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 gam...
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 pre... (read more)