Minimax Regret

Quick facts

Mechanism: Produces a regret (opportunity-loss) matrix with the minimax pick and the binding worst-case state, choosing among options over un-probabilized states of nature.

Produces: regret-matrix

Evidence: P · Domain: Decision and Option Evaluation

Use when a few discrete options face a few discrete uncontrollable states and no defensible probabilities exist. Not an expected-value tree (which needs probabilities) and not an attribute scorecard.

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.

Instructions

When asked to choose among options under uncertain, un-probabilized states - or whenever a decision has the discrete-options-by-uncontrollable-states shape and no probabilities are available - follow these steps:

1. Frame the decision and confirm no probabilities. State, in one line, the choice under pressure. Confirm that the states of nature genuinely cannot be assigned defensible probabilities. If they can, stop and route to think-expected-value-decision-tree - that is the right tool, and using minimax regret would discard information.
2. List the options (rows). Enumerate the discrete options you actually control and could choose. Freeze this set: because the criterion violates the independence of irrelevant alternatives, an unstable or padded option list can steer the answer. Drop options no one would seriously consider, and say you did.
3. List the states of nature (columns). Enumerate the discrete, uncontrollable, mutually exclusive states the world could be in (market hot / flat / cold; rival in / out). If you cannot enumerate them, the matrix breaks here - this is a framing problem, not a scoring one.
4. Build the payoff matrix. For each option-by-state cell, record the payoff of that option in that state (profit, net value, utility - state the unit and the sign convention). Do not invent numbers; if a cell is genuinely unknown, mark it and flag the uncertainty rather than fabricating a value.
5. Transform payoffs into regrets, column by column. For each state (column), find the best payoff any option achieves in that state. Replace every cell with the gap between that column-best and the cell’s payoff - the regret (opportunity loss) for having chosen this option rather than the one that turned out best. The best option in each column gets regret 0; every other cell is a positive number.
6. Take each option’s maximum regret. For each option (row), find its single largest regret across all states. This is the worst-case opportunity loss that option exposes you to. Record it in a max-regret column.
7. Apply the minimax rule and name the binding state. Choose the option whose maximum regret is smallest. Mark it as the minimax pick. Name the state in which that chosen option incurs its worst-case regret - the binding state that the whole recommendation turns on.
8. Sanity-check against the sibling criteria and the IIA flaw. Note briefly what maximin (best worst-payoff) would pick, and whether any plausible added or removed option would flip the result. If the pick is fragile to the option set, say so. Present minimax regret as a worst-case-opportunity-loss hedge, not the single rational answer.
9. Emit the regret matrix artifact per references/TEMPLATE.md: the payoff matrix, the regret matrix with the max-regret column, the minimax pick, and the binding state - with the no-probabilities precondition stated plainly.

Output Format

Use the template in references/TEMPLATE.md. The deliverable is the filled regret analysis - the payoff matrix, the derived regret matrix with each option’s maximum-regret column, the marked minimax choice, and the binding worst-case state - not a prose recommendation. State explicitly that no probabilities were placed over the states. Never attach likelihoods to the columns.

Quality Checklist

Before finalizing, verify:

• The decision is one line, and it is confirmed that no defensible probability distribution over the states exists (otherwise this is the wrong tool - route to think-expected-value-decision-tree).
• The option set (rows) is frozen and defensible; no padding, and any dropped options are named - so the IIA flaw cannot steer the answer.
• The states of nature (columns) are discrete, uncontrollable, and actually enumerable.
• Payoffs are real inputs with a stated unit and sign convention, not fabricated cell values; unknown cells are flagged, not invented.
• The regret transform is done correctly: column-best gets 0, every other cell is (column-best minus cell), no arithmetic slips.
• Each option’s maximum regret is taken across all states, and the minimax pick is the smallest of those maxima.
• The binding state (where the chosen option incurs its worst-case regret) is named.
• No probabilities are attached to the columns, and the worlds are not ranked by likelihood.
• The pick is presented as a worst-case-opportunity-loss hedge, with a note on sibling-criterion disagreement and IIA fragility - not as the uniquely rational answer.
• No overclaiming: the evidence is practitioner-grade and transferred; claim a coherent no-probability choice rule, not a measured improvement in decision outcomes (see evidence/dossier.md).

