Problem 1
Annoyed by student complaints, the Department of Psychology fired Dr. Pitz and decided to hire someone else to teach the course in decision theory. There were four candidates for the position, Molly, Nollie, Ollie, and Polly. The department appointed a selection committee consisting of Professors Alfer, Baiter, and Gammer. The committee decided that its decisions would be based on a simple majority vote among the three of them.
Grumpy as always, Dr. Pitz muttered to the committee as he left, "You realize your decisions may well be irrational!" Why did Dr. Pitz draw this conclusion?
Hint: Assume that when they are asked privately to rank order the candidates from most to least preferred, the committee members respond as follows:
1st 2nd 3rd 4th
Alfer Mollie Nollie Ollie Polly
Baiter Nollie Ollie Molly Polly
Gammer Ollie Mollie Nollie Pollie
Obviously no-one likes Polly, but there's disagreement over the other candidates.
Explain why in this case a majority voting rule would violate an important principle of rational choice.
Problem 2
Whenever someone buys an automobile, an appliance, or almost anything else, the salesman will try to convince the customer to purchase an extended warranty (a warranty that extends beyond the one that comes with the item). Many companies make more money on the extended warranties than they do on the item itself.
(a) Explain why one should never, ever, buy an extended warranty.
(b) Except, perhaps, there might be a rare situation when buying an extended warranty is rational. When? [Note: The answer must use only information that is always available to the customer, so "If the product is likely to break" is not an acceptable answer]
(c) So why do many people buy these things anyway?