Define a function’s wackiness is easy. If you don’t believe me, suffer through the following paragraph, in which I demonstrate my cleverness in a remarkably economist-like manner.
Let’s say a utility function goes from world-states to real numbers on the interval [-1, 1]. −1 is the worst thing you can imagine and 1 is the best. Your function periodically re-normalizes as the best or worst thing you can imagine changes. To compute two utility functions’ wackiness with respect to each other, compute the root-mean-squared differences between them across all world-states they are both defined on. Define a function A(world-state) which is defined on all world-states for which at least half of the human revealed utility functions are defined on and for which the standard deviation in the human revealed utility functions’ computed values is less than 0.2. Its value for any given world-state is the average of all humanity’s revealed utility functions’ values for that world state. Observing all humanity’s revealed utility functions’ wackiness with respect to A, we designate humans as “insane” if their revealed utility functions’ wackiness with respect to A is more than two standard deviations above the average.
In other words, insane people want really different things than other people.
That’s probably not a good definition though, because those people are more likely to be called weird than insane. Probably the fast-changing revealed utility function definition is a better one. For that you’d compute the wackiness of a person’s current revealed utility function with respect to the one they had five minutes ago over the last four days and add all the wackinesses together. If this result is more than four standard deviations above the average they can be considered insane.
For that you’d compute the wackiness of a person’s current revealed utility function with respect to the one they had five minutes ago over the last four days and add all the wackinesses together. If this result is more than four standard deviations above the average they can be considered insane.
I’m not sure that really captures most of what passes for ‘insane’.
Define a function’s wackiness is easy. If you don’t believe me, suffer through the following paragraph, in which I demonstrate my cleverness in a remarkably economist-like manner.
Let’s say a utility function goes from world-states to real numbers on the interval [-1, 1]. −1 is the worst thing you can imagine and 1 is the best. Your function periodically re-normalizes as the best or worst thing you can imagine changes. To compute two utility functions’ wackiness with respect to each other, compute the root-mean-squared differences between them across all world-states they are both defined on. Define a function A(world-state) which is defined on all world-states for which at least half of the human revealed utility functions are defined on and for which the standard deviation in the human revealed utility functions’ computed values is less than 0.2. Its value for any given world-state is the average of all humanity’s revealed utility functions’ values for that world state. Observing all humanity’s revealed utility functions’ wackiness with respect to A, we designate humans as “insane” if their revealed utility functions’ wackiness with respect to A is more than two standard deviations above the average.
In other words, insane people want really different things than other people.
That’s probably not a good definition though, because those people are more likely to be called weird than insane. Probably the fast-changing revealed utility function definition is a better one. For that you’d compute the wackiness of a person’s current revealed utility function with respect to the one they had five minutes ago over the last four days and add all the wackinesses together. If this result is more than four standard deviations above the average they can be considered insane.
I’m not sure that really captures most of what passes for ‘insane’.