Principle of Maximum Expected Utility

utility-theory

Definition

Principle of Maximum Expected Utility

The Principle of Maximum Expected Utility states that a rational agent, given evidence $\mathbf{e}$, should choose the action $a$ that maximises its expected utility $EU(a\mid \mathbf{e})$:

$$a^{\star }=\arg \underset{a\in A}{\max }EU(a\mid \mathbf{e}).$$

Concretely, with the expected utility

$$EU(a\mid \mathbf{e})=\sum _{s^{\prime }}P(\mathrm{RESULT}(a)=s^{\prime }\mid a,\mathbf{e})\cdot U(s^{\prime })$$

given outcomes $s^{\prime }$ and utility function $U$, the principle says: pick the action whose probability-weighted average outcome utility is highest.

Reading

The principle is the decision rule that turns a rational agent’s goal — “do the right thing” — into a concrete selection criterion over the action set $A$. It is the bridge between expected utility as a numerical evaluation of a single action and rationality as behaviour: rationality asks for the best action, and “best” is defined here as maximum expected utility.

Not Omniscience

Not omniscience

Evidence $\mathbf{e}$ may be incomplete, so $a^{\star }$ can be wrong in hindsight; the principle only commits the agent to the best action given what it knows.

This mirrors the same limit on rationality: rational $\ne$ omniscient, because the agent’s percepts may lack relevant information.

Vacuous Without a Utility Function

Vacuous without a utility function

If $U$ is unspecified, every action trivially maximises $EU$. The principle prescribes behaviour only once $U$ fixes what counts as desirable.

Without $U$, the maximisation is a comparison of unlabelled numbers; with $U$, the same comparison becomes a meaningful preference ordering over actions.