IdleRich
IdleRich
My girlfriend just said that she is going to a lecture on this and I thought it was quite interesting.
Suppose that I am told that some guy is going to come round and fit me with cable tv sometime tomorrow between 8am and 4pm and I'm going to have to wait in for him. A friend agrees to wait with me to keep me company and to make things more interesting we decide to have a bet on when the guy will come. We divide the interval into two (approximately) equal bits, the first being any time after eight up to twelve and the second part being any time after twelve and before four and each person can pick an interval with the person who picks the interval in which the guy comes collecting ten pounds off the loser. I get first pick and it at first seems that the two intervals are effectively the same and that it shouldn't matter which one I pick as there is absolutely no reason to believe that the guy should come in one interval rather than the other.
Then it occurs to me that, if I choose the first interval, then, after any given period of time in which the cable guy doesn't show it will appear to me that the second interval will now be more attractive as the remaining part of the first interval in which the guy can arrive is now smaller than the second interval. Whatever time the cable guy does come after eight, there is a time before that when he could have come so there will have been a point where the person who picked the first interval, if rational, would have desired to change to the second interval.
In other words, if I pick the first interval I am certain to rationally want to change it at some point and surely, if I know that I am going to want to change it at some point, I should not pick it now. As no similar argument can be made for the second interval (as time goes in one direction) I should surely pick the second interval - even though there is clearly a fifty-fifty chance of the guy coming in each interval. Can anyone explain this?
Suppose that I am told that some guy is going to come round and fit me with cable tv sometime tomorrow between 8am and 4pm and I'm going to have to wait in for him. A friend agrees to wait with me to keep me company and to make things more interesting we decide to have a bet on when the guy will come. We divide the interval into two (approximately) equal bits, the first being any time after eight up to twelve and the second part being any time after twelve and before four and each person can pick an interval with the person who picks the interval in which the guy comes collecting ten pounds off the loser. I get first pick and it at first seems that the two intervals are effectively the same and that it shouldn't matter which one I pick as there is absolutely no reason to believe that the guy should come in one interval rather than the other.
Then it occurs to me that, if I choose the first interval, then, after any given period of time in which the cable guy doesn't show it will appear to me that the second interval will now be more attractive as the remaining part of the first interval in which the guy can arrive is now smaller than the second interval. Whatever time the cable guy does come after eight, there is a time before that when he could have come so there will have been a point where the person who picked the first interval, if rational, would have desired to change to the second interval.
In other words, if I pick the first interval I am certain to rationally want to change it at some point and surely, if I know that I am going to want to change it at some point, I should not pick it now. As no similar argument can be made for the second interval (as time goes in one direction) I should surely pick the second interval - even though there is clearly a fifty-fifty chance of the guy coming in each interval. Can anyone explain this?