Evidence

Tier P (governing). Minimax regret is a real, named, long-lived decision criterion with an unambiguous lineage (Savage 1951, building on Wald’s minimax) and a serious formal literature (Manski 2004; Stoye 2009; and RAND’s Robust Decision Making, Lempert et al. 2006). That record supports that the rule is mathematically coherent and has attractive worst-case-regret properties given its formal setup. It does NOT support that a decider - human or AI - who builds a regret matrix and applies minimax makes better real-world decisions than one who uses a cheaper rule; no controlled study measures the generic criterion as a decision procedure against an alternative and finds it improves outcomes. The behaviorally validated “regret” evidence (Bell 1982; Loomes and Sugden 1982; Zeelenberg et al. 1996) belongs to regret theory - a descriptive model of anticipated regret under known probabilities - which is a different operation in the very probability regime minimax regret exists to escape; it is deliberately NOT counted toward this grade (borrowing it would launder a cousin’s evidence). The criterion also carries a genuine negative formal result - the Chernoff 1954 violation of independence of irrelevant alternatives - which argues for never inflating the grade. Transfer caveat: every datum is a mathematical property of the rule or a finding from human subjects; none studies minimax regret performed by or with an AI agent, so the evidence is transferred and not validated for AI-augmented use. For an agent the honest value is mechanical: build the matrix, run the regret transform without slips, surface the binding state, and refuse to invent cells. Full grading, sources, and caveats: evidence/dossier.md.

Examples

See references/EXAMPLE.md for a completed regret analysis on a real decision.

Deep dive: worked example

A full worked run (the shared Northwind scenario)

Regret (Opportunity-Loss) Matrix - Worked Example

A completed run of the minimax-regret skill on a real, consequential decision. This is the quality bar a generated regret analysis should meet.

Uses the shared recurring scenario (Northwind, a B2B SaaS weighing a self-serve free-tier launch). Where think-scenario-planning builds four uncontrollable external worlds and think-expected-value-decision-tree would price the launch if the adoption states could be probabilized, this skill handles the case where Northwind genuinely cannot attach defensible probabilities to how the market adopts a free tier - so it chooses the launch option that minimizes worst-case opportunity loss, with no probabilities over the states. See docs/internal/AUTHORING.md.

No probabilities are placed on the states below. The columns are not ranked or weighted by likelihood. The value is the minimax pick and the binding state, not a forecast.

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Focal decision and no-probability precondition

• Decision: Choose Northwind’s self-serve packaging for the next product cycle - among (A) no free tier (stay sales-led trial-only), (B) a limited free tier (tight usage caps, few integrations), and (C) a generous free tier (broad individual-value features, open integrations).
• Why no probabilities: This is a one-shot launch into a market whose response to a Northwind free tier has no precedent. Adoption could be weak, healthy-and-converting, or high-volume-but-low-converting, and there is no base rate or comparable launch to ground a defensible probability on any of those. Expected value cannot legitimately run, so a no-probability criterion is appropriate. (If Northwind could source credible adoption probabilities, the right tool would be think-expected-value-decision-tree, not this.)
• Payoff unit and sign convention: three-year contribution to net new ARR, in $M, net of the incremental cost to serve the free tier. Higher is better.

Options (rows) - frozen set

• Option A: No free tier - keep the sales-led, time-boxed-trial motion; spend nothing on free-tier infrastructure or support.
• Option B: Limited free tier - ship a capped free tier (low usage limits, a thin integration set) that acquires users cheaply but converts modestly and costs little to serve.
• Option C: Generous free tier - ship a broad free tier (real individual-value features, open integrations) that acquires and activates strongly but carries a heavy cost to serve if volume is high and conversion is weak.

(Set frozen at these three. A fourth idea - “freemium plus a paid prosumer tier” - was dropped as a separate decision for a later cycle; noting it here because, under this criterion, padding the option list could move the column maxima and steer the pick.)

States of nature (columns) - uncontrollable, un-probabilized

• State 1: Cold - the market shrugs at a free tier; self-serve signups are low and Northwind’s buyers keep behaving sales-led.
• State 2: Convert - a free tier lands well and a healthy share of signups convert to paid; the self-serve motion works as hoped.
• State 3: Flood - a free tier draws high signup volume but a low conversion rate; the funnel fills with users who consume support and infrastructure without paying.

