Solutions to Sunk Costs 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.)

Fallacious Reasoning: If I ditch the car I will lose the 3K I already put into it so even though 1.5 for the new transmission is more that the 1K for a different car, I'd still come out ahead to get the transmission fixed.

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

I can either pay 1K for a car of unknown quality or put 1.5K into a car that I know is a loser. Time to trade.

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?

For the person thinking in terms of sunk costs, they would replace 3K in the answer above with 0K and thus make the same decision as in the answer to b.

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

No change.

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.

I guess this would look like the sunk cost fallacy if one assumes that the fish don't distinguish between broods and so the more babies total they have had the more they have invested in off spring and so the more willing they are to risk their life by fighting predators.

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 cichlid behavior avoids the sunk-cost fallacy.

On this analysis it is AS IF the fish were reasoning, well since I have already had lots of broods I am getting on and won't be having many more in the future. Therefore my reproductive future is less valuable than this present brood so it's worth risking my life.

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

Well, first of all find out whether it is true that the number of past broods is inversely related to future production. Perhaps keep some fish from breeding but let them age and see whether their productivity falls more or less than that of the freely breeding fish.

Also perhaps it would be possible to intervene in the size of the broods. If it really is sunk cost behavior then one might expect small brood size to have less of an effect on aggressive behavior as large brood size.

This example is not as "clean" as one might hope but I guess it does illustrate how difficult it is for biologists to figure out what's going on.

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".

Fish whose genes predispose them to engage in this behavior (defending later broods more aggressively than earlier broods) are more apt to leave more offspring thus the predisposing genes will become more widespread in the cichlid population as a whole. In general, genetically determined behavior that corresponds to what a rational actor would intentionally choose tends to become predominant within a population. Behavior which if deliberately chosen would be deemed irrational, tends to get weeded out over many generations.

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.

The original loan officers would be keenly aware of sinking money into the loan and would be committed to trying to rescue the business if at all possible. The new officers could more easily ignore the history of the bank's involvement in the loan (and the history of the loan's officer's personal involvement) and simply ask: Is this a prudent loan to make?

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.

You can avoid the sunk cost fallacy but not ignore the fact that you had made a promise IF you look at it this way: There is a future cost to breaking the promise if in the future the kid will not believe me when I make a good faith promise, etc. On the other hand, if the kid is old enough to understand this, there could also be a future benefit in breaking the promise IF you explain that sometimes it is better to break a promise than to keep it, carefully explaining how circumstances must have changed in order for this to be true and that you never do it lightly, etc.

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 - 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 - 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 boldface 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?

I think the author is just being confusing! Of course the opening bars written in the past become more valuable if the symphony is completed, but they become more valuable in the future - there is no backwards projecting of value going on.

The author seems to be saying that if I turn out to be Picasso then my pre-school scribblings turn out to be valuable, not just now that I'm famous, but in fact were valuable back in my Pabulum period?!

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?)

Maybe I've missed the subtlety of the author's appeal to organicity, but it seems to me that IF we were to allow the analysis of a symphony to work as the author suggests, then we would have to say the same thing about the big public works projects that we want to criticize. The foundation of the dam of course gains tremendously in value if the dam is finished but that is no reason to keep pouring money into the half-finished project IF we reason today that the whole dam will not be worth the additional future investment.