Problem Set C: Probabilistic Reasoning
(1) Ask 5 people to make educated guesses about the following two scenarios and record their respoonses (OK to team up with other class members and report the same data):
Question A: Estimate the probability that a rancher from Wyoming who
is in the market for a vehicle buys a Toyota.
Question B: Estimate the probability that this rancher buys a Toyota
truck.
(a) Report your participants' responses in a table.
(b) According to the laws of probability, should the probability
estimate be higher in Question A or Question B? (Note: the laws of
probability
do allow for the possibility that the two estimates will be
equal.
We take that as a given.)
(c) Describe the responses you found. Were they in
accordance
with the normative response determined by probability theory?
(d) If you answered "no" to question (c), explain your
results.
(Hint: Which heuristic would produce this behavior?) If you
answered "yes" to question (c), explain your results.
(e) Do you think little experiments like this are a valid
indicator
of people's probabilistic reasoning abilities? Explain why or why
not. (You're being graded on the quality of your explanation, not
whether you say "yes" or "no".)
Hint: One good answer would appeal to Grice's maxims.
But, there are lots and lots of other good ones!
Extra Credit (worth up to 5 points): Reverse the order
of questions A and B (putting the information about Wyoming , etc.
into question B) and ask 5 new people. Report your results and explain
why you think they are similar to your findings in (a), (if they're
similar), or, why you think they're different, (if they're different).
(2) Give examples of the use of each of the following
heuristics
(in a and b) and fallacies (in c and d):
(a) the availability heuristic
(b) the representativeness heuristic
(c) the gambler's fallacy
(d) the conjunction fallacy
(3) (The Allais Paradox)
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. You have the following
options:
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
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
(a) Assuming the worth of each possible outcome is the number
of years you would live, calculate the expected utility of Option A.
(b) Calculate the expected value of Option B.
(c) Calculate the expected value of Option C.
(d) Calculate the expected value of Option D.
(e) Assuming expected value theory, explain the relationship
between Option A and Option C (how would you transform Option A to
yield
Option C?)
(f) Assuming expected value theory, explain the
relationship
between Option B and Option D.
(4) [Note: the sample answer is only illustrative. Your
decision does not have to do with banks or money...]
(a) Give an example of a decision you made -- anytime in the
last 4 years -- that involved the consideration of probabilistic
information.
(e.g. For Dr. Coulson, a good example is the decision to get a new
mortgage.)
(b) What was the probabilistic information? (e.g. the
probability
that interest rates would go up as opposed to down)
(c) In thinking about any of the probabilistic variables
involved
in your decision, what is one heuristic, bias, or fallacy that could
have
led you astray? (e.g. Because interest rates have recently been going
down,
and recent events influence memory more than distant events, use of the
availability heuristic might lead you to think that interests rates are
likely to go down.)
(5) Is human decision making rational? Write 1-2 paragraphs that address this question. Be sure to clearly (but briefly) define what counts as rational, and back up your argument with a brief reference to relevant experimental evidence. Depending on what your answer is, you may (though you do not have to!) want to provide a reasoned critique of some research in this area.