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Use regret as a comparison rule without pretending the scenario set is neutral
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Full chapter index · Independent practice · Judgement subject guide
Minimax regret compares each option with the best option that would have been available in each scenario. It then chooses the option with the smallest worst regret. The rule can be useful when probabilities are unavailable or not credible, but it does not remove judgement: results depend on options, scenarios, outcome measures, time horizon and what counts as a tolerable sacrifice.
The examples use fictional scores. Regret is a modelled opportunity loss, not an emotion score and not a universal substitute for expected utility, rights, safety constraints or professional duty.
A useful regret analysis therefore remains modest. It exposes a particular kind of vulnerability—falling behind the best modelled option after a scenario becomes known—while keeping the construction of those scenarios open to review. The calculation is valuable when another reader can reproduce it, challenge the boundaries and see whether a different but credible future would reverse the choice.
Keep decision ownership separate from arithmetic. Analysts can calculate regrets, but accountable decision makers must approve the options, constraints, outcome scale and treatment of stakeholders. Record disagreements about scenarios and weights instead of averaging them away. A transparent disagreement can reveal where further evidence, consultation or a staged option is useful; a single unexplained score can conceal the same issue while appearing more precise.
Before acting, write one sentence naming the selected rule, one naming the worst-regret scenario, and one naming the condition that would reopen the choice. Add the strongest feasible alternative and why it was not selected. This short record prevents the table from becoming detached from the real decision and gives a future reviewer a precise place to update the analysis.
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Full chapter index
See the mechanism · Chapters 1–2
Build the worked model · Chapters 3–5
Test what changes · Chapters 6–8
Check evidence and limits · Chapters 9–10
Practise and continue · Chapters 11–12
CHAPTER 1 OF 12 · See the mechanism
1. Start with options, scenarios and one outcome scale
List feasible options in rows and mutually distinct scenarios in columns. Every cell must use the same outcome direction and unit. If higher is better, larger values represent more desirable outcomes; if lower cost is better, transform consistently before calculating regret.
The scenario set should cover decision-relevant uncertainty without double-counting near-duplicates. “Strong demand” and “very strong demand” may be useful separately only if they change option performance or the decision.
State the horizon. A five-year capacity decision can reverse when evaluated over twenty years. Regret inherits every boundary of the payoff table.
Evidence check: for Start with options, scenarios and one outcome scale, preserve the observation before the interpretation. Record population, binary action, outcome and time horizon. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
For each scenario, find the best payoff among options. Regret for an option is the difference between that scenario’s best payoff and the option’s payoff. The best option in a column has zero regret.
This is a relative measure. An option can have low regret even when every option performs poorly in an absolute sense. Keep minimum safety or service standards beside the regret table.
For costs where lower is better, regret is the option’s cost minus the lowest cost in that scenario. Check the sign before doing anything else.
Evidence check: for Convert payoffs into opportunity loss, preserve the observation before the interpretation. Record whose tradeoff the threshold represents. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
Imagine three capacity plans with net benefit scores under low, medium and high demand. Plan A scores 70, 68 and 45. Plan B scores 60, 75 and 72. Plan C scores 40, 66 and 90.
Column bests are 70, 75 and 90. Regrets are A: 0, 7, 45; B: 10, 0, 18; C: 30, 9, 0. The maximum regrets are 45, 18 and 30, so minimax regret selects B.
Show the original payoffs and regret table together. A reader should be able to reproduce every subtraction and see what the score means.
| Plan | Low payoff / regret | Medium payoff / regret | High payoff / regret | Maximum regret |
|---|---|---|---|---|
| A | 70 / 0 | 68 / 7 | 45 / 45 | 45 |
| B | 60 / 10 | 75 / 0 | 72 / 18 | 18 |
| C | 40 / 30 | 66 / 9 | 90 / 0 | 30 |
Evidence check: for A worked three-option table, preserve the observation before the interpretation. Record the formula, denominator and threshold weight. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
Maximin looks at each option’s worst payoff and chooses the highest of those worst outcomes. In the example, worst payoffs are 45, 60 and 40, so maximin also chooses B. That agreement is contingent.
Minimax regret asks how far an option could fall behind the scenario-specific best. Maximin asks how bad the option itself can become. A new extreme option can change regret benchmarks even if nobody would choose it, while maximin may remain unchanged.
Name the rule before reporting the winner. “Robust” is too vague when different rules happen to agree.
Evidence check: for Minimax regret is not maximin, preserve the observation before the interpretation. Record TP and FP counts recalculated at that threshold. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
Minimax rules avoid assigning probabilities, but they do not avoid assumptions. Adding one scenario with a very large payoff gap can determine the maximum regret. Removing it can reverse the choice.
Trace each scenario to evidence, stakeholder concern or a physical boundary. Use scenario discovery or stress testing to find conditions where a candidate fails rather than inventing dramatic columns for balance.
Test density. If ten nearly identical scenarios favour one option and one distinct scenario favours another, minimax regret treats only the worst regret, not how many columns repeat. That is a feature, not a hidden frequency estimate.