(Discrete, mutually exclusive, and outside Northwind’s control - Northwind sets the packaging, not how the market responds. Enumerable, so the matrix holds at step one.)

Payoff matrix

Three-year net new ARR contribution, $M, net of cost to serve. Estimates are Northwind’s planning figures; no cell is invented to force a result, and each is a real planning input.

Option \ State	State 1: Cold	State 2: Convert	State 3: Flood
A: No free tier	6	6	6
B: Limited free tier	5	12	4
C: Generous free tier	2	20	-3
Column best	6 (A)	20 (C)	6 (A)

(Read the rows: A is flat at 6 because a sales-led motion is roughly indifferent to how a free tier would have done. B gives up a little in the Cold state, gains in Convert, and is only mildly hurt in Flood because its caps limit the cost to serve. C swings hardest - biggest upside in Convert, biggest loss in Flood where the generous tier’s cost to serve outruns conversion.)

Regret matrix

For each column, regret = (column-best payoff) minus (this cell’s payoff). Column-best gets 0; every other cell is a positive opportunity loss. Then take each row’s maximum regret.

Option \ State	State 1: Cold	State 2: Convert	State 3: Flood	Max regret (row)
A: No free tier	0	14	0	14
B: Limited free tier	1	8	2	8
C: Generous free tier	4	0	9	9

(Worked: in Convert the best is C at 20, so A’s regret is 20 minus 6 = 14 and B’s is 20 minus 12 = 8. In Flood the best is A at 6, so C’s regret is 6 minus (-3) = 9. Each row’s max is its single worst opportunity loss across the three states.)

Minimax pick and binding state

• Minimax pick: Option B, the limited free tier - its maximum regret is 8, the smallest of the three max-regret values (14, 8, 9).
• Binding state: Convert - B’s worst-case regret of 8 occurs in the Convert state, where a generous tier (C) would have captured 8 more $M of ARR. That is the opportunity loss B accepts in exchange for never being badly exposed.
• What this means: choosing the limited free tier guarantees Northwind’s opportunity loss never exceeds 8 $M whatever the market does. The generous tier (C) has a higher ceiling on regret (9, in Flood) despite its huge Convert upside, and no free tier (A) has the highest regret of all (14, in Convert) because it forfeits the entire self-serve upside. B is the worst-case-opportunity-loss hedge.

Sibling-criterion and IIA check (honesty rail)

• What maximin would pick (best worst-payoff): Option A. Its worst payoff is 6 (in every state), versus B’s worst of 4 (Flood) and C’s worst of -3 (Flood). Pure maximin protects the floor and picks “no free tier.” Minimax regret disagrees: it judges that A’s safety costs too much forgone upside (a regret of 14 in Convert), and prefers B. The two criteria pointing at different options is exactly why this pick is reported as a hedge, not as the one rational answer.
• Where the criteria disagree: maximin says A (protect the floor), minimax regret says B (limit the worst opportunity loss), and a maximax optimist would say C (chase the 20 in Convert). On the same matrix, three defensible criteria give three different answers - this is reported, not hidden.
• IIA fragility: the pick is moderately sensitive to the option set. If a fourth option were added that beat C in the Convert column, B’s regret in Convert (and so its max regret) could rise and the ranking could shift, even though nothing about B changed. This is the Chernoff (1954) independence-of-irrelevant-alternatives flaw in action, and the reason the option set was frozen and the dropped “prosumer tier” idea was named rather than silently included.

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Note how this differs from its neighbors on the same Northwind decision. think-expected-value-decision-tree would attach probabilities to Cold / Convert / Flood and roll back an expected ARR - which is the right move only if those probabilities are defensible; here they are not, so that tool cannot legitimately run. think-scenario-planning would build the uncontrollable external worlds as narratives and look for moves robust across all of them, without ever scoring a single best option. think-decision-option-review would score A, B, and C on weighted attributes Northwind asserts (cost, strategic fit, effort) with no states of nature at all. Minimax regret does the one thing none of those does: it chooses a single option by minimizing the maximum opportunity loss across states it refuses to probabilize, and it names the state that binds that choice.

Grounding: the full evidence dossier

What the research does and does not show, with graded sources

Evidence Dossier: Minimax Regret

The single source of truth for the minimax-regret skill. The SKILL.md, the sidecar (skill.meta.yml), and the eval cases all derive from this file. If a claim is not here, it does not belong in the skill. Promoted from frameworks/_proposed/minimax-regret/dossier.md and admitted as a Build at tier P.

