# Random utility function

A ‘random utility function’ is a utility function selected according to some simple probability measure over a logical space of formal, compact specifications of utility functions.

For example: suppose utility functions are specified by computer programs (e.g. a program that maps an output description to a rational number). We then draw a random computer program from the standard universal prior on computer programs: $$2^{-\operatorname K(U)}$$ where $$\operatorname K(U)$$ is the algorithmic complexity (Kolmogorov complexity) of the utility-specifying program $$U.$$

This obvious measure could be amended further to e.g. take into account non-halting programs; to not put almost all of the probability mass on extremely simple programs; to put a satisficing criterion on whether it’s computationally tractable and physically possible to optimize for $$U$$ (as assumed in the Orthogonality Thesis); etcetera.

Complexity of value is the thesis that the attainable optimum of a random utility function has near-null goodness with very high probability. That is: the attainable optimum configurations of matter for a random utility function are, with very high probability, the moral equivalent of paperclips. This in turn implies that a superintelligence with a random utility function is with very high probability the moral equivalent of a paperclip maximizer.

A ‘random utility function’ is not:

• A utility function randomly selected from whatever distribution of utility functions may actually exist among agents within the generalized universe. That is, a random utility function is not the utility function of a random actually-existing agent.

• A utility function with maxentropy content. That is, a random utility function is not one that independently assigns a uniform random value between 0 and 1 to every distinguishable outcome. (This utility function would not be tractable to optimize for—we couldn’t optimize it ourselves even if somebody paid us—so it’s not covered by e.g. the Orthogonality Thesis.)

Parents:

• Paperclip maximizer

This agent will not stop until the entire universe is filled with paperclips.