Decision Under Uncertainty Calculator

What this generator does

Takes each option's best, worst and average payoff, builds the regret matrix by subtracting every payoff from the best available in that state, and reports what each of the five classical criteria chooses along with the value behind it.

How to use this tool

1. List the states of the world — the futures you cannot put odds on.
2. Enter one row per option with its payoff in each state.
3. Set how optimistic the Hurwicz blend should be.
4. Read what each criterion picks, and the regret table behind the least obvious one.

Understanding the controls

States of the world

What might happen, separated by commas. These are futures you cannot put probabilities on — if you can, expected value is the better tool.

Payoffs

One row per option: the name, then what it is worth in each state, in the same order as the states. Negative numbers are fine and the units are yours.

Optimism

How much weight the Hurwicz criterion gives the best case rather than the worst. Fifty per cent is neutral between them, nought is pure caution and a hundred is pure optimism.

Common use cases

• Choosing between options when no probabilities are available
• Showing a board that the answer depends on the criterion, not the data
• Working out the regret you would feel under each choice
• Testing whether a decision is robust to how cautious you are
• Teaching decision theory with a table you can change and re-run

How this generator works

Maximin takes each option's worst payoff and picks the best of those; maximax does the same with the best payoffs. Hurwicz blends the two in whatever proportion you set. Laplace averages the row, which quietly assumes every state is equally likely. Minimax regret is the different one: it first works out, for each state, how much worse each option is than the best available in that state, then picks the option whose worst such regret is smallest. Before display the regret table is rebuilt from the payoffs, every state is confirmed to have at least one option with no regret, each verdict is found again by scanning the finished tables, and any option beaten in every state is checked never to have been chosen.

Randomness and fairness

Nothing here is random. A payoff table gives exactly one answer under each criterion, computed rather than sampled.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

• None of these criteria uses probabilities, which is the point of them. If you can estimate how likely the states are, expected value will serve you better.
• The criteria genuinely disagree, and no arithmetic here can tell you which one you should be using — that depends on what you can afford to lose.
• Payoffs are assumed comparable across states, which is often the weakest assumption in the whole exercise.
• Minimax regret can be changed by adding an option nobody would choose, which is a known and slightly uncomfortable property of it.

Privacy and your data

The analysis runs in your browser and the options and payoffs you enter are never transmitted, stored or included in analytics.