Positive Liberty

Via Arts & Letters Daily, I bring you the following puzzle, from an article in Scientific American by Kaushik Basu:

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?

…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.

Don’t say “I’d write the price I actually paid.” This isn’t an option, although it probably should be. If the game were ever run using the situation actually posited by the author, Lucy and Pete would very likely give identical numbers that matched exactly what they both paid for their items.

The article, meanwhile, describes a curious series of experiments that purport to enact the Traveler’s Dilemma. The strangest thing about these experiments is that none of them involve an actual purchase prior to the game. Each participant must simply guess a number between 2 and 100, with no point of reference to aid them in thinking about the possible actions of the other player. This is a serious design flaw, to say the least.

In the real world, market prices tend strongly toward uniformity. This tells Pete and Lucy that the “best” guess, the one which makes a penalty least likely while tending to maximize reward, is the very same price they have already paid. By happy coincidence, this also happens to be the honest answer. Even if I am not entirely certain that the other player is honest, I still have some idea that he might be, and this alone pushes me strongly toward honesty as well. Thinking further, I will realize that the same dynamic applies to him, and if you’re going to be caught in some recursive logic — which will happen in any case if you try to undercut — then you might as well use it to your advantage.

Attempts to guess lower might reap a greater reward, true — but why begin a race to the bottom when both sides have a very good shot at getting a full refund? And why begin the race to the bottom, when it makes no difference who begins it, and when the penalty for deviating will be the same, whether we guess high, low, or truthfully?

The smallest figure only becomes a reasonable strategy when neither Pete nor Lucy have any guidance whatsoever about how the other traveler might respond. In the world of actual prices, this never happens. In other words, the $2 solution is only plausible when it is entirely divorced from economics, and when neither player has any cues at all for giving an answer.

Don’t say, “Like any shopper with half a brain, I kept the receipt.” This too is not an option. Yet receipts are nearly ubiquitous; in the real world, they are almost as common as the price mechanism itself. Let either Pete or Lucy present documentation on the spot, and the airline can no longer play its puerile games with them. (This, by the way, is one reason why we have receipts in the first place.)

To the author, none of this matters. To him, the design of the game shows the obvious faults… of capitalism. He brags as follows:

I crafted this game, “Traveler’s Dilemma” 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.

But this game does nothing to subvert the libertarian consequences (I don’t say “presumptions”) of economics. Instead, it shows only that the libertarian character of economics is underwritten by institutions.

Some of these institutions are designed and conscious, like receipts; some are undesigned and spontaneous, like prices. Each, though, encourages honesty and transparency in all of our transactions. Insofar as this game touches the real world at all, it tells us 1) that market prices are important for normalizing expectations and 2) that fraud must be banished from the market for it to function effectively.

Hate to break it to you, but this isn’t news to libertarians.

It’s a pattern I see quite often in social science research purporting to challenge free-market economics: A researcher finds a way to jettison one or more necessary properties or preconditions of a market economy. Without them, he finds that the market doesn’t work — and so, he declares, the market itself is broken.

In this case, the experiment’s design tossed out two key safeguards — market prices and receipts. Either one would have been enough to prevent the whole charade. Is something broken? You bet it is. But it’s not the market. Weirdly, by testing what happens when these two institutions are lacking, the experiment shows the strength, and not the weakness, of the libertarian argument.

(On rereading this post, I can think of at least two other market mechanisms that would make the Traveler’s Dilemma unlikely in a genuine market: First, the airline would eventually fear for its reputation if it treated its customers in such a high-handed and suspicious way. Second, the customers, perhaps resentful of the awful treatment they had received, would tell others to defeat the game by always guessing the highest possible number. After a while, the travelers would always break the bank, and “damaged” antiques would become de rigeur.)

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