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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. ____
2. ____
3. ____
4. ____
5. ____
6. ____
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.
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. ____
2. ____
3. ____
4. ____
5. ____
6. ____
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.
Choice 5 includes choice 2, yet in the survey 21% rated “5” more
likely than “2”. Everyone should rank “2” more likely than “”5”.
1. Conjunction Fallacy:
For more information, see:
Tversky, A. and Kahneman, D. (1983). Extensional versus intuitive
reasoning: The conjunction fallacy in probability judgment.
Psychological Review, 90, 293-315.
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 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%
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%
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 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%
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%
100%
90%
80%
70%
60%
A/C
50%
B/D
40%
30%
20%
10%
0%
A
B
2. Reflection Framing Effect:
For more information, see: Kahneman, D. and Tversky, A. (1984).
Choices, values, and frames. American Psychologist, 39,
341-350.
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 antiinflammatory 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 antiinflammatory 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 antiinflammatory 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.
89%
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 antiinflammatory 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 antiinflammatory 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%
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. Refer to orthopedics and do not start any new medication.
3. Multiple Alternatives:
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.
3. Refer to orthopedics and do not start any new medication.
89%
11%
Group B:
1. Refer to orthopedics and also start ibuprofen.
2. Refer to orthopedics and also start piroxicam.
3. Refer to orthopedics and do not start any new medication.
35%
4%
58%
100%
80%
60%
40%
20%
0%
1
2
3
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),
302-305
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.
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 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%
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%
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:
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.