Homework #11: Sunk Costs and Miscellaneous Probability Problems

1. Here is a standard example used to present the sunk-cost fallacy:

Three months ago, your eight-year-old car suddenly required serious repairs. Faced with spending $3,000 on the engine work or junking the car and buying a different one, you chose the repairs. Now, however, your transmission's shot, and fixing it will cost you another $1,500. Alternatively, you could sell the car as is for $1,000 and buy a different one. You know that the car will likely require further repairs in the future, though you hope it won't happen soon. What do you decide and why?

a. Give an answer that clearly spells out the kind of reasoning we describe as the "sunk-cost fallacy". (Include numbers in your answer.)

b. Now give an answer that avoids the sunk-cost fallacy, again including numbers.

c. Suppose that the first repair job did not cost $3,000 but was performed for free by a vocational school auto repair class. How, if at all, would this change in the scenario change the answer given in (a) above?

d. How, if at all, would it change the answer in (b)?

2. The following is an example of research that looks for a biological example of sunk-cost behavior. We will discuss it in two stages.

According to a study by Robert Lavery at Queen's University at Kingston, Ontario, cichlid fish that have had three previous broods defend their current brood more aggressively against a fake predator than those protecting their first brood. In his 1995 report in Behavioral Ecology and Sociobiology (vol 36, p 193), Lavery favoured the idea that the fish were exhibiting the Concorde fallacy---

a. Explain carefully why the cichlid behavior appears to be formally similar to the sort of things humans do when we say they are committing the "sunk-cost" fallacy.

The report on this study then continues:

But Lavery also acknowledged that prior investment could be a good indicator of future reward if the past efforts reduce the fish's ability to procreate in the future. In that case, aggression that could put the fish's life in jeopardy would become "cheaper" because fewer potential future broods would be at risk. The fish would be quite "rational" to defend its later broods more aggressively.

b. Explain carefully why this analysis of the "reasons" for the chichlid behavior avoids the sunk-cost fallacy.

c. What sort of data might one collect to find out which of the two proposed explanations of the chichlid behavior is more likely to be correct?

d. When evolutionary biologists speak of the "rational" behavior of cichlids, etc., they are speaking metaphorically. Translate the last sentence of the above paragraph ("The fish would be quite 'rational' to defend....") into Darwinian lingo that talks about survival rates, or passing on one's genes, or whatever, instead of "reasons" or "rationality".

3. One of the many popular books on how to avoid decision traps reports the following success story:

Fifteen years ago, we helped a major U.S. Bank recover after

making many bad loans to foreign businesses, often in several stages. We solved the problem for them by suggesting they implement a policy requiring that a loan be immediately reassigned to another loan officer as soon as any problem with it became serious.

a. Briefly explain the reason for the consultants' recommendation and why it solved the problem.

4. Suppose yesterday you promised a nine-year old to take her swimming, but now it's quite clear that it would not be such a good idea to do so because she seems to be coming down with a cold. "But you promised," she says. "If you hadn't promised, I would understand your decision not to take me. But you did promise."

a. If you include the fact that you made the promise yesterday as relevant to today's decision, are you committing the sunk-cost fallacy?
The answer to this question may depend on your interpretation of the situation or additional assumptions you make so explain your answer carefully.

5. Here is a philosopher's attempt to argue that it can sometimes be rational to honor sunk costs:

Consider goods that are produced by human action that have the following properties: First, they must be produced (if at all) over an extended period of time. Second, they are complex in that they have multiple distinguishable parts. Third, they possess what some philosophers have called organic unity C their value as goods depends to some extent on the way that their parts fit together, not just upon the value of the parts separately considered. Fourth, the action which produces the good has the same kind of structure delineated in the three conditions above in that it is temporally extended, composed of multiple distinguishable parts and the parts are organically related to the completion of the productive activity C that is, they are valued more highly as parts fitting together into the production of the good than they would be separately. This may seem excessively abstract and perhaps it is, but it is meant to provide a passable portrait of what often happens in the production of works of art.

Now, suppose that you are in the process of producing such a work. For illustrative purposes, I shall stipulate that it is a symphony and that you are a talented composer. You have written part of the symphony and are faced with a question as to whether to finish it. Many factors may enter into this decision. One is whether you might write something better if you laid this one aside. Another has to do with how other demands on your time may compare to the value of this completed work (should you complete it). But it seems that one thing that may properly enter into your decision -- and may make a difference if other considerations are sufficiently close to being balanced -- has to do not with the future consequences of completing the symphony but with the fact that effort that you have put into it in the past may be more valuable if the symphony is completed. For remember, we were assuming that your work on the project has an organic structure such that its parts are more valuable as parts of the whole than they are considered separately. So, in a certain sense, as strange as it sounds, a current action may contribute not only to a stream of benefits to be realized in the future, but may have as a consequence that something that has already occurred is better than it would otherwise be. (If you do not complete your symphony in A#, it will not be true that six weeks ago you wrote the opening chords of that symphony. At most, you will have written the opening chords of an uncompleted symphony.)

a. Note the bold-face assertion in the above paragraph. Has the author successfully argued, in your opinion, that in this case it is not a fallacy to honor sunk costs?

b. Assume the critics of the Tennessee-Tombigbee Waterway Project discussed in the Dawes reading were correct. Could the defenders of continuing the project produce a line of argument in terms of organic unity and the bestowing of value on past investment such as the one given above to argue that the project should be finished? (In other words, if we allow the above argument in the case of symphonies can we still criticize sunk cost reasoning elsewhere?)

6. The following example was used in a psychological study. Which answer do you think most subjects would choose and why? What do you think the rational/correct answer(s) is and why?

Mr. Munn and Mr. Fry each live in an apartment near the local movie theater. Mr. Munn can go to the movies only on Monday night. Mr. Fry can go to the movies only on Friday night. Each movie costs $5, no matter which night it is shown. Each movie is generally shown for a whole week.

Since Monday night is generally a pretty "slow" night at the movies, the manager of the theater offers a package to those who go to the movies on Mondays. Although the individual tickets are $5, the manager will sella three-pack for $12. The three-pack can be used on any three Mondays during the next month. Mr. Munn looks over the schedule for the next month and sees only two movies he is interested in seeing. So he decides not to buy the three-pack. Instead he pays $5 on each of the first two Mondays of the month to see a movie. Mr. Fry also pays $5 on each of the frst two Fridays of the month to see a movie.

There is a change of schedule. One of the movies scheduled cannot be obtained. Instead the manager substitutes a new movie that both Munn and Fry are interested in seeing. Had Mr. Munn bought the three-pack, he could have seen the new movie for just an extra $2.

Question: Will one of the men be more likely to pay to see the new movie, or will they be equally likely? Check the option that corresponds to your prediction:

(A) equally likely (B) Munn more likely (C) Fry more likely