Decision Theory is the study of principles and algorithms for making correct decisions—that is, decisions that allow an agent to achieve better outcomes with respect to its goals. Every action at least implicitly represents a decision under uncertainty: in a state of partial knowledge, something has to be done, even if that something turns out to be nothing (call it “the null action”). Even if you don’t know how you make decisions, decisions do get made, and so there has to be some underlying mechanism. What is it? And how can it be done better? Decision theory has the answers.
Note: this page needs to be updated with content regarding Functional Decision Theory, the latest theory from MIRI.
Related: Game Theory, Robust Agents, Utility Functions
A core idea in decision theory is that of expected utility maximization, usually intractable to directly calculate in practice, but an invaluable theoretical concept. An agent assigns utility to every possible outcome: a real number representing the goodness or desirability of that outcome. The mapping of outcomes to utilities is called the agent’s utility function. (The utility function is said to be invariant under affine transformations: that is, the utilities can be scaled or translated by a constant while resulting in all the same decisions.) For every action that the agent could take, sum over the utilities of the various possible outcomes weighted by their probability: this is the expected utility of the action, and the action with the highest expected utility is to be chosen.
Thought experiments
The limitations and pathologies of decision theories can be analyzed by considering the decisions they suggest in the certain idealized situations that stretch the limits of decision theory’s applicability. Some of the thought experiments more frequently discussed on LW include:
Commonly discussed decision theories
Standard theories well-known in academia:
Theories invented by researchers associated with MIRI and LW:
ADT: Ambient Decision Theory (a variant of UDT)
Other decision theories are listed in A comprehensive list of decision theories.
Blog posts
Decision Theories: A Less Wrong Primer by orthonormal
Decision Theory FAQ by lukeprog and crazy88
Highlighting this note in case someone more knowledgeable about FDT than me would like to update this wiki-tag.
Note to self (or others): Add link from https://wiki.lesswrong.com/wiki/Decision_theory when this exists.
How about having both this and a Utility article be parents/prerequisites of Expected utility formalism; then, you could have
Utility → Marginal Utility → Supply and Demand
(Or maybe have utility and marginal utility be the same?)