Explicitly working out the probabilities for a situation is not always possible or desirable for real world situations. We’re just not that smart.
You should not, however, take that to mean that decision theory cannot work at all. You should certainly, if you find yourself losing money, stop and do the math and find out if you’re being dutch booked. You should certainly do the math on investments to find out if they have positive expected utility. Anywhere that you have real numbers, probability theory suddenly outstrips all the hazy heuristics you normally rely on.
It can even be applied closer to home. When I’m looking at whether or not to drop a class, I plot a probability distribution for my past grades, figure out the scores I need to pass, and compute, if I continue to perform at past levels, my probability of passing the class with the minimum grade to maintain my scholarships. Then I figure out how much money I would pay to suddenly, magically, have passed the class, how much money someone would have to pay me to take the class, and how much someone would have to pay me to do the paperwork to switch. If the math doesn’t wash, I drop the class, study up over the break, and re-take it the next semester with a better utility forecast.
Explicitly working out the probabilities for a situation is not always possible or desirable for real world situations. We’re just not that smart.
You should not, however, take that to mean that decision theory cannot work at all. You should certainly, if you find yourself losing money, stop and do the math and find out if you’re being dutch booked. You should certainly do the math on investments to find out if they have positive expected utility. Anywhere that you have real numbers, probability theory suddenly outstrips all the hazy heuristics you normally rely on.
It can even be applied closer to home. When I’m looking at whether or not to drop a class, I plot a probability distribution for my past grades, figure out the scores I need to pass, and compute, if I continue to perform at past levels, my probability of passing the class with the minimum grade to maintain my scholarships. Then I figure out how much money I would pay to suddenly, magically, have passed the class, how much money someone would have to pay me to take the class, and how much someone would have to pay me to do the paperwork to switch. If the math doesn’t wash, I drop the class, study up over the break, and re-take it the next semester with a better utility forecast.