Regret Analysis¶
Comparative method — instantiates Robust Solution Selection
Compares how much each option would underperform the scenario-specific best choice, supporting decisions that avoid severe ex post regret.
Regret Analysis scores each candidate not by its raw outcome but by its shortfall relative to the best choice you could have made in that scenario. For every scenario it first finds the winner — the candidate that would have been optimal had that future been known — then measures how far each other candidate falls short of it. That gap is the regret. The method then selects to keep regret small, typically by minimizing the maximum regret across scenarios. Its defining idea is relative rather than absolute: it cares about being caught having chosen wrongly when a better option was available, not about the raw level of the outcome and not about how often you succeed. This is the anticipated hindsight of "we should have picked the other one" made into a number.
Example¶
A national carrier must decide how many units of a new narrow-body aircraft to order for delivery over the next five years — a low, medium, or high commitment — against three demand futures: a travel boom, steady growth, and a demand shock from recession or fuel spikes. Each ordering level performs differently in each future, and no level wins everywhere.
Regret Analysis reframes the choice. In the boom future, the high order is best, so its regret there is zero — but the low order, having turned away full planes it couldn't serve, carries large regret. In the shock future the low order is best, and the high order's regret is the cost of grounded, financed aircraft. The medium order is never the outright winner, yet its worst regret across the three futures is the smallest: it never leaves as much on the table as the extremes do in their bad scenarios. Minimizing maximum regret points to the medium order — the choice least likely to look foolish in hindsight whichever future arrives. The airline commits to it knowing exactly what it is buying: freedom from a large "if only we'd known" gap.
How it works¶
The method builds a regret table from a scenario-by-candidate outcome grid. Column by column (scenario by scenario) it identifies the best-performing candidate and sets its regret to zero, then computes every other candidate's regret in that scenario as the difference between its outcome and that column's best. This converts raw outcomes into a matrix of relative shortfalls. It then applies a regret-based selection rule — most commonly minimax regret (choose the candidate whose largest regret is smallest), sometimes expected regret if scenario probabilities are trusted. The result is the option that stays closest to the achievable best across the whole scenario set.
Tuning parameters¶
- Regret aggregation — minimize the maximum regret, or the expected regret. Max-regret needs no probabilities and guards the worst hindsight; expected regret uses probabilities and rewards the likely futures.
- Regret scale — absolute units or percentage of the scenario-best. Percentage regret stops large-magnitude scenarios from dominating purely by size.
- Scenario weighting — equal treatment vs. probability weights on scenarios. Weighting sharpens the answer but re-imports the forecasting the method was meant to hedge.
- Best-in-scenario definition — whether the per-scenario benchmark is the best available candidate or an idealized unconstrained optimum. The latter inflates every regret uniformly and can distort the ranking.
When it helps, and when it misleads¶
Its strength is that it targets the emotion and politics of decisions directly: it minimizes the "we should have chosen differently" exposure that dominates post-mortems, and it often rescues a sensible middle option that neither the raw-optimum nor the pure worst-case view would surface — the logic of Savage's minimax-regret criterion.[n1] It is especially apt when a decision will be judged in hindsight against what was achievable.
Its notorious failure mode is that regret depends on the menu: adding or removing a candidate can change another candidate's regret and flip the ranking, an independence-of-irrelevant-alternatives violation that pure worst-case rules don't suffer. It also says nothing about absolute survivability — an option can have low regret while every outcome is poor. The classic misuse is padding the candidate set with a decoy to shift the regret math toward a favored option. The guarding discipline is to fix the candidate set before computing regret, report absolute outcomes alongside regrets so a uniformly-bad-but-low-regret option is caught, and disclose the aggregation rule chosen.
How it implements the components¶
regret_measure— constructing the per-scenario shortfall-from-best is the method's core artifact and its unit of comparison.solution_comparison— candidates are ranked against each other through the regret matrix, a comparison anchored on relative rather than absolute performance.robust_selection_rule— the minimax-regret (or expected-regret) rule turns the matrix into a selection the decision acts on.
This method reasons in relative shortfall: it does not cap an absolute worst_case_bound on loss — that's Minimax Decision Rule — nor sample an uncertainty_scenario_set to estimate how often each option survives, which is Monte Carlo Robustness Screen.
Related¶
- Instantiates: Robust Solution Selection — supplies the regret-minimizing evidence and selection rule for hindsight-sensitive choices.
- Consumes: Scenario Robustness Check supplies the scenario-by-candidate outcomes the regret table is computed from.
- Sibling mechanisms: Monte Carlo Robustness Screen · Robust Optimization Model · Minimax Decision Rule · Maximin / Satisficing Rule · Decision Matrix Under Uncertainty · Robust Policy Design Review · Scenario Robustness Check · Stress-Tested Plan Review
Editorial Notes¶
Form Classification¶
Form family: Analysis, Modeling & Optimization
Rationale: Regret Analysis operates as an analytical, modeling, inference, comparison, or optimization procedure that derives insight or a solution because it compares how much each option would underperform the scenario-specific best choice, supporting decisions that avoid severe ex post regret.
Independent corroboration: The frozen evidence defines Regret Analysis as 'Compares how much each option would underperform the scenario-specific best choice, supporting decisions that avoid severe ex post regret', so its operative form is Analysis, Modeling & Optimization.
Review outcome: Independent reviewer agreement; medium confidence.
Origin Attribution¶
Primary origin: Operations Research
Origin pattern: Convergent development
Present-day reach: Universal
Rationale: Minimax regret and scenario-relative opportunity loss are established decision-analysis methods.
Related originating lineages:
- Economics & Finance — Regret and foregone-value comparisons independently developed in economic choice theory.
Review resolution: Both blind reviewers agree that operations_research is the primary origin. Explicit reconciliation of origin mode disagreement, domain reach disagreement adopts reviewer_a's classification because minimax regret and scenario-relative opportunity loss are established decision-analysis methods. The resulting lineage records alternates=economics_finance, origin_mode=convergent, and domain_reach=universal; these describe formative provenance separately from later applicability.
Review outcome: Reconciled after independent review; high confidence.
Notes¶
[n1] Leonard Jimmie Savage's minimax-regret criterion selects the option whose maximum regret — its largest shortfall from the best choice achievable in any scenario — is smallest. It is distinct from minimax loss, which measures absolute damage rather than shortfall relative to the scenario-specific best. ↩