The Sunk-Cost Fallacy Fallacy

Economists seem to get a perverse pleasure from finding a particular widespread behaviour which they deem to be irrational. Saving and spending behaviour (particularly a reluctance to borrow against future income and a reluctance to save in anticipation of an income reduction), altruism in non-repeated games, particular forms of risk aversion, letting investment decisions be influenced by past performance, systemic under- or over- insurance in some areas, reluctance to take some arbitrage opportunities... economists love to point out areas where people could be better off if only they were more rational. The "sunk-cost fallacy" is one such widespread irrational behaviour economists regularly urge people against.

Basically the sunk-cost fallacy is the idea that people should ignore sunk costs and not let them influence decision making. The theory goes that if you, say, lose an item of clothing you should ignore the "lost" purchase price when determining whether or not you buy a replacement. You should instead work out how much you would value a new jumper (ie your willingness to pay) and then see how much a new item would cost and buy it if your WTP is higher than the cost.

Most people don't work like this. Say you just bought a jumper half and hour ago and then you lose it. An economist would say that you would/should always replace the jumper because neither your WTP nor the price would have changed very much in that short amount of time. However, Most of us would code the loss of a new jumper as a loss and thus put off buying a replacement until another day. Behavioural economists describe this behaviour as mental accounting. I won't go into all the details of this concept, but basically it says we divide our money and transactions up into seperate mental accounts. General principles are loss aversion, diminishing marginal returns, reference point prices, an unwilingness to close accounts in the red and linking of certain behefits with certain losses and vice versa.

In the jumper example the initial purchase would be coded as a gain of some amount (studies have been on this, people tend to ignore the actual purchase price in mental accounting, they merely look at the price relative to what they were prepared to pay for it. By definition you don't buy something unless the transaction results in at least a small positive). The subsequent losing of this would wipe this benefit out, the "jumper" account would be zero. If you then went and replaced the jumper you would end up with the same item of clothing but you've paid double what you were originally going to pay for it. This will probably put you above your initial relative valuation of the product (unless it's really cheap), and thus the account will be in the red. Loss aversion says you probably won't take this course of action. However, the initial purchase price gets discounted in your mind over time (have you ever bought something which wasn't quite right but then waited ages before replacing it? That's time discounting) and so you will eventually replace it.

I surely haven't done mental accounting justice here. It's fairly involved, but I hope you get the general idea. The interesting thing is that economists would say most of the sorts of behaviour described by mental accounting - and it does have good explanatory power - is completely irrational, the implication being that we shouldn't operate in that way. But that misses the point. We aren't completely rational creatures and mental accounting provides us with good rules of thumb for financaial management. Taking into account sunk costs gives us incentives to be careful with what we buy and coding different moneys in different accounts can be a good shorthand way of managing our complicated financial affairs, even if it isn't optimal.

A Slate article this week discussed the sunk cost fallacy in a way typical of normal economists. It's interesting that one of the examples he gives is one which has been studied by behavioural economists:

You have good tickets to a basketball game an hour drive away. There's a blizzard raging outside, and the game is being televised. You can sit warm and safe at home by a roaring fire and watch it on TV, or you can bundle up, dig out your car, and go to the game. What do you do?

The implied rational answer to this hypothetical is that you stay at home. The ticket price is a sunk cost. Your current decision should be which gives me more value now - staying at home or going out? Due to the weather it's assumed that staying at home would give you more value and thus that's the optimal response:

The money is gone. Do you "waste" it, or do you go to the game? It is claimed by economists and psychologists that the right way to approach questions like these is only by looking to the future. Since the money is spent no matter what you do, the only real question you should be asking is what will give you more satisfaction—watching the game by a roaring fire or sliding to it in a blizzard. The "sunk costs" are sunk whatever your decision; only the future matters. The fallacy in thinking about sunk costs is precisely that people feel compelled to get their "money's worth," even if it makes them suffer.

But behavioural economists note that people don't actually do that. They have a "basketball game" account and don't like to close it in the red, which it would be if they didn't go to the game. Thus, people go because they don't actually ignore the sunk cost of the ticket. Rather than dismissing real world behaviour as irrational, behavioural economists modify their models using mental accounting and thus can describe the real world better.

The article primarly puts the sunk cost fallacy in the context of the Iraq war:

My suggestion here is modest: You may justify the Iraq occupation in many ways—perhaps you think it will prevent further terror, democratize the Middle East, or restrain Iran—but it is unacceptable to justify it on the grounds that we "owe" it to those who have already fallen. That is a justification that no one should be allowed to get away with. But it is a justification that is coming increasingly to the fore, usually implicitly but sometimes explicitly, as other arguments about staying the course in Iraq become less and less compelling.

On this point I'm inclined to agree with him. Mental accounting is a personal decision making tool, it shouldn't be used as the basis for public policy which should hopefully be determined by more rational considerations. While the feelings of the families of those who have died in this war and who might feel their loved one's sacrifice could be devalued by a withdrawal is a real world consideration, their moral authority isn't absolute and this argument can't be alllowed to trump all others. I've argued before that a short-term withdrawal is a really bad idea but if circumstances change or when the time comes for withdrawal, even under fire, the fact that there is an enormous sunk cost in the war should have only a minimal impact on the decision.