Pocahontas as told by an admirer

1
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
2
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?  
3
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)
4
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?
5
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)
6
1. Sunk Cost
For Group A the results are Yes (63) and No
(37)
For Group B the results are Yes (27) and No
(73)
But the situation for A is very similar to that
for B
7
1. Sunk Cost
For Group A the results are Yes (63) and No
(37)
For Group B the results are Yes (27) and No
(73)
But the situation for A is very similar to that
for B
For more info., see Arkes, H.R. Blumer, C.
(1985). The psychology of sunk cost. OBHDP,
35, 124-140.
8
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. (1more likely to be true, 6least
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.
9
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. (1more likely to be true, 6least
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.
10
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. (1more likely to be true, 6least
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.
11
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
12
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
13
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.
14
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 
15
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.
16
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
17
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.
18

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
19

4. 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
20

4. 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.
21
4. Reflection Framing Effect    
For more information, see Kahneman, D. and
Tversky, A. (1984). Choices, values, and frames.
American Psychologist, 39, 341-350.
22
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.  
23
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.
24
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
25
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
26
5. 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.
89 3. Refer to
orthopedics and do not start any new medication.
11
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
27
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.
28
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
29
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.  
30
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.
31
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
32
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.
33
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
34
6. 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
35
6. 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.
36
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.
37
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
38
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.
39
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
40
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
41
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.
42
7. Outcome bias   For more information see
Baron, J. and Hershey, J.C. (1988). Outcome bias
in decision evaluation. JPSP, 54, 569-579.