“The target” is not always something you can aim at and hit. Sometimes there are two outcomes which are very close together in actualizing, but very far apart in desirability.
For example, launching a satellite might be the most desired outcome, while scrapping the project is of intermediate desirability and botching the launch has the lowest desirability. You can’t aim away from ‘botched launch’ very much before you need to shift your aim all the way to ‘scrap the project’.
The highest value on the dartboard is the triple-20, but the best place for someone with moderate accuracy to aim is somewhere between triple-16 and the bullseye; if one assumes that a player will hit a random point within a circular area with radius related to accuracy, the best point of aim is not a continuous function of the accuracy of the player, but jumps from region to region. So it is with aiming at real targets- one doesn’t choose the outcome, but chooses the region from which an outcome will be chosen.
What I’m saying is that a rational darts thrower who just hit triple-1 is likely has a higher estimation of his own skill than one that just hit triple-14, and the one who just hit the bullseye likely has the lowest estimation of his own skill. (assuming all players are maximizing points on one throw).
“The target” is not always something you can aim at and hit. Sometimes there are two outcomes which are very close together in actualizing, but very far apart in desirability.
For example, launching a satellite might be the most desired outcome, while scrapping the project is of intermediate desirability and botching the launch has the lowest desirability. You can’t aim away from ‘botched launch’ very much before you need to shift your aim all the way to ‘scrap the project’.
The highest value on the dartboard is the triple-20, but the best place for someone with moderate accuracy to aim is somewhere between triple-16 and the bullseye; if one assumes that a player will hit a random point within a circular area with radius related to accuracy, the best point of aim is not a continuous function of the accuracy of the player, but jumps from region to region. So it is with aiming at real targets- one doesn’t choose the outcome, but chooses the region from which an outcome will be chosen.
Hence the bit about expected utility.
What I’m saying is that a rational darts thrower who just hit triple-1 is likely has a higher estimation of his own skill than one that just hit triple-14, and the one who just hit the bullseye likely has the lowest estimation of his own skill. (assuming all players are maximizing points on one throw).