Minimax regret
For each option, find the worst regret it could produce, then choose the option whose worst regret is smallest.
- Time cost
- 30 min
- Output
- A regret table with the maximum per option.
- Steps
- 5
Use when
- You cannot put probabilities on the states of the world.
- The decision happens once and you will know afterwards what you should have done.
- Regret about a foregone alternative is itself a real cost.
Do not use when
- You have usable probabilities. Expected value uses more information.
- Adding an irrelevant option would change the answer, which it can here — check before trusting it.
Inputs required
- Options
- Possible states of the world
- A payoff for each option in each state
Procedure
- 01
Build the payoff table
Options down the side, states across the top, payoff in each cell. No probabilities are needed.
- 02
Find the best per state
For each state — each column — note the best payoff available from any option.
- 03
Compute regret
Regret in a cell is the best payoff in that column minus this cell’s payoff. It is what you lose by having chosen this option, given that state occurred.
- 04
Take each option’s maximum regret
Across the row. This is the worst you could feel about this choice.
- 05
Choose the smallest of those maxima
The option whose worst case of being wrong is least bad. Note that this is not the option with the best worst outcome — that is maximin, a different rule.
Characteristic failure mode
Worked example
Choosing insurance excess without any probability for a claim.
- 01States: no claim, one small claim, one large claim.
- 02Three excess levels, each with a different premium and exposure.
- 03Regret table shows the low-excess option regrets £340 at most; the high-excess option regrets £1,200 at most.
Result
The low-excess option minimises maximum regret. Expected value, had a claim rate been available, would have chosen the high-excess option — the two rules genuinely disagree here.
Where to go next