Decision robustness

Compare worst-case performance across stated scenarios without inventing probabilities for them.

13 minutes · advanced · Original Poker4Quant lesson

What you will learn

Distinguish expected-value choice, maximin choice and model uncertainty.

Prerequisites: Sensitivity and model error · Exploitability and model limits

A scenario set is not a probability distribution

Suppose the plausible model set contains several payoff scenarios but assigns no probabilities to them. An expected-value average over those scenarios requires extra weights. A maximin rule instead chooses the action with the best worst-scenario payoff.

This is a chosen robustness objective, not a theorem that everyone should use it. The result depends on which scenarios are considered plausible. Adding an extreme scenario can change the answer; excluding a relevant scenario can create false confidence.

Stability of a ranking is useful evidence about assumptions

For a final call with fixed P and C, EV is increasing in q. If every plausible q lies above the threshold, its sign is positive throughout that set. If the set crosses the threshold, the action’s EV sign is not robust.

Even a stable sign does not ensure the payoff estimates cover future costs, dependence or risk constraints. Document the model dimensions varied and those held fixed. Robustness within a narrow set is not a guarantee against every unmodeled event.

Worked example

Two scenario payoffs are A=[12,−4] and B=[3,2]. Compare maximin with an expected-value choice that assigns 80% to the first scenario.

Worst payoffs are −4 for A and 2 for B, so maximin chooses B.
At weights 80% and 20%, EV(A)=9.6−0.8=8.8.
EV(B)=2.4+0.4=2.8, so that weighted mean objective chooses A.

The choices differ because the objectives and weighting assumptions differ. Neither calculation by itself justifies a universal real-world decision rule.

Hands-on: Stress a policy and change the objective explicitly

Allocate a finite lottery policy, inspect every scenario, build supplied probability weights and compare grid maximin with weighted expectation. Extend the scenario set without extending its guarantee beyond stated assumptions.

Reading scenarios…

Common mistakes

Averaging scenarios without justifying their weights.
Calling a worst-case policy the expected-value optimum.
Claiming a model-set guarantee covers omitted scenarios.

Keep these ideas

Name the decision objective and model set.
Distinguish scenario uncertainty from probabilistic risk.
State what was held fixed during sensitivity checks.