The Irrationality Of Rationality (Or Is It The Rationality Of Meta-Rationality?)

You've all heard of the Prisoner's Dilemma, but have you heard of the Traveller's Dilemma? I'll let the creator explain it.

Lucy and Pete, returning from a remote Pacific island, find that the airline has damaged the identical antiques that each had purchased. An airline manager says that he is happy to compensate them but is handicapped by being clueless about the value of these strange objects. Simply asking the travelers for the price is hopeless, he figures, for they will inflate it.

Instead he devises a more complicated scheme. He asks each of them to write down the price of the antique as any dollar integer between 2 and 100 without conferring together. If both write the same number, he will take that to be the true price, and he will pay each of them that amount. But if they write different numbers, he will assume that the lower one is the actual price and that the person writing the higher number is cheating. In that case, he will pay both of them the lower number along with a bonus and a penalty--the person who wrote the lower number will get $2 more as a reward for honesty and the one who wrote the higher number will get $2 less as a punishment. For instance, if Lucy writes 46 and Pete writes 100, Lucy will get $48 and Pete will get $44.

What numbers will Lucy and Pete write? What number would you write?

Scenarios of this kind, in which one or more individuals have choices to make and will be rewarded according to those choices, are known as games by the people who study them (game theorists). I crafted this game, "Traveler's Dilemma, in 1994 with several objectives in mind: to contest the narrow view of rational behavior and cognitive processes taken by economists and many political scientists, to challenge the libertarian presumptions of traditional economics and to highlight a logical paradox of rationality.

Traveler's Dilemma (TD) achieves those goals because the game's logic dictates that 2 is the best option, yet most people pick 100 or a number close to 100--both those who have not thought through the logic and those who fully understand that they are deviating markedly from the "rational choice. Furthermore, players reap a greater reward by not adhering to reason in this way. Thus, there is something rational about choosing not to be rational when playing Traveler's Dilemma.

In the years since I devised the game, TD has taken on a life of its own, with researchers extending it and reporting findings from laboratory experiments. These studies have produced insights into human decision making. Nevertheless, open questions remain about how logic and reasoning can be applied to TD.

Common Sense and Nash
To see why 2 is the logical choice, consider a plausible line of thought that Lucy might pursue: her first idea is that she should write the largest possible number, 100, which will earn her $100 if Pete is similarly greedy. (If the antique actually cost her much less than $100, she would now be happily thinking about the foolishness of the airline manager's scheme.)

Soon, however, it strikes her that if she wrote 99 instead, she would make a little more money, because in that case she would get $101. But surely this insight will also occur to Pete, and if both wrote 99, Lucy would get $99. If Pete wrote 99, then she could do better by writing 98, in which case she would get $100. Yet the same logic would lead Pete to choose 98 as well. In that case, she could deviate to 97 and earn $99. And so on. Continuing with this line of reasoning would take the travelers spiraling down to the smallest permissible number, namely, 2. It may seem highly implausible that Lucy would really go all the way down to 2 in this fashion. That does not matter (and is, in fact, the whole point)--this is where the logic leads us.

What is the point of all this? As Basu says, there are two broad lessons to be taken from this. First, the assumption of classical economics that a society of selfish people acting in their self-interest will produce the greatest economic good needs to be challenged. In this case, the greatest economic good would come from both players choosing 100. The deductive logic, however, suggests both players should choose 2, leaving them considerably worse off than if they had behaved irrationally.

Second, because repeated experiments have shown that players don't choose 2, and that these choices aren't a reflection of stupidity or not understanding the deductive logic behind the game - even a group of game theorists, when playing this game, by and large chose numbers other than 2 - we must recognize the limits of game theoretic or logical reasoning to explain social scientific outcomes. According to Basu, we must somehow account for what he calls "meta-rationality," which contains an explicit rejection of formal rationality. Anyways, it's a really interesting piece and I highly recommend going and reading the whole thing.

Link courtesy Freakonomics