A random action that ranks in the top 5% is not the same as the action that maximizes the chance that you will end up at least 95% certain the cauldron is full.
For EU quantilization. But you could apply quantilization to beliefs rather than the utilities. (I don’t think it would work as well because I immediately wonder how many different ways belief quantilization breaks the probability axioms and renders any such agent inconsistent & Dutch-bookable, and this illustrates why people generally discuss EU quantilization instead.)
A random action that ranks in the top 5% is not the same as the action that maximizes the chance that you will end up at least 95% certain the cauldron is full.
For EU quantilization. But you could apply quantilization to beliefs rather than the utilities. (I don’t think it would work as well because I immediately wonder how many different ways belief quantilization breaks the probability axioms and renders any such agent inconsistent & Dutch-bookable, and this illustrates why people generally discuss EU quantilization instead.)