## Tuesday, October 23, 2007

### The sunk-cost fallacy

In contrast with last time, today's fallacy is considerably more obscure, and yet has wide applications. In brief, the sunk-cost fallacy is when you make a suboptimal decision only to keep past efforts from going to waste.

Say you are playing a gambling game that I just made up with dice. First, you pay one dollar to start the game. Then, I roll one die. After you see the roll, you may either give up, or pay another dollar. If you've paid, I roll another die. If the total of the two dice is at least 7, you win four dollars.

The probability of getting at least a 7 is equal to 21/36. Since you have over 1/2 chance of winning, and the payback is double the cost, this game is overall profitable to you. However, what if you got unlucky with a 1 on the first die? Should you continue or quit? In this case, you have a 1/6 chance of winning, and the payback is 4 times the investment. Therefore, it would be more profitable to quit. But won't that cause your previous dollar to go to waste?

Take this more realistic example. Let's say that we have invested a lot of money in a war. And let's say that in the middle of the war, we suddenly realize that the rest of the war will cost significantly more than our previous expectations, and will achieve far less than we thought. Let's assume that upon the cost-benefit analysis of the remaining war, we find it would be better to give up at this point. But if we give up, won't all those lost lives have been in vain?

Well, yes. The sunk-cost fallacy doesn't necessarily mean that making the initial investment was an incorrect decision; at least in the gambling game, you were correct to pay the initial cost. New information or unlucky outcomes can make that initial investment have been for nothing. But we have no control over this, at least not anymore--what's done is done. The key is that it's not the previous investments that are relevant to the decision, but the future ones, the ones we have control over. In both of the examples, it's the future investment that will go to waste if we choose incorrectly.

Of course, in any "real" situation like a war, there are a lot more complicated issues involved, and no one actually uses the sunk-cost fallacy as their primary argument. Nobody relies on the argument that "soldiers' lives will have been in vain" or uses any sort of catchphrase like "stay the course", right? Right.

One of the reasons that the sunk-cost fallacy can be so compelling is that in real life, things like honor and image seem to have intrinsic value. We don't want to admit to having made a bad decision. We don't want to look bad in front of others. We feel bad about having wasted lives, and damn it, emotions are powerful. But it's not always best to go with emotions, and the sunk-cost fallacy is an excellent example of when this is the case.