV infection. Also, it is apparent that their vaccine is more effective and less expensive than the vaccine your company is developing. The question is: should you invest the last 1 million dollars of your research funds to finish your HIV vaccine? _____ Yes (85%) _____ No (15%) b. As the president of a large pharmaceutical company, you have received a suggestion from one of your employees. The suggestion is to use the last 1 million dollars of your research funds to develop a vaccine that would prevent people from acquiring HIV. However, another firm has just begun marketing a vaccine that prevents HIV infection. Also, it is apparent that their vaccine is more effective and less expensive than the vaccine your company could develop. The question is: should you invest the last 1 million dollars of your research funds to develop the proposed HIV vaccine? _____ Yes (17%) _____ No (83%) 5. Allais paradox (adapted from Allais, M. (1953). Le comportement de l'homme rationnel devant le reque: Critique des postulates et axioms de l'ecole americaine. Econometrica, 21. 503-546.) Tragically, you have just discovered that you suffer from a fatal disease. Although you are only 25 years old, you will die within the next few months if you do not receive treatment. However, two new treatments are available that could prolong your life. The treatments differ in the number of extra years of life they could grant you, and the probability of achieving those extra years of life. Which treatment do you choose? a. Option A: live 10 years with p = 1.0 Option B: live 10 years with p = .89 live 50 years with p = .10 live 0 years with p = .01 b. Option C: live 10 years with p = .11 live 0 years with p = .89 Option D: live 50 years with p = .10 live 0 years with p = .90 6. Loss aversion (from Thaler, R. (1980). Toward a positive theory of consumer choice. Journal of Economic Behavior and Organization, 1, 39-60.) a. Assume you have been exposed to a disease which if contracted leads to a quick and painless death within a week. The probability you have the disease is 0.001. What is the maximum you would be willing to pay for a cure? b. Suppose volunteers were needed for research on the above disease. All that would be required is that you expose yourself to a 0.001 chance of contracting the disease. What is the minimum payment you would require to volunteer for this program? (You would not be allowed to purchase the cure.) Maximum willingness to pay: $200 Minimum willingness to accept: $10,000 7. Reflection framing effect (from Kahneman, D. & Tversky, A. (1984). Choices, values, and frames. American Psychologist, 39, 341-350.) Imagine that the U.S. is preparing for outbreak of an unusual disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the program are as follows: a. If Program A is adopted, 200 people will be saved. (72%) If Program B is adopted, there is a one-third probability that 600 people will be saved and a two-thirds probability that no people will be saved. (28%) b. If Program C is adopted, 400 people will die. (22%) If Program D is adopted, there is a one-third probability that nobody will die and a two-thirds probability that 600 people will die. (78%) 8. Framing effect (McNeil, et al. (1982). On the elicitation of preferences for alternative therapies. NEJM, 306, 1259-1262.) Surgery for lung cancer involves an operation on the lungs. Most patients are in the hospital for two or three weeks and have some pain around their incision; they spend a month or so recuperating at home. After that, they generally feel fine. Radiation therapy for lung cancer involves the use of radiation to kill the tumor and requires coming to the hospital about four times a week for six weeks. Each treatment takes a few minutes and during the treatment, patients lie on a table as if they were having an x-ray. During the course of treatment, some patients develop nausea and vomiting, but by the end of the six weeks they also generally feel fine. Thus, after the initial six or so weeks, patients treated with either surgery or radiation feel about the same. a. Of 100 people having surgery, 90 live through surgery and the post operative period, 68 are alive at the end of the first year, and 34 people are alive at the end of 5 years. Of 100 people having radiation therapy, all live through the treatment, 77 are alive at the end of the first year and 22 are alive at the end of 5 years. The treatment summaries are: Number of people alive surgery radiation during treatment 90% 100% by 1 year 68% 77% by 5 years 34% 22% Which treatment do you prefer? ____ surgery (82%) _____ radiation (18%) b. Of 100 people having surgery, 10 die in surgery or the post operative period, 32 are dead at the end of the first year, and 66 have died at the end of 5 years. Of 100 people having radiation therapy, none die in the treatment, 23 die by the end of the first year and 78 have died at the end of 5 years. The treatment summaries are: Number of people dead surgery radiation during treatment 10% 0% by 1 year 32% 23% by 5 years 66% 78% Which treatment do you prefer? ____ surgery (56%) _____ radiation (44%) 9. Competing hypothesis heuristic (Wolf, F.M., Gruppen, L.D., & Billi, J.E. (1985). Differential diagnosis and the competing- hypothesis heuristic. JAMA, 253, 2858-2862.) A patient has either disease A or disease B. Disease A and disease B have equal frequencies in the population. The patient has both a fever and a rash. 66% of people with disease A have a fever (that is, p(fever/A)=.66). The table below shows 4 pieces of information. You already have one of them. You may have one more piece of information before you make your diagnosis. What information do you choose? Disease A Disease B Fever p(fever/A)=.66 p(fever/B)= ? Rash p(rash/A)= ? p(rash/B)= ? Please circle the 1 additional piece of information you would like to have before making a diagnosis. 