It seems just a classic case of people being naturally unwilling to fully dive into the abstraction.
Firstly, the fully abstracted problem provides only indifference between the choices. So, as much as we are able to dive in and cut out all external influences in our thinking, even when we do, the problem at best tells us that we should be indifferent. So we’re indifferent, then we’re asked us to make a choice. If you’re the sort of person who, when faced with an indifferent choice will say “I am provably indifferent, and thus refuse to choose”, you will generally be less functional in life than somebody who just picks one. So we all make a choice, and I would say when it’s indifferent then any choice is as good as any other. My point is, since the abstract problem gives us nothing, then even an infinitessimal hole in our ability to accept the rules of the problem makes all the difference.
If you don’t accept the abstraction fully, then there’s plenty of reasons to make the choices people make, as other comments already mention—assuming the game is more likely rigged against you than for you, and risk aversion in the case where there at least might be multiple plays.
Of course, I do think there still is a thinking failure people are making here. People see there being two levels and don’t realise they can’t really be separated. The problem people think they are solving is something like the following: “I will give you $X, where is the number of balls of the colour(s) you choose in the urn”. Normally that would seem to be an equivalent problem, and in that problem risk aversion trumps indifference and people’s choices are, well, as rational as risk aversion anyway. Strangely, a decreasing average utility of larger amounts of money both justifies risk aversion while at the same time causes my money version of the problem to no longer be equivalent.
Overall, the only thing I think is ridiculous is the suggestion that rule 2 should be dropped because of this. The justification for rule 2 is not in any way damaged by this paradox. Rationality should not be defined as what reasonable people choose to do anyway, as people have been wrong before and will be wrong again. At best it shows that perfectly reasonable people can be infinitessimally irrational in a contrived corner case, at worst it shows nothing.
A more interesting setup would be with either 29 or 31 balls. In that case there’s a finite cost to the wrong decision. How many “reasonable” people still stick to their suboptimal choice in that case though?
It seems just a classic case of people being naturally unwilling to fully dive into the abstraction.
Firstly, the fully abstracted problem provides only indifference between the choices. So, as much as we are able to dive in and cut out all external influences in our thinking, even when we do, the problem at best tells us that we should be indifferent. So we’re indifferent, then we’re asked us to make a choice. If you’re the sort of person who, when faced with an indifferent choice will say “I am provably indifferent, and thus refuse to choose”, you will generally be less functional in life than somebody who just picks one. So we all make a choice, and I would say when it’s indifferent then any choice is as good as any other. My point is, since the abstract problem gives us nothing, then even an infinitessimal hole in our ability to accept the rules of the problem makes all the difference.
If you don’t accept the abstraction fully, then there’s plenty of reasons to make the choices people make, as other comments already mention—assuming the game is more likely rigged against you than for you, and risk aversion in the case where there at least might be multiple plays.
Of course, I do think there still is a thinking failure people are making here. People see there being two levels and don’t realise they can’t really be separated. The problem people think they are solving is something like the following: “I will give you $X, where is the number of balls of the colour(s) you choose in the urn”. Normally that would seem to be an equivalent problem, and in that problem risk aversion trumps indifference and people’s choices are, well, as rational as risk aversion anyway. Strangely, a decreasing average utility of larger amounts of money both justifies risk aversion while at the same time causes my money version of the problem to no longer be equivalent.
Overall, the only thing I think is ridiculous is the suggestion that rule 2 should be dropped because of this. The justification for rule 2 is not in any way damaged by this paradox. Rationality should not be defined as what reasonable people choose to do anyway, as people have been wrong before and will be wrong again. At best it shows that perfectly reasonable people can be infinitessimally irrational in a contrived corner case, at worst it shows nothing.
A more interesting setup would be with either 29 or 31 balls. In that case there’s a finite cost to the wrong decision. How many “reasonable” people still stick to their suboptimal choice in that case though?