Rationality Alan Kaylor Cline Department of Computer Sciences The University of Texas at Austin Based upon classic decision puzzlers collected by Gretchen Chapman of Rutgers University

1. Conjunction Fallacy: 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 random 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) 1. ____ Mr. F smokes more than 1 cigarette per day on average. 2. ____ Mr. F has had one or more heart attacks. 3. ____ Mr. F had a flu shot this year. 4. ____ Mr. F eats red meat at least once per week. 5. ____ Mr. F has had one or more heart attacks and he is over 55 years old. 6. ____ Mr. F never flosses his teeth.

1. Conjunction Fallacy: 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 random 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) 1. ____ Mr. F smokes more than 1 cigarette per day on average. 2. ____ Mr. F has had one or more heart attacks. 3. ____ Mr. F had a flu shot this year. 4. ____ Mr. F eats red meat at least once per week. 5. ____ Mr. F has had one or more heart attacks and he is over 55 years old. 6. ____ Mr. F never flosses his teeth. Choice 5 includes choice 2, yet in the survey 21% rated “5” more likely than “2”. Everyone should rank “2” more likely than “”5”.

For more information, see: Tversky, A. and Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90, Conjunction Fallacy:

2. Reflection Framing Effect: 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:

2. Reflection Framing Effect: 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: Group A is told: If Program A is adopted, 200 people will be saved. 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.

2. Reflection Framing Effect: 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: Group A is told: If Program A is adopted, 200 people will be saved. 67% 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. 33%

2. Reflection Framing Effect: 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: Group B is told: If Program C is adopted, 400 people will die. 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.

2. Reflection Framing Effect: 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: Group B is told: If Program C is adopted, 400 people will die. 8% 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. 92%

2. Reflection Framing Effect: Group B is told: If Program C is adopted, 400 people will die. 8% 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. 92% Group A is told: If Program A is adopted, 200 people will be saved. 67% 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. 33% The results are almost inverted even though Program A for Group A is logically equal to Program C for Group B and Program B for Group A is logically equal to Program D for Group B.

2. Reflection Framing Effect: Group B is told: If Program C is adopted, 400 people will die. 8% 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. 92% Group A is told: If Program A is adopted, 200 people will be saved. 67% 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. 33%

2. Reflection Framing Effect: For more information, see: Kahneman, D. and Tversky, A. (1984). Choices, values, and frames. American Psychologist, 39,

3. Multiple Alternatives: 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.

3. Multiple Alternatives: 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. Group A: 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? 1. Refer to orthopedics and also start ibuprofen. 2. Refer to orthopedics and do not start any new medication.

3. Multiple Alternatives: 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. Group A: 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? 1. Refer to orthopedics and also start ibuprofen. 89% 2. Refer to orthopedics and do not start any new medication. 11%

3. Multiple Alternatives: 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. Group B: 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? 1. Refer to orthopedics and also start ibuprofen. 35% 2. Refer to orthopedics and also start piroxicam. 4% 3. Refer to orthopedics and do not start any new medication. 58%

3. Multiple Alternatives: 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. Group B: 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? 1. Refer to orthopedics and also start ibuprofen. 35% 2. Refer to orthopedics and also start piroxicam. 4% 3. Refer to orthopedics and do not start any new medication. 58% But option 2 in for Group A is the same as option 3 Group B, thus we conclude that discovery of a new drug may lead to worse patient care.

3. Multiple Alternatives: Group B: 1. Refer to orthopedics and also start ibuprofen. 35% 2. Refer to orthopedics and also start piroxicam. 4% 3. Refer to orthopedics and do not start any new medication. 58% 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? Group A: 1. Refer to orthopedics and also start ibuprofen. 89% 3. Refer to orthopedics and do not start any new medication. 11%

3. Multiple Alternatives: For more information, see: Redelmeier, D.A. & Shafir, E. (1995). Medical decision making in situations that offer multiple alternatives. JAMA, 273(4),

4. Attraction effect: 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.

4. Attraction effect: 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. Group A: Three options Drug A: 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: 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: 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.

4. Attraction effect: 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. Group A: Three options Drug A: 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. 11% Drug B: 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. 88% Drug C: 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. 0%

4. Attraction effect: 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. Group B: Two options Drug A: 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: 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.

4. Attraction effect: 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. Group B: Two options Drug A: 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. 35% Drug B: 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. 65%

4. Attraction effect: Group B: Two options Drug A: 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. 35% Drug B: 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. 65% Group A: Three options Drug A: 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. 11% Drug B: 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. 88% Drug C: 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. 0% But the information about Drugs A and B in the three option version is the same as the information about Drugs A and B in the two option version. The addition of the Drug C, although chosen by no one, has increased the selection of Drug B.

4. Attraction effect: Group B: Two options Drug A: 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. 35% Drug B: 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. 65% Group A: Three options Drug A: 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. 11% Drug B: 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. 88% Drug C: 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. 0%

4. Attraction effect: For more information, see: 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; and Chapman, G.B. & Malik, M.M. (1995). The attraction effect in prescribing decisions and consumer choice. Medical Decision Making, 15, 414.