Evidence check: for Scenario choice can dominate the result, preserve the observation before the interpretation. Record treat-all, treat-none and current-practice comparators. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
When outcomes combine money, delay, health, reliability or equity, the payoff score already contains value judgements. Regret arithmetic does not make those weights objective.
Normalising each criterion can change the maximum gap. Preserve raw outcomes and document transformations. If a small monetary difference overwhelms a safety threshold because of scaling, the model is misaligned with the decision.
Use constraints for non-compensable conditions. Options that violate law, minimum safety or rights should not become eligible because their numerical regret is low.
Evidence check: for Scaling and aggregation need explicit values, preserve the observation before the interpretation. Record the relevant range and uncertainty around differences. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
Two options may share the same maximum regret while failing in different scenarios. Report the scenario producing each maximum and the second-largest regrets. The pattern can matter more than the tie.
If estimates are uncertain, a one-point difference should not be treated as decisive. Calculate ranges or repeat the table under plausible parameter values.
A tie can prompt value-of-information analysis: which observation would separate the options, when will it arrive and is waiting worth the cost?
Evidence check: for Ties and near-ties call for another question, preserve the observation before the interpretation. Record calibration in the intended validation population. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 8 OF 12 · Test what changes
8. Irrelevant alternatives can change the benchmark
Because regret uses the best payoff in each scenario, adding an option can raise a column benchmark and change other options’ regrets even if the new option is not selected. This violates the independence-of-irrelevant-alternatives property.
Worked change: add Plan D with payoffs 71, 20 and 20. It raises only the low-demand benchmark from 70 to 71. A and B each gain one point of regret there, while C does too. In another table, a strategically extreme option could reverse the minimax result.
Audit why every option is feasible and included. Do not allow a dominated or impossible design to manipulate regret benchmarks.
| Plan | Low-demand payoff | Old regret (best 70) | New regret (best 71) |
|---|---|---|---|
| A | 70 | 0 | 1 |
| B | 60 | 10 | 11 |
| C | 40 | 30 | 31 |
| New D | 71 | — | 0 |
Evidence check: for Irrelevant alternatives can change the benchmark, preserve the observation before the interpretation. Record target prevalence and sampling weights. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 9 OF 12 · Check evidence and limits
9. Deep uncertainty needs iterative stress testing
Under deep uncertainty, analysts may not agree on models, probabilities or values. A single regret table is therefore an exploratory view, not the final truth.
Test candidate strategies across many plausible futures, identify vulnerability conditions and modify strategies. Robust Decision Making focuses on satisfactory performance across futures rather than one predicted optimum.
Minimax regret can be one metric within that process. Pair it with absolute thresholds, distributional consequences and the ability to adapt when signposts change.
Evidence check: for Deep uncertainty needs iterative stress testing, preserve the observation before the interpretation. Record resampling boundaries and external validation. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
A static option may look inferior to a staged plan that can expand after demand is observed. Model the decision rule, not only the first action. The future branch, trigger and cost of switching belong in the payoff.
Reversible options can reduce regret by preserving choices, but delay also has costs. State the last responsible decision time and the evidence expected before it.
Do not award flexibility without testing execution. A nominal option to expand is worthless if permits, staff or supply chains make the later move infeasible.
Evidence check: for Add adaptation and reversibility, preserve the observation before the interpretation. Record capacity, downstream harms and missing utilities. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 11 OF 12 · Practise and continue
11. Independent practice and changed-context transfer
Practice: Reproduce the three-plan regret table and verify Plan B’s maximum regret of 18. Then change Plan C’s high-demand payoff from 90 to 120. Recompute the column benchmark, all high-demand regrets and the selected option.
Changed context: impose a minimum payoff of 50 in every scenario. Plan C now fails the low-demand constraint before regret is considered; Plan A fails high demand. Explain whether B is selected by minimax regret, feasibility or both.
Transfer to costs. Reverse the subtraction rule and test a table of project overruns. If your regret values become negative, the direction is wrong.
Evidence check: for Independent practice and changed-context transfer, preserve the observation before the interpretation. Record which changed context reverses the preferred rule. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
Does minimax regret need scenario probabilities?
No. That is useful when probabilities are not credible, but the scenario set and payoff model still require evidence and judgement.
Is regret psychological remorse?
Not in this calculation. It is opportunity loss relative to the best modelled option in each scenario.
Should the lowest maximum regret always decide?
No. Feasibility, law, safety, rights, stakeholder distribution and model uncertainty can constrain or override the numerical rule.
For connected methods, read expected utility and certainty equivalents, robust decisions and switching assumptions, and value of information.
Technical background includes Anderson and Zachary’s paper Minimax decision rules for planning under uncertainty, which analyses sensitivity to scenario choice and irrelevant alternatives, and RAND’s Robust Decision Making overview. Sources and links were checked on 22 October 2026.
Evidence check: for FAQ, sources and connected reading, preserve the observation before the interpretation. Record the decision sentence that the curve is meant to support. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.