Skill	thinking-framework-skills.minimax-regret (installable name think-minimax-regret)
Family	decision-and-option-evaluation
Evidence tier	P governing (a recognized, formally well-founded practitioner and textbook criterion; no direct controlled evidence that applying it improves decisions - see “What the evidence shows”)
Confidence	High that the rule is mathematically coherent and runs without arithmetic slips; low that any decision-outcome benefit transfers to an applied decision or to agents
Status	draft (admitted as a Build at tier P; a narrow, lower-priority build kept formally distinct from the candidate regret-minimization entry)

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1. The mechanism (what actually does the work)

Minimax regret is a formal criterion for choosing among options when you face distinct “states of the world” but have no trustworthy probabilities to attach to them. Introduced by Leonard J. Savage in 1951, it reframes a choice around opportunity loss instead of payoff. The move has three mechanical steps:

1. Lay out a payoff matrix. Rows are the options you control; columns are the states of nature you do not (the market is hot / flat / cold; the rival enters / stays out; the regulation passes / fails). Each cell is the payoff of that option in that state.
2. Transform it into a regret matrix. For each column (state), find the best payoff any option achieves in that state, then replace every cell with the gap between that column-best and the cell - the regret (opportunity loss) you would feel, in that state, for having chosen this option rather than the one that turned out best. The best option in each column gets regret 0.
3. Apply the minimax rule. For each option (row), take its single worst (maximum) regret across all states. Choose the option whose worst-case regret is smallest - the option that minimizes the maximum opportunity loss.

The durable cognitive move is transforming a payoff matrix into a regret (opportunity-loss) matrix and choosing the option whose maximum regret across un-probabilized states is smallest. The deliverable is a regret matrix with the per-option maximum-regret column and the minimax choice marked, plus the state that binds it (the state in which the chosen option incurs that worst-case regret).

The defining, load-bearing feature is what it does NOT use: probabilities. Minimax regret is a member of the classic family of no-probability decision criteria - maximin (most pessimistic: maximize the worst payoff), maximax (most optimistic: maximize the best), Hurwicz (a tunable blend of the two), Laplace (assume all states equally likely and average) - and within that family it is the one that scores on opportunity loss rather than raw payoff, which makes it less brutally pessimistic than maximin. It is the criterion you reach for precisely when expected value cannot run because no defensible probability distribution over the states exists. In the deep-uncertainty literature it is the robustness criterion at the heart of RAND’s Robust Decision Making (Lempert and colleagues): generate a set of plausible futures, then prefer the strategy whose worst-case regret across that set is smallest.

2. Lineage

The criterion is Leonard J. Savage’s, from “The Theory of Statistical Decision,” Journal of the American Statistical Association 46 (1951): 55-67, where he proposed minimizing maximum opportunity loss (regret) as a less-pessimistic relative of Abraham Wald’s minimax loss rule - read these together for the original move. Herman Chernoff, “Rational Selection of Decision Functions,” Econometrica 22 (1954): 422-443, is the essential counterweight: it establishes that regret-based choice violates the independence of irrelevant alternatives, the criterion’s central formal weakness. For the modern formal revival, read Charles Manski (“Statistical Treatment Rules for Heterogeneous Populations,” Econometrica, 2004) and Jorg Stoye (“Minimax Regret Treatment Choice with Finite Samples,” Journal of Econometrics, 2009), who put minimax regret on rigorous footing for treatment choice; and Robert Lempert and colleagues at RAND for Robust Decision Making, where minimax regret is the robustness criterion applied across computationally generated scenario sets.

Keep these separate from the regret-theory tradition - David E. Bell (1982) and Graham Loomes and Robert Sugden (1982) - which is a descriptive model of anticipated regret under known probabilities, the evidenced cousin this entry deliberately does not borrow grade from; Marcel Zeelenberg and colleagues carry that into the experimental behavioral literature.

“Minimax regret” and “Savage criterion” are generic descriptive terms in common use - no trademark, attribution to Savage suffices - so this entry is documented descriptively and is not flagged as branded.

3. What the evidence shows, and what it does NOT show

The honest governing grade is P (practitioner), and the dossier has to be careful here because “regret” names two different research programs that grade very differently, and only the weaker-graded one is actually this skill’s move.

