## 11/14/12

In casual conversation, I said something seemingly non-controversial like "gaining information is always good". And a friend challenged me. He said no, sometimes more information is bad. And he sent me a link to Braess's paradox.

Here's the setup for the paradox...

image from Wikipedia, which on a side note managed to get me to donate money today

...4000 cars start at START. It takes 45 minutes to go from START to B or from A to END. It takes T/100 minutes (where T is the number of cars or "travelers" using the road) to go from START to A or from B to END. There is a quick, zero time path from A to B, but nobody knows about it.

Here's the paradoxical result (see the Wikipedia page for details): everyone can drive from START to END in 65 minutes, with 2000 cars taking the top path, and 2000 taking the bottom path. But if everyone discovers the quick road from A to B, then everyone will end up spending 80 minutes travelling from START to END, with everyone going from START to A to B to END. So introducing information, namely the existence of a road, was somehow bad.

Of course, this assumes everyone will be selfish, doing things that help themselves at the expense of everyone else. Knowledge of the road from A to B could be good in an "enlightened" society. In fact, a society could use the road from A to B to decrease the total human-minutes spent travelling from 260,000 to 258,750, if 2250 cars go from START to A, and 500 cars take the road from A to B. Of course, it might be hard to agree who those lucky 500 people will be, since they'll each spend only 45 minutes travelling, whereas everyone else will spend 67.5 minutes.

So I guess if everyone is selfish and greedy, then introducing new information can be bad. But if everyone is enlightened — for some suitable definition of enlightened — then I still think gaining information is always good.