Abstract

Every textbook decision theory is a single operator carrying a different assumption. Bayesian decision theory, causal and evidential decision theory, functional decision theory, no-regret learning, minimax, and Nash equilibrium are each recovered by taking one worst-case operator and adding an ingredient the encounter itself does not supply. This paper identifies that operator as Miximin Decision Theory (MDT): worst-case on both sides of an encounter, under Knightian uncertainty, with no privileged position reserved for a decider. Its population-level fixed point is miximin, the settlement that a substrate of interacting parties reaches without any party computing it.

The unifying result is de-metering. Each standard theory takes a resource the encounter must pay for — energy, computation, samples, memory, or precision — and sets its cost to zero, admitting an infinity that allows the governing equations to close. Removing the imported infinity returns the theory to MDT. The catalog is exhaustive: every entry either imports one of these five costs, in which case it is confined, or posits genuinely new content at the meeting, which constitutes the open frontier. The one worked frontier candidate resolves into the operator's nearest relative rather than escaping it.

The operator is not an abstraction. Physical systems ranging from the rocket equation and the Maxwell-Boltzmann distribution to quantum measurement and the standard genetic code are instances of miximin settling on different substrates. In each case the configuration that persists is the worst-case-secured one that a maximin reading selects and an averaging metric conceals.