10. Multiple alternatives (from Redelmeier, D.A. & Shafir, E. (1995). Medical decision making in situations that offer multiple alternatives. JAMA, 273(4), 302-305.) The patient is a 67-year-old farmer with chronic right hip pain. The diagnosis is osteoarthritis. You have tried several nonsteroidal anti-inflammatory agents (e.g., aspirin, naproxen, and ketoprofen) and have stopped them because of either adverse effects or lack of efficacy. You decide to refer him to an orthopedic consultant for consideration for hip replacement surgery. The patient agrees to this plan. basic version: Before sending him away, however, you check the drug formulary and find that there is one nonsteroidal medication that this patient has not tried (ibuprofen). What do you do? A. refer to orthopedics and also start ibuprofen B. refer to orthopedics and do not start any new medication (53%) expanded version: Before sending him away, however, you check the drug formulary and find that there are two nonsteroidal medications that this patient has not tried (ibuprofen and piroxicam). What do you do? A. refer to orthopedics and also start ibuprofen B. refer to orthopedics and also start piroxicam C. refer to orthopedics and do not start any new medication (72%) 11. Attraction effect (Huber, J., Payne, J.W. & Puto, C. (1982). Adding asymmetrically dominated alternatives: Violations of regularity and the similarity hypothesis. Journal of Consumer Research, 9(1), 90-98; Chapman, G.B. & Malik, M.M. (1995). The attraction effect in prescribing decisions and consumer choice. Medical Decision Making, 15, 414.) Imagine that one of your patients suffers from migraine headaches that last about 3 hours and involve intense pain, nausea, dizziness, and hyper-sensitivity to bright lights and loud noises. The patient usually needs to lie quietly in a dark room until the headache passes. Out of every 365 days (1 year), this patient has a migraine headache on about 100 of those days (8.3 per month). Of course, on a day when the patient has a headache, she doesn't spend the entire day in pain, but only about 3 hours of that day. You are considering three medications that you could prescribe for this patient. All three medications have only negligible side effects, and any side effects are the same for the three. Each medication comes in the form of pills that must be taken once per day. The medications differ in effectiveness and cost. The patient has a low income and must pay the cost because her insurance plan does not cover any of these medications. And of course the patient is also the one who appreciates the effectiveness. 3 option version: drug A: 9% reduces the number of headaches from 100 days with a headache per year to 30 days with a headache per year. It costs $350 per year. drug B: 81% reduces the number of headaches from 100 days with a headache per year to 50 days with a headache per year. It costs $100 per year. drug C: 0% reduces the number of headaches from 100 days with a headache per year to 60 days with a headache per year. It costs $100 per year. 2 option version: drug A: 36% reduces the number of headaches from 100 days with a headache per year to 30 days with a headache per year. It costs $350 per year. drug B: 64% reduces the number of headaches from 100 days with a headache per year to 50 days with a headache per year. It costs $100 per year. 12. Outcome bias (Baron, J. and Hershey, J.C. (1988). Outcome bias in decision evaluation. JPSP, 54, 569-579.) A 55-year-old man had a heart condition. He had to stop working because of chest pain. He enjoyed his work and did not want to stop. His pain also interfered with other things, such as travel and recreation. A type of bypass operation would relieve his pain and increase his life expectancy from age 65 to age 70. However, 8% of the people who have this operation die from the operation itself. His physician decided to go ahead with the operation. (a) The operation succeeded. (b) The operation failed and the man died. You may assume the following: 1. The physician who made the decision first consulted the patient. The patient could not decide and asked the physician's advice. The physician knew that the patient would accept this advice. Hence, it is the physician who makes the decision on the patient's behalf. 2. The physician who made the decision is not the one who carried out the procedure. 3. The physician who made the decision had no more relevant information than you are given, and there is no more relevant information that can be discovered. Evaluate the physician's decision to go ahead with the operation (circle one): 3 =clearly correct, and the opposite decision would be inexcusable 2 =correct, all things considered 1 =correct, but the opposite would be reasonable too 0 =decision and its opposite are equally good -1 =incorrect, but not unreasonable -2 =incorrect, all things considered -3 =incorrect and inexcusable (results: 0.85 (a) -.05 (b)) 13. Hindsight bias (Arkes, et al. (1981). Hindsight bias among physicians weighing the likelihood of diagnoses. J. of Applied Psych., 66, 252-254.) version a. This is a case history of Post streptococcal arthritis in an adult (rheumatic fever) version b. This is a case history of Serum hepatitis in pre- icteric (pre-jaundice) phase. A 37-year-old male bartender had been well until he developed increasing pain in his left knee, which became hot and swollen. A few days later, pain, swelling, and heat developed in his left wrist and right knee. Examination revealed swelling, heat, and effusion in both knees and left wrist. There were no deformities, His liver was enlarged 2 cm below the costal margin. CBC was normal. ESR was 30 mm (westergren). Latex test was neg. SMA 12 was not back yet. HbsAg was not back yet. Joint fluid contains 20,000 WBC; 80% ploys: viscosity low. There were excess pus cells in urine. Fever was 100oF. Now, please assign to each of the four possible diagnoses the probability you think you would have assigned if you did not know the actual diagnoses. Be sure the probabilities sum to 100%. A B 37% 35% _____ Reiter's syndrome (incomplete) (disease of uncertain cause characterized by arthritis, inflammation of eyelid (conjunctivitis), and inflammation of urethra (urethritis). 31% 16% _____ Post streptococcal arthritis in an adult (rheumatic fever) 10% 12% _____ Gout (a metabolic disease marked by inflammation of the joints) 22% 38% _____ Serum hepatitis in pre-icteric (pre-jaundice) phase. 14. 3 doors problem You are a contestant on a game show. Your host, Monty Hall, presents you with three doors: door A, door B, and door C. Behind one of these doors lies $1 million. Behind the other two doors lies nothing. Monty Hall asks you to select one of the doors without knowing what is behind each door. After you have selected one of the doors, Monty Hall removes one of the remaining doors. The door he removes definitely does not have prize. Monty Hall then asks you whether you would like to keep the door you originally selected, or whether you would like to switch to the other remaining door ***. After you have made your selection, you will receive whatever is behind the door you selected. At the point marked by the *** above, would you (check one). ____ keep the door you originally selected or ____ switch to the other remaining door What is the probability that the $1 million is behind ____ the door you originally selected ____ the other remaining door.