With the preparations for Europe going on at full steam, I find myself drawn toward psychology articles about traveling. Take, for example, this article in Scientific American. Kaushik Basu explains the “traveler’s dilemma,” a scenario in which identical items purchased by two travelers are both damaged in transit. The airline agent is worried that they’ll claim the price of the item is higher than what they actually paid, so he devises the following 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.
Your first hunch is probably just like mine: Lucy and Peter should both write $100, and then they’d each get a hundred bucks. But there’s a problem with this logic: if Lucy “cheats,” and writes $99, then she’ll get $101, so it’d be better for her to write $99. Then the logic collapses in a chain reaction:
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.
This, of course, is why economists aren’t psychologists. Any normal person would just write $100. Psychologists have taken a different approach to the problem and conducted a study of how people really behave in the travelers’ dilemma. A team led by C. Monica Capra found that as the reward for guessing a lower number than the other traveler increased, the guessed value decreased. In their study, volunteers played with real money, with an allowed range of guesses from 80 to 200 cents.
The experiment confirmed the intuitive expectation that the average player would not play the Nash equilibrium strategy of 80. With a reward of 5 cents, the players’ average choice was 180, falling to 120 when the reward rose to 80 cents.
I saw a rather more benign connection, to this post, where a London commuter rates the preferred seating positions in a Tube train car, complete with a handy diagram.
Position 1 is supreme, because you have only one neighbour, and (usually) a wider seat, with windows behind and beside you, plus a door which might give some hope of a breeze.
Position 2 has only one neighbour, and the breeze factor, though usually someone’s arse squished up against the glass partition beside you.
Meg says the trains fill up in roughly the order she indicates, which strikes me as a bit odd. Why would someone take position 2 next to someone if 3 and 4 were available? Don’t people want to maximize the area around them? But perhaps commuters realize that eventually all the seats will be taken, so it’s preferable to sit next to someone in a temporarily inferior seat with the knowledge that eventually it will be the preferred position.
I suspect the reality is much more like the results of Capra’s study on the traveler’s dilemma. Even though passengers know that in a full car seat 2 is better than 3 or 4, they’d rather take the optimistic view that the car won’t fill up completely and they’ll have more personal space sitting there compared to sitting next to someone in seat 1. Even when it’s certain the train will eventually fill, several people will sit in seats 3 and 4 before sitting next to a stranger by occupying seat 2.