What the record supports. Minimax regret is a real, named, long-lived decision criterion with an unambiguous lineage (Savage 1951, building on Wald’s minimax) and a serious formal literature. Within mathematical statistics and econometrics, Stoye (2009) and Manski (2004) derive finite-sample and large-sample results showing the minimax-regret rule has good worst-case-regret properties for statistical treatment choice, and it is an established robustness objective in robust optimization and in RAND’s Robust Decision Making (Lempert et al. 2006) for planning under deep uncertainty. That is genuine support - but for what? It supports that the rule is mathematically coherent, has attractive worst-case-regret guarantees given the formal setup, and is widely applied. It is an S-tier mathematical fact about the rule’s properties, in the same way the von Neumann-Morgenstern axioms are an S-tier mathematical fact about expected utility.

What the record does NOT support, and the laundering trap. None of that is evidence that a decider (human or AI agent) who constructs a regret matrix and applies minimax makes better real-world decisions than one who uses a cheaper rule. There is no controlled or comparative study locatable that measures generic minimax regret as a decision procedure against an alternative and finds it improves outcomes. The evidence that does get quoted to make “regret” look behaviorally validated belongs to a different operation - regret theory - and attaching it here would be exactly the transferred-evidence laundering this library exists to prevent:

• Regret theory (Bell 1982; Loomes and Sugden 1982; Fishburn 1982) is a descriptive model of how the anticipation of regret shifts choices under risk (known probabilities). It successfully predicts preference reversals, status-quo bias, and inaction inertia. The Zeelenberg programme of experiments (Zeelenberg et al. 1996, 1999; and recent replications) shows anticipated regret reliably pushes people toward safe options and raises post-choice satisfaction. This is solid, roughly M-tier behavioral work - but it measures the emotion’s effect on human choice, not the prescriptive minimax-regret rule, and it operates in the known-probability world that minimax regret is explicitly for escaping. It is the descriptive cousin, mechanically closer to risk-aversion and to anticipated-emotion research than to Savage’s criterion. Borrowing its robustness to lift minimax regret to M would launder a cousin’s evidence onto a move the cousin did not test.

• The formal optimality results (Stoye 2009; Manski 2004) measure the rule’s statistical properties, not whether using it improves a messy applied decision. Counting them as effectiveness evidence would launder the criterion’s mathematics into a claim about its practical value that the record does not make - the identical pattern the shipped expected-value-decision-tree dossier guards against for EV.

The conservative governing grade is therefore P: a recognized, formally well-founded practitioner and textbook criterion, with no direct controlled evidence that applying it improves decisions, and with the M-tier regret-theory and anticipated-regret work explicitly not counted toward the grade because it measures a different operation. (It is worth noting the criterion also carries a genuine negative formal result - the Chernoff 1954 IIA violation - which is a real mark against it; that argues for not inflating the grade, never for lifting it.)

4. Transferred-evidence flag (required honesty for this library)

Every datum above is either a mathematical property of the rule or a finding from human subjects in lab and field settings; none studies minimax regret performed by or with an AI agent. The evidence is transferred from human and formal contexts and not validated for AI-augmented use. For an agent the realistic value is mechanical and honest - build the payoff matrix, run the regret transform without arithmetic slips, surface which state binds the worst case, and refuse to invent the cells - none of which depends on any unproven outcome claim. The skill ships honestly as a P-tier no-probability choice rule with a hard “use EV when you have probabilities” wall and a hard “freeze the option set” (IIA) wall, never as the uniquely rational decision criterion.

5. When it works / when it fails (drives the eval negative cases and “When NOT to Use”)

Works best when:

• The structure of the decision is genuinely “a few discrete options against a few discrete, uncontrollable, un-probabilizable states,” the stakes justify being explicit, and you want a rule that hedges against being badly wrong rather than one that bets on a guessed distribution.
• New-product launches into speculative market scenarios, one-shot investments where historical frequencies do not apply, and policy choices under deep uncertainty are the textbook homes.
• Its specific virtue over plain maximin is psychological realism: it targets the “if only I had chosen the other one” feeling, and it is less likely than maximin to throw away upside to protect a worst case that barely differs across options.

