Rationality

Alan Kaylor ClineDepartment of Computer SciencesThe University of Texas at Austin

Based upon classic decision puzzlers collected by Gretchen Chapman of Rutgers University

1. Sunk Cost: 

Group A is told: 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? 

1. Sunk Cost: 

Group A is told: 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?

The results are: Yes (63%) and No (37%)

1. Sunk Cost: 

Group B is told: 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?

1. Sunk Cost: 

Group B is told: 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?

The results are: Yes (27%) and No (73%)

1. Sunk Cost:

For Group B the results are: Yes (27%) and No (73%)

For Group A the results are: Yes (63%) and No (37%)

But the situation for A is very similar to that for B

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A B

yes

no

1. Sunk Cost:

For Group B the results are: Yes (27%) and No (73%)

For Group A the results are: Yes (63%) and No (37%)

But the situation for A is very similar to that for B

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yes

no

For more info., see: Arkes, H.R. & Blumer, C. (1985). The psychology of sunk cost. OBHDP, 35, 124-140.

2. 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.

2. 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 21% rated “5” more likely than “2”. Everyone should

rank “2” more likely than “”5”.

2. 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 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,

293-315.

3. Omission Bias:  

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 ____ 6 in 10,000

____ 1 in 10,000 ____ 7 in 10,000

____ 2 in 10,000 ____ 8 in 10,000

____ 3 in 10,000 ____ 9 in 10,000

____ 4 in 10,000 ____ 10 in 10,000

____ 5 in 10,000

3. Omission Bias:  

 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: 

8% 0 in 10,000 4% 6 in 10,000

2% 1 in 10,000 0% 7 in 10,000

2% 2 in 10,000 0% 8 in 10,000

2% 3 in 10,000 47% 9 in 10,000

0% 4 in 10,000 15% 10 in 10,000

21% 5 in 10,000

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45%

50%

0 1 2 3 4 5 6 7 8 9 10

3. Omission Bias:  

 For more information, see: Ritov, I. & Baron, J. (1990). Reluctance to vaccinate: Omission

bias and ambiguity. Journal of Behavioral Decision Making, 3, 263-277.

4. 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: 

4. 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.

4. 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%

4. 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.

4. 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%

4. 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%

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A B

A/C

B/D

4. 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.

4. Reflection Framing Effect:

  

For more information, see: Kahneman, D. and Tversky, A. (1984). Choices, values, and

frames. American Psychologist, 39, 341-350.

5. 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.  

5. 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.

5. 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%

5. 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%

5. 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%

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1 2 3

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%

5. 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.

5. 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

6. 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.  

6. 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.

6. 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%

6. 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.

6. 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%

6. 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%

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A B

6. 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.

6. 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.

7. Outcome bias:  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.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

7. Outcome bias:  Group A:

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. The operation succeeded.

7. Outcome bias:  Group A:

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. The operation succeeded. The mean score was 1.52

A

0

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0.8

-3 -2 -1 0 1 2 3

B

0

0.10.2

0.30.4

0.50.6

0.7

-3 -2 -1 0 1 2 3

7. Outcome bias:  Group A:

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. The operation failed and the man died..

The mean score was 1.57

7. Outcome bias:  

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. The operation succeeded. or The operation failed and the man died.

The operation succeeded : The mean score was .85

The operation failed and the man died: The mean score was -.05.

Thus the advice, that had to given before the operation, was declared to be correct or incorrect based upon the result.

7. Outcome bias:  

For more information see: Baron, J. and Hershey, J.C. (1988). Outcome bias in decision evaluation. JPSP, 54, 569-579.