I’d be happy to buy lots of lottery tickets that had a 1⁄132 chance of winning, given the typical payoff structure of lotteries of the kind you describe.
To act rationally, it isn’t enough to arrive at the correct (probabilities of) beliefs; to act on a belief, the degree of belief you need in it might not be very great.
Given the strong tendency to collapse all degrees of belief into a two-point scale (yea or nay) , I suspect that our intuitions about how much one has to believe in something in order to act accordingly are often too stringent, since the actual strengths of our beliefs are so often much too large.
(Note: “often” doesn’t mean “always” or even “usually”.)
Of course acting on beliefs is a decision theory matter. You don’t have terribly much to lose by buying a losing lottery ticket, but you have a very large amount to gain if it wins, so yes 1⁄132 chance of winning sounds well worth $20 or so.
I’d be happy to buy lots of lottery tickets that had a 1⁄132 chance of winning, given the typical payoff structure of lotteries of the kind you describe.
To act rationally, it isn’t enough to arrive at the correct (probabilities of) beliefs; to act on a belief, the degree of belief you need in it might not be very great.
Given the strong tendency to collapse all degrees of belief into a two-point scale (yea or nay) , I suspect that our intuitions about how much one has to believe in something in order to act accordingly are often too stringent, since the actual strengths of our beliefs are so often much too large.
(Note: “often” doesn’t mean “always” or even “usually”.)
Of course acting on beliefs is a decision theory matter. You don’t have terribly much to lose by buying a losing lottery ticket, but you have a very large amount to gain if it wins, so yes 1⁄132 chance of winning sounds well worth $20 or so.