Fails or misleads when (poor-fit / anti-patterns):

• A defensible probability distribution actually exists. If you can source even rough base rates for the states, discarding them to run a probability-free criterion throws away information; price the uncertainty with an expected-value tree (think-expected-value-decision-tree) instead. Minimax regret is for the regime where EV legitimately cannot be computed, not a substitute for doing the probability work when it is available.
• The option set is unstable or gameable. This is the criterion’s deepest 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, never-chosen one - can recompute the column maxima and flip the recommendation. This is a formal 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.
• States or payoffs are invented and then trusted. 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.
• It is treated as the single “rational” answer. It is one criterion among several (maximin, maximax, Hurwicz, Laplace) that can each recommend a different option on the same matrix. The honest use is to state that minimax regret is a hedge against worst-case opportunity loss and to note where the criteria disagree, not to present its pick as the uniquely correct choice.
• 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.

6. Distinctness (closest shipped neighbors - the When-NOT routing targets)

Verdict: Build, at governing tier P - a narrow, lower-priority build that must be kept formally distinct from the candidate regret-minimization entry, and whose nearest shipped neighbor (expected-value-decision-tree) was tested as a fold and rejected for concrete reasons. The durable move is specific and emittable: transform a payoff matrix into a regret (opportunity-loss) matrix and choose the option whose maximum regret across un-probabilized states is smallest. Tested against the closest shipped skills:

• think-expected-value-decision-tree (closest; shipped) - tested as a fold, rejected. These are sibling criteria in the formal decision-under-uncertainty family, and the temptation is to fold minimax regret in as EV-tree’s “no-probabilities mode.” That fails on mechanism, artifact, and precondition. EV-tree’s load-bearing ingredient is the chance node - explicit probabilities that sum to one - rolled back to an expected value; its mechanism cannot run when no probability distribution exists, which is exactly the regime minimax regret is built for. Minimax regret deliberately refuses probabilities and instead performs a regret transform plus a minimax-over-states selection - a different operation producing a different artifact (a regret matrix, not a probability tree with rolled-back EVs). They share only the options-by-states scaffold; the scoring engine, the output, and even the formal pathologies differ (minimax regret violates independence of irrelevant alternatives, Chernoff 1954; EV does not). Folding it into EV-tree would be like folding maximin into EV-tree - collapsing siblings into a parent that structurally excludes them. The shared mechanism is below the overlap ceiling, so this is a hard wall, not a near-twin. The EV-tree dossier’s own “when it fails” wall (“deep uncertainty - you cannot probability the outcomes - breaks the rollback”) names the precise gap this skill fills.

• think-decision-option-review (shipped). Scores options on weighted attributes you can assert; there are no states of nature, no opportunity-loss transform, and no worst-case logic. Low overlap. It answers “which option scores best on my criteria,” not “which option minimizes worst-case regret across uncontrollable futures.”

• regret-minimization (candidate, NOT shipped) - the load-bearing collision, kept distinct. The registry carries a separate regret-minimization entry (the “imagine yourself at 80 and minimize anticipated regret” life-decision heuristic, family risk-failure-and-resilience). It shares the word “regret” and nothing else: it is an introspective, single-actor, no-matrix prompt about a felt future emotion, whereas minimax regret is a formal opportunity-loss matrix criterion over discrete states. They must not be merged. Because regret-minimization is status: cand, not shipped, it is NOT a routing target in this skill’s “When NOT to Use” - only shipped skills are named there.

So there is a separable, named, artifact-emitting move that no shipped skill produces, comfortably above the overlap ceiling against every shipped skill. It clears the four commitments: a real mechanism (the regret transform plus minimax), an honest P grade, a concrete artifact (the regret matrix and minimax pick), and a sharp “when NOT to use” (the IIA / gameable-option-set wall and the use-EV-when-you-have-probabilities wall). The honest qualifier: it is a lower-priority P-tier build - the move is narrow (it applies only to the discrete-options-by-un-probabilized-states shape), it sits one slot away from a shipped skill, and it carries a genuine formal defect (IIA violation) that the build teaches as a guardrail rather than hides.

7. Output artifact

The skill must emit a regret analysis, not prose: the focal decision with the no-probabilities precondition stated; the payoff matrix (options as rows, states of nature as columns, payoffs in the cells with a stated unit); the derived regret matrix (each cell = column-best minus that cell’s payoff, column-best = 0); a max-regret column giving each option’s single worst regret; the marked minimax pick (smallest maximum regret); and the named binding state (where the chosen option incurs its worst-case regret). No probabilities are attached to the columns and the states are never ranked by likelihood. A short sibling-criterion and IIA-fragility note belongs alongside it.

