think-minimax-regret

Minimax Regret

Some choices pit a few options you control against a few states of the world you do not - the market runs hot, flat, or cold; the rival enters or stays out; the regulation passes or fails - and there is no defensible way to attach probabilities to those states. Expected value cannot run there, because it needs a distribution that does not exist. Minimax regret is the criterion built for exactly that regime. The durable cognitive move is to stop scoring raw payoff and start scoring opportunity loss: for each state, ask how much worse off this option leaves you than the option that turns out best in that state, then choose the option whose single worst regret across all states is smallest. It is Savage's less-pessimistic relative of Wald's maximin - it hedges against being badly wrong without throwing away all upside to protect a worst case that barely moves. The output is a regret matrix with the per-option maximum regret, the minimax pick marked, and the state that binds that pick - built with no probabilities over the states.

When to Use

• A few discrete options face a few discrete, uncontrollable states of nature, and no trustworthy probability distribution over those states exists (so an expected-value calculation cannot legitimately run).
• The stakes justify making the trade-offs explicit, and you want a rule that hedges against the "if only I had chosen the other one" outcome rather than one that bets on a guessed distribution.
• One-shot decisions where historical frequencies do not apply: a new-product launch into speculative market scenarios, a one-time investment, a policy choice under deep uncertainty.
• You want a choice rule that is less brutally pessimistic than pure maximin because it scores opportunity loss, not raw worst payoff.

When NOT to Use

• Do not use it when a defensible probability distribution exists. If you can source even rough base rates for the states, discarding them to run a probability-free criterion throws away real information. Price the uncertainty with think-expected-value-decision-tree instead (chance nodes whose probabilities sum to one, rolled back to an expected value). Minimax regret is for the regime where expected value legitimately cannot be computed, not a substitute for doing the probability work when it is available. This is the closest sibling and the most important wall.
• Do not use it to score options on attributes you can assert. Ranking options on weighted criteria you control (cost, fit, speed, risk) with no states of nature and no opportunity-loss transform is think-decision-option-review. That answers "which option scores best on my criteria"; minimax regret answers "which option minimizes worst-case regret across uncontrollable futures." If there are no states of nature, this is the wrong tool.
• Do not use it when the option set is unstable or gameable. This is the criterion's deepest formal flaw, not a quibble. Because regret in each state is defined relative to the best option in the current set, adding or removing an option - even a dominated one that would never be chosen - can recompute the column maxima and flip the recommendation (a violation of the independence of irrelevant alternatives, Chernoff 1954). If someone can pad the option list, or the set is fluid, the answer can be steered without changing anything real. Freeze a defensible option set first, or do not use the criterion.
• Do not invent the states or the payoffs and then trust them. Like any matrix method, it renders fabricated inputs in an authoritative grammar; a regret table built on made-up cell values produces a confident answer about nothing.
• Do not present its pick as the one rational answer. It is one criterion among several (maximin, maximax, Hurwicz, Laplace) that can each recommend a different option on the same matrix. Report it as a hedge against worst-case opportunity loss and note where the criteria disagree, never as the uniquely correct choice.
• Do not use it when the states cannot even be enumerated. True deep uncertainty where you cannot list the relevant futures breaks the matrix at step one. That is a framing problem, not a scoring one.