On 1/20/2014 9:38 AM, Bruno Marchal wrote:
On 20 Jan 2014, at 10:50, LizR wrote:
On 20 January 2014 22:39, Russell Standish <[email protected]
<mailto:[email protected]>> wrote:
The point about acting randomly is that clearly you are not optimising
your utility. You a choosing something other than the optimum action,
so are behaving irrationally by definition. Yet, it could be a
beneficial strategy to do so, for all the reasons raised (fooling your
opponents, making a timely decision, and so on).
Sorry to be dense, but I still don't see this. When I say "acting randomly", I assume
we don't mean just doing anything, deciding to go swimming in the arctic or declaring
yourself to be Napoleon, I assume we mean picking one of a number of options that
appear to have equal utility.
Let's say we're playing scissors-paper-rock. The best strategy - the one that gives you
the best chance of winning at least half the time - is to choose randomly. Anyone who
doesn't choose randomly is open to having their moves predicted, and losing more often
than they otherwise would. So in this case acting randomly is rational... isn't it?
OK. But now acting randomly is not that simple, and studies have shown that the humans
are very bad at that. A machine can easily distinguish a human from a good pseudorandom
generator. Humans have a tendency to homogenize adding an order implicitly. Most humans
get wrong when shown ten pictures of random and non random pictures.
When presented with true randomness, humans extract order which are not there.
Most people are amazed of the presence of long sequence of 1 and 0, and 10, ... in the
binary development of PI (11.001001000011111101101010100010001000010110100011...).
Can we act randomly? Well, we might do that when panicking. Or we can use some random
generator, or the rest of coffee in a cup, or the shape of the clouds, ...
Of course what we need to do is to act unpredictably, and random is just a limit of
extreme unpredictability. In an actual finite sequence of actions there's no way to
distinguish true random from just sufficiently random.
Brent
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