definition v1 of decision theory

Decision theory is a human-made mathematical and computational framework for making optimal choices under uncertainty. It formalizes the process of selecting among alternatives by assigning utilities to outcomes, probabilities to states of the world, and combining them through expected utility calculations (expected utility = Σ p_i · u_i). The framework persists through mathematical formalism in economics, statistics, operations research, philosophy, and artificial intelligence. Decision theory encompasses two major branches: normative decision theory, which specifies how rational agents ought to make decisions (classical expected utility theory, von Neumann-Morgenstern axioms), and descriptive decision theory, which models how actual humans make decisions (incorporating behavioral economics findings on risk aversion, loss aversion, and cognitive heuristics). The mathematical framework was established by von Neumann and Morgenstern (1944) and Savage (1954), and extends to sequential decisions (dynamic programming, Markov decision processes), games with multiple agents (game theory), and learning under uncertainty (reinforcement learning, Bayesian decision theory). The core mechanism is the decision matrix: mapping actions to consequences via states of nature, evaluated by a utility function and weighted by subjective or objective probabilities. [formal: theoria decisionis | substrate: mind | horizon: a life | explicit: yes | epoch: 0.13]