8. Excluded-figures note

No specific “minimax regret improves decisions by N%” figure, and no decision-quality effect size for the criterion, traces to any nameable primary source; none is asserted here or counted toward the grade. The regret-theory and anticipated-regret effect sizes (Bell; Loomes and Sugden; Zeelenberg) are real but belong to the descriptive sibling under known probabilities and are excluded from this entry’s grade by the same rule.

9. Named sources

• Leonard J. Savage, “The Theory of Statistical Decision,” Journal of the American Statistical Association 46(253) (1951): 55-67. The origin of the minimax-regret criterion: minimize the maximum opportunity loss, presented as a less-pessimistic alternative to Wald’s minimax. Foundational; defines the actual move. (P)
• Herman Chernoff, “Rational Selection of Decision Functions,” Econometrica 22(4) (1954): 422-443. Establishes that regret-based selection violates the independence of irrelevant alternatives (adding a dominated option can change the choice). The criterion’s central, named formal weakness; cited to drive the “when NOT to use” wall, and as a reason never to inflate the grade. (S, for the formal critique - a mathematical result about the rule, not effectiveness evidence)
• Charles F. Manski, “Statistical Treatment Rules for Heterogeneous Populations,” Econometrica 72(4) (2004): 1221-1246. Finite-sample bounds showing minimax-regret-type empirical success rules have attractive worst-case-regret properties for treatment choice. Measures the rule’s statistical properties, not whether using it improves an applied decision - explicitly not counted as effectiveness evidence. (S, for the mathematics)
• Jorg Stoye, “Minimax Regret Treatment Choice with Finite Samples,” Journal of Econometrics 151(1) (2009): 70-81. Exact finite-sample minimax-regret rules for treatment choice; later axiomatized the criterion as a choice correspondence. Same caveat as Manski: a property result, not a decision-quality study. (S, for the mathematics)
• David E. Bell, “Regret in Decision Making under Uncertainty,” Operations Research 30(5) (1982): 961-981. Regret theory: modeling anticipated regret as an attribute of consequences to better describe and prescribe choice under risk. A different operation from Savage’s rule (descriptive, known-probability) - the evidenced cousin, cited to show the behavioral evidence belongs elsewhere and is excluded from this grade. (M, descriptive - for regret theory, NOT for minimax regret)
• Graham Loomes and Robert Sugden, “Regret Theory: An Alternative Theory of Rational Choice Under Uncertainty,” Economic Journal 92(368) (1982): 805-824. The conceptual statement of regret theory; predicts preference reversals and status-quo effects. Same caveat as Bell: descriptive sibling, not Savage’s criterion, excluded from this entry’s grade. (M, descriptive - for regret theory)
• Marcel Zeelenberg, Jane Beattie, Joop van der Pligt and Nanne K. de Vries, “Consequences of Regret Aversion: Effects of Expected Feedback on Risky Decision Making,” Organizational Behavior and Human Decision Processes 65(2) (1996): 148-158 (and Zeelenberg, Journal of Behavioral Decision Making 12, 1999). Experiments: anticipated regret (driven by expected feedback) reliably shifts choice toward safer options. Behavioral evidence for the emotion’s effect, not the prescriptive rule - excluded from this entry’s grade. (M, descriptive - adjacent operation)
• Robert J. Lempert, David G. Groves, Steven W. Popper and Steven C. Bankes, “A General, Analytic Method for Generating Robust Strategies and Narrative Scenarios,” Management Science 52(4) (2006): 514-528. Robust Decision Making; minimax regret used as the robustness criterion for choosing strategies across computationally generated deep-uncertainty scenario sets. Locates the criterion’s modern applied home and its pairing with scenario sets. Practitioner / applied. (P)

Excluded under the evidence rule: no “minimax regret improves decisions by N%” or comparable decision-quality effect size traces to any nameable primary source measuring the criterion; none is asserted or counted. The regret-theory and anticipated-regret effect sizes (Bell 1982; Loomes and Sugden 1982; Zeelenberg et al. 1996, 1999) are real but measure the descriptive sibling under known probabilities and are excluded from this entry’s grade.