Reflecting on the Sunk Cost Fallacy

I was discussing the sunk cost fallacy with some colleagues over dinner the other day, and posed the following question: What would happen if people were immune to the sunk cost fallacy? “People would make better decisions”. How could acting more rationally be a bad thing? Yet it seemed strange that our natural inclination would always lead to maladaptive behavior. Perhaps, there are some scenarios in which we arrive at better outcomes by accident, thanks to the false logic of sunk cost.

Somewhat recently, I was reading a post on about the Spiderman musical, which is currently being worked on. One of the notable things about it is that it’s going to be the most expensive musical ever. It also features lots of acrobatics (you really can’t create a show about Spiderman that doesn’t feature people flying across the stage). Unfortunately, the project has been plagued with performers injuring themselves during rehearsal, and rising costs. At this point, it seems unlikely that the show will turn a profit. Despite this, investors keep pouring money into it. Because alot of money has already been spent putting the show together, it seems that sunk cost might be at play here; however, that’s not necessarily the case. As I pointed out in the comments on Dan Ariely’s blog, the rational choice is a matter of future costs, not total cost, vs. revenue.

After dinner, I came up with a simple model, in the form of a table, to think about what might be happening in the case of the Spiderman musical:

Time Total Project Cost (expected) Spent Revenue (constant, expected) Cost to Project Completion Profit (expected)
0 75 0 100 75 25

This first row of the table tells us a promising story: even though a price tag of $75M is pretty high for a Broadway musical, we expect that throngs of people will come out to see it, yielding $100M. If all goes according to plan, we’ll come out $25M ahead. Sounds great! Where do I sign up? Unfortunately, things don’t go according to plan. In the first year, we incur some unexpected costs, which leaves us in the following situation:

Time Total Project Cost (expected) Spent Revenue (constant, expected) Cost to Project Completion Profit (expected)
1 100 25 100 75 25

Oops. The total expected cost of the production has gone up by $25M. Is it still a good idea to continue investing in the musical? Well, we’ve already covered $25M of the total expected cost. This leaves us with $75M in future costs. Furthermore, we still think it’s a good musical, good enough to bring in $100M (same as last year’s prediction). This means that if we choose to continue investing, we’ll wind up with $100M – $75M = $25M that we don’t have now; therefore, the rational choice is to continue investing.

You may have noticed that the total cost of the musical is now equal to the amount we expect it to bring in, which means the project as a whole is not going to turn a profit. In the mind of a rational investor, this is completely irrelevant. That’s because we are rationally disregarding sunk cost. If we could go back in time, we could change our minds about whether to start investing in the musical. Unfortunately, we are stuck in the present, where it is not possible to recover the $25M that we’ve already spent.

Anyway, another year passes with more unexpected costs:

Time Total Project Cost (expected) Spent Revenue (constant, expected) Cost to Project Completion Profit (expected)
2 125 50 100 75 25

Yikes! The total expected cost of putting on the show now exceeds the amount that we expect it to bring in! Surely, we should stop investing now. Not so fast. Yes, the musical saw some set backs during the year, but it has also been making progress in other areas. How does it all add up? Again, the cost of completion = the total expected cost – how much we’ve spent so far, as shown in the penultimate column. We still haven’t changed our minds about how much audiences are going to love this musical; it’s still going to bring in $100M. By performing a simple cost-benefit analysis, we see that pouring more money into the project continues to be the rational choice.

At this point, you can probably see where I’m going with this. As it turns out, this degenerate behavior can continue indefinitely. It’s as if we’re taking a $25M pile of cash, and burning it every year, not to mention all those performers who were disfigured during rehearsal! At least, that’s what a rational person would do.

How does this compare with what we’d expect a regular person would do? Assuming one does not run out of money, we’d expect a person to give up at some point. A typical person can only put up with a certain amount of failure, even if the outlook for continuing with the present course looks very bright. Paradoxically, a less rational person ends up losing less, because he ends up limiting his losses, instead of endlessly throwing money down a rat hole.

I can think of a few objections to this line of reasoning, but I don’t think any of them is fatal. First, you might question whether it’s possible for a truly rational person to keep misestimating the total cost, year after year. A truly rational person is probably really smart, which means he should be good at coming up with accurate cost estimates. I definitely agree that this tends to be the case. On the other hand, there’s no way for a person, even a perfectly rational person, to predict the future with much accuracy. Like it or not, the unexpected is a part of everyday life.

The second objection is that this scenario might not seem very realistic; nobody is so unlucky that misfortune befalls him year after year. This might be true for most people on an individual level, but it’s much harder to say that nobody has this problem.

As much as I hate to admit it, the field of engineering is littered with the wreckages of projects that went way over budget. Consider everyone’s favorite engineering punching bag: The Big Dig. I’m not familiar with all the sordid details, but it’s infamy seems to be fairly widespread.

Anyway, to return to my original question, Is the sunk cost fallacy all bad? It’s probably not clear how any of this is related to the sunk cost fallacy. Doesn’t the sunk cost fallacy cause us to keep going, i.e. the opposite of giving up? Bear with me for a moment. Consider what happens in the mind of a person who is falling for the sunk cost fallacy. The thing that he’s needlessly concerning himself with is past costs. By contrast, a rational being sees no point in crying over spilled milk.

Now, compare this mode of thinking to what happens in the mind of a person who gives up “prematurely” compared to what a rational being would do. What is causing the person so much grief that he is willing to pass up a great opportunity? I believe he is thinking of all the resources he’s thrown away, and how continuing can’t possibly be worth it anymore. This irrational thinking isn’t all that different from the kind of thinking we see in the case of the sunk cost fallacy: being concerned about resources spent in the past.

I have some thoughts about what this all means, but I’m going to ruminate over it for a while. I the mean time, I’d love to hear your thoughts on the matter :).

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2 Responses to Reflecting on the Sunk Cost Fallacy

  1. Thomas says:

    > At this point, you can probably see where I’m going with this. As it turns out, this degenerate behavior can continue indefinitely.

    True, it *can*. But we don’t *expect* it to. At some point you should stop trusting your judgement on the matter and either get a second opinion that takes your failed predictions into account or pull out.

  2. allyourcode says:

    Completely valid points. I think your comments fall under the “can a rational being really get the estimates wrong this many times?” argument, which I outlined. Certainly, a rational agent is likely to resort to advisors for second (and third) opinions, especially when the stakes are this high.

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