jsalvata

Elezier:

The results of the two experimenters in the example are different: to begin with, the 2nd experimenter's first result is a non-cure (otherwise he would have stopped there with a 100% success); one of the three following results is also a non-cure (otherwise he would have stopped with a 75%); etc. Also, his last result is a cure (otherwise he would have stopped one patient earlier).

The first experimenter certainly got different results -- or you may as well win the lottery: the odds that a Bernoulli trial produces a sequence x1..x100 in which no prefix x1...xN has a higher rate of successes than the whole sequence are really small.

Note that this argument... (read more)

While Elezier's argument is still correct (that you should multiply to make decisions based on probabilistic knowledge), I see a perfectly rational and utilitarian explanation for choosing 1A and 2B in the stated problem.

The clue lies in Colin Reid's comment: "people do not ascribe a low positive utility to winning nothing or close to nothing - they actively fear it". This fear is explained by Kingreaper: "in scenario 1B if you lose you know it's your fault you got nothing".

That makes the two cases, stated as they are, different. In game 1 the utility of U1($0) has negative value: a sense of guilt (or shame) over having made the bad choice, which... (read 383 more words →)