one life to live
Maximin selects the option with the best worst-case payoff. Minimax regret selects the option with the smallest worst-case loss relative to what could have been chosen. The criteria can recommend different options.
One person declines a startup offer because failure could cost her house. Another accepts because he wants to avoid missing a larger payoff. They are comparing different costs of the same decision.
The payoff table · scores −100…100 · every cell is editable
The regret matrix · regret = the column's best − this cell
Three prudences
Maximin takes the lowest payoff in each row, then selects the row with the highest of those minima. It requires no probabilities.
Minimax regret subtracts each payoff from the best payoff in its column. It selects the row with the smallest maximum regret. Like maximin, it requires no probabilities.
Expected value weights each outcome by its probability and sums the results for each option. Unlike the other two criteria, it requires probabilities. The default table gives each criterion a different preferred option.
What to try
On the maximin tab, reduce the firm’s bust payoff from 15 to −80. Maximin abandons the firm because its worst payoff has fallen. Switch to the regret tab: the firm’s worst regret and the selected option remain unchanged.
Restore the example, then reduce the school’s boom payoff from 45 to 10. Its minimum payoff is unchanged, so maximin keeps its selection. Minimax regret abandons the school because its shortfall in the boom scenario has increased.
Edit the table until all three criteria select the same option. Use the agreement note below the verdicts to check the result.
Which pain is yours
Choose the criterion according to what you want to limit: the worst payoff, the largest forgone payoff, or the probability-weighted average loss.
Regret's strange arithmetic
On the regret tab, reduce the startup’s boom payoff from 90 to 45. The startup remains the least preferred option, but the preferred option changes from school to firm. The edit changes the best payoff used to calculate regret in that column. Maximin’s selection is unchanged.
This is a violation of independence of irrelevant alternatives: changing an unselected option changes the ranking of the remaining options.
The mapping
| Mathematics | Life |
|---|---|
| payoff table | Choices whose worth depends on futures you can't control — the offer is only good or bad jointly with how the world turns. |
| column | One way the world might go, indifferent to what you chose inside it. |
| maximin | Prudence as armor: secure the floor, ignore the ceiling, ask no probabilities. |
| regret matrix | Every outcome compared to the neighbor who chose best for that same future — the road not taken, made numerical. |
| minimax regret | Prudence as protection from hindsight: minimize the worst sentence your older self can say. |
| probability sliders | The confidence you may not have earned — expectation's whole authority rests on them. |
Where the metaphor tears
The table cannot evaluate an outcome you have not included. Add plausible missing scenarios before comparing the criteria.
The regret matrix represents imagined hindsight. It does not measure how a person will feel after an outcome occurs.
Unbounded worst cases can prevent maximin from distinguishing options. Include inaction as an option so its possible losses are compared with those of acting.