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The same irrationality as seen, say, in the individual family purchase of a plasma screen TV that draws up to 8 times more electricity. "TV is important to family life - we can afford a bigger electricity bill"

But society can't afford it when 1 million other families make the same choice. In Finland, it would require the output of a dedicated nuclear reactor.

Or the same idea can be applied to litter. One wrapper dropped in the street is not a problem. Thousands are.

Sam Loyd (1841 - 1911), the American puzzler and 'recreational mathematician' has a rather un-PC visual puzzle called the 'Vanishing Chinaman.' 12 chinamen are printed around the edge of a double dial, with one dial slightly large than the other. The figures are half on the inner dial and partly on the outer dial. But rotating the dial causes the 'appearance' of a thirteenth chinaman.

i.e. how fractional amounts become a problem when multiplied ;-)

You can't be me, I'm taken

by Sven Triloqvist on Tue Sep 29th, 2009 at 11:04:59 AM EST
[ Parent ]
Sven Triloqvist:
But society can't afford it when 1 million other families make the same choice. In Finland, it would require the output of a dedicated nuclear reactor.
I am reminded of the concept of Superrationality
The idea behind superrationality is that two logical thinkers analyzing the same problem will come up with the same, correct, answer. For example, if two persons are both good at arithmetic, and both have been given the same complicated sum to do, it can be predicted that both will get the same answer before the sum is known. In arithmetic, knowing that the two answers are going to be the same doesn't change the value of the sum, but in game theory, knowing that the answer will be the same might change the answer itself.
In game-theory terms, the "rational" strategy is one that is leads to the "best" result for the individual player, without assuming anything about what other players will do. It leads to the concept of "Nash equilibrium" which may be suboptimal. In the prisoner's dilemma,
Superrationality is an alternative way to reason. First, it is assumed that the answer to a symmetric problem will be the same for all the superrational players. Thus the sameness is taken into account before knowing what the strategy will be. The strategy is found by maximizing the payoff to each player, assuming that they all use the same strategy. Since the superrational player knows that the other superrational player will do the same thing, whatever that might be, there are only two choices for two superrational players. Both will cooperate or both will defect depending on the value of the superrational answer. Thus the two superrational players will both cooperate, since this answer maximizes their payoff. Two superrational players playing this game will each walk away with $100.

Note that a superrational player playing against a game-theoretic rational player will defect, since the strategy only assumes that the superrational players will agree. A superrational player playing against a player of uncertain superrationality will sometimes defect and sometimes cooperate.

For example,
One example discussed by Hofstadter is the platonia dilemma: an eccentric trillionaire contacts 20 people, and tells them that if one and only one of them sends him a telegram (assumed to cost nothing) by noon the next day, that person will receive a billion dollars. If he receives more than one telegram, or none at all, no one will get any money, and cooperation between players is forbidden. In this situation, the superrational thing to do (if it is known that all 20 are superrational) is to send a telegram with probability p=1/20, which maximizes the probability that exactly one telegram is received.

Notice though that this is not the solution in a conventional game-theoretical analysis. Twenty game-theoretically rational players would each send in a telegram and therefore receive nothing. This is because sending the telegram is the dominant strategy; if an individual player sends a telegram he has a chance of receiving money, but if he sends no telegram he cannot get anything.

I think the Platonia Dilemma has some bearing on the issue of the business cycle and speculative bubbles. When a new investment opportunity opens up, it is "rational" for each individual to invest as much as they can in it. But if everyone follows this strategy they crow each other out, diminishing returns set in, and the average return on investment drops substantially with respect to what it appeared initially to individual "players". Since, when the playing field is empty, it is rational to borrow to invest (leverage) it follows that a multitude of rational players will invest on credit and so the crowding-out and diminishing returns will eventually result in defaults.

With a superrational strategy, people only invest a fraction of their available wealth, such that if everyone invests the same fraction they don't go bankrupt. The "rational" strategy for each individual can well be to invest more, even with leverage, in order to capture more for themselves.

En un viejo país ineficiente, algo así como España entre dos guerras civiles, poseer una casa y poca hacienda y memoria ninguna. -- Gil de Biedma

by Migeru (migeru at eurotrib dot com) on Tue Sep 29th, 2009 at 11:17:12 AM EST
[ Parent ]
Or, as Jerome put it:

Chuk Prince (The Citi CEO) said it best: "as long as the music plays, we have to dance"

What amazed me most in 2006-07 was the number of bankers that were expecting a crash, even hoping to benefit from it (and thus were planning to do exactly that) but yet were still playing the games according to the rules of the over-inflate bubble they knew they were in ("covenant-lite" loans, "pik" (payment in kind) loans, extreme leverage, rockbottom pricing of risk).

- Jake

If you only spend 20 minutes of the rest of your life on economics, go spend them here.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Tue Sep 29th, 2009 at 11:32:56 AM EST
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