While this is a mathematically correct argument, it implies a real world relationship that does not hold in all cases. To illustrate while a platonic agent would be correct to select 1b let’s instead imagine an impoverished Somalian living on a few dollars a day. 24,000 dollars would be a life-changing amount of money. The increased utility of $3000 additional dollars would in no way make up for a 1⁄34 chance of losing such an opportunity.
Conversely imagine a billionaire in the same situation. For him the optimal choice is neither 1a or 1b instead he should turn around and leave instead of wasting his time on such a small sum of money. For a middle class American 1b would indeed be the correct choice. So you see naive rationality can be very irrational.
For another example consider the lottery. Occasionally the pot increases such that you’re expected return is more than one dollar per dollar spent. In such a case you should still not buy lottery tickets, because your chance of winning back your money is still tiny. The increased size of the pot does not provide much more utility than its normal size for most lottery players. Of course if you possess a lot of capital and there are no rules against it you might make a return with a large investment but such possibilities are normally blocked.
My examples are purposefully extreme, but they work to illustrate that you can’t just translate mathematical probabilities directly into real life and call that rational. Real conditions have to be taken into account.
While this is a mathematically correct argument, it implies a real world relationship that does not hold in all cases. To illustrate while a platonic agent would be correct to select 1b let’s instead imagine an impoverished Somalian living on a few dollars a day. 24,000 dollars would be a life-changing amount of money. The increased utility of $3000 additional dollars would in no way make up for a 1⁄34 chance of losing such an opportunity.
Conversely imagine a billionaire in the same situation. For him the optimal choice is neither 1a or 1b instead he should turn around and leave instead of wasting his time on such a small sum of money. For a middle class American 1b would indeed be the correct choice. So you see naive rationality can be very irrational.
For another example consider the lottery. Occasionally the pot increases such that you’re expected return is more than one dollar per dollar spent. In such a case you should still not buy lottery tickets, because your chance of winning back your money is still tiny. The increased size of the pot does not provide much more utility than its normal size for most lottery players. Of course if you possess a lot of capital and there are no rules against it you might make a return with a large investment but such possibilities are normally blocked.
My examples are purposefully extreme, but they work to illustrate that you can’t just translate mathematical probabilities directly into real life and call that rational. Real conditions have to be taken into account.