# Decision theory

**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.

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.

## Contents

## 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:

- Newcomb's problem
- Counterfactual mugging
- Parfit's hitchhiker
- Smoker's lesion
- Absentminded driver
- Sleeping Beauty problem
- Prisoner's dilemma
- Pascal's mugging

## Commonly discussed decision theories

Standard theories well-known in academia:

Theories invented by researchers associated with SingInst and LW:

- TDT, Timeless Decision Theory
- UDT, Updateless Decision Theory
- ADT: Ambient Decision Theory (a variant of UDT)

## Blog posts

## Sequence by AnnaSalamon

- Decision theory: An outline of some upcoming posts
- Confusion about Newcomb is confusion about counterfactuals
- Why we need to reduce “could”, “would”, “should”
- Why Pearl helps reduce “could” and “would”, but still leaves us with at least three alternatives

## Sequence by orthonormal (Decision Theories: A Semi-Formal Analysis)

- Part 0: Decision Theories: A Less Wrong Primer
- Part I: The Problem with Naive Decision Theory
- Part II: Causal Decision Theory and Substitution
- Part III: Formalizing Timeless Decision Theory

## See also

- Instrumental rationality
- Causality
- Expected utility
- Timeless decision theory, Updateless decision theory
- AIXI