Business Management · Decision-making process, attitude to risk and competition

Decision Criteria and Decision Trees: Expected Value, Maximin and Minimax Regret

Updated 11 October 2026 · Fact-checked

Decision criteria are rules for choosing between options when outcomes are uncertain. Expected value picks the best probability-weighted payoff, maximin picks the best worst case, and minimax regret picks the smallest worst regret. A decision tree lays out choices and chance events, then you fold back from the right using expected values.

Understand Decision Criteria and Decision Trees

A business often must pick one option before it knows what will happen. A firm may launch a product, delay it or drop it. The payoff depends on the state of the world, such as strong, moderate or weak demand. Decision criteria give you a consistent rule for choosing. They do not remove the uncertainty. They make the choice transparent and defensible.

The standard set-up is a payoff table. Rows are the options you control. Columns are the states you do not control. Each cell is the payoff for that option in that state. If you can attach probabilities to the states, you can use expected value. If you cannot, you use criteria that need no probabilities.

Expected value is the probability-weighted average payoff of each option. You choose the highest. It suits repeated decisions and a decision maker who is risk neutral. Its weakness is that it hides the spread of outcomes. An option with a small chance of ruin can still have the best average.

Maximin looks at the worst payoff of each option and picks the option whose worst payoff is highest. It is cautious and pessimistic. Maximax picks the best of the best payoffs and is optimistic. Minimax regret first builds a regret table. Regret is the best payoff in that state minus your payoff. You find the maximum regret of each option and choose the option with the smallest maximum regret. It protects you from looking back and wishing you had chosen differently.

A decision tree is a diagram for sequences of decisions. Square nodes are decisions you make. Round nodes are chance events with probabilities on the branches. You work from right to left, a method called folding back. At a chance node you take the expected value. At a decision node you take the best branch. Costs paid along the way are subtracted. The tree also lets you value extra information, such as a market survey, before committing.

Key rules to remember

Expected value of an option: EV = Σ pᵢ × xᵢ; pᵢ is the probability of state i and xᵢ the payoff in that state. The probabilities must sum to 1.
Maximin rule: Choose the option with the largest value of (minimum payoff); Use payoffs where higher is better. If the table shows costs, the equivalent rule is minimax cost.
Maximax rule: Choose the option with the largest value of (maximum payoff); Optimistic rule. Ignores downside completely.
Regret: Regret(option, state) = best payoff in that state − payoff of the option in that state; Calculate down each column. Regret is never negative.
Minimax regret rule: Choose the option with the smallest value of (maximum regret); Take the maximum regret along each row, then pick the smallest.
Folding back a tree: Chance node value = Σ p × value of branch; decision node value = best branch value; Subtract costs on the branches taken. Work right to left.
Expected value of perfect information: EVPI = EV with perfect information − best EV without information; EV with perfect information = Σ p × best payoff in each state. It is the most you should pay for information.

How to solve Decision Criteria and Decision Trees questions

Use this method for any question on decision criteria or decision trees. It keeps your working clear for the markers.

1Identify the options you control and the states you do not. Check whether payoffs are profits or costs, because this reverses the direction of best and worst.
2Write the payoff table, or draw the tree with squares for decisions and circles for chance events. Put probabilities and costs on the branches.
3Check that probabilities at each chance node sum to 1.
4Apply the criterion asked for. For expected value, compute Σ p × x for each option. For maximin, list each row minimum. For minimax regret, build the regret table column by column, then take row maxima.
5For a tree, fold back from right to left. Use expected values at circles and the best branch at squares. Subtract costs along the way.
6State the recommended option and its value clearly.
7Comment on the result. Say what the criterion assumes, such as risk neutrality or pessimism, and note any limits like uncertain probabilities.
8If different criteria give different answers, say so and explain why, using the decision maker's attitude to risk.

Quickest way: Row-and-column scan for payoff tables

When to use it: Use this for multiple-choice questions and short written parts where you have a small payoff table and limited time.

For expected value, multiply and add one row at a time. Write each total beside its row.
For maximin, circle the smallest number in each row, then pick the row with the largest circled number.
For minimax regret, circle the largest number in each column. Subtract every cell from it to get regret. Circle the largest regret in each row and choose the smallest circle.
Check by testing whether your answer is sensible. An option that is never best in any state is rarely chosen by regret.
For trees, write the value at each node directly on the diagram so you do not lose your place.

Common mistakes in Decision Criteria and Decision Trees

Taking the minimum regret instead of the maximum regret in each row.
Students hear 'minimax' and 'minimise regret' and mix up the two stages.
Fix: First take the maximum regret of each option. Then choose the option with the smallest of those maxima.
Calculating regret across rows instead of down columns.
The best payoff for regret is the best in each state, but students compare options in the same row.
Fix: Fix a state (column). Find the best payoff in it. Subtract each option's payoff from that best.
Forgetting to subtract costs on tree branches.
Students focus on the end payoffs and treat the upfront cost as already included.
Fix: Read the question for each cost. Subtract it on the branch where it is paid, and state whether payoffs are net or gross.
Using maximin on a cost table as if higher is better.
The rule is learnt on profit tables.
Fix: For costs, find each option's worst (highest) cost and choose the option with the lowest of these. Say that you are doing this.
Choosing at a chance node or averaging at a decision node.
Students forget that decision nodes are your choice and chance nodes are not.
Fix: Take the best branch at squares and the probability-weighted average at circles.
Giving a number with no recommendation or comment.
Students think the calculation is the whole answer.
Fix: Finish with the chosen option, the criterion used and one line on its limits, such as ignoring risk or needing reliable probabilities.

Worked examples

Example 1

A company can launch Product A, Product B or Product C. Profit (₹ lakh) depends on demand. Low demand (probability 0.3): A = 20, B = 50, C = 10. High demand (probability 0.7): A = 80, B = 60, C = 100. Find the best option under (a) expected value, (b) maximin and (c) minimax regret.

Show the solution

(a) EV of A = 0.3 × 20 + 0.7 × 80 = 6 + 56 = 62.
EV of B = 0.3 × 50 + 0.7 × 60 = 15 + 42 = 57.
EV of C = 0.3 × 10 + 0.7 × 100 = 3 + 70 = 73. C is highest.
(b) Row minima: A = 20, B = 50, C = 10. The largest is 50, so maximin chooses B.
(c) Best payoff in low demand is 50 (B). Best in high demand is 100 (C).
Regret low demand: A = 50 − 20 = 30, B = 0, C = 50 − 10 = 40.
Regret high demand: A = 100 − 80 = 20, B = 100 − 60 = 40, C = 0.
Maximum regret: A = 30, B = 40, C = 40. The smallest is 30, so minimax regret chooses A.

Answer: Expected value chooses C (₹73 lakh), maximin chooses B (₹50 lakh worst case), and minimax regret chooses A (maximum regret ₹30 lakh). The criteria disagree because they reflect different attitudes to risk.

Example 2

A firm can build a plant now at a cost of ₹40 crore. Demand is high with probability 0.6, giving revenue of ₹100 crore, or low with probability 0.4, giving revenue of ₹30 crore. Alternatively, it can pay ₹3 crore for a survey first. The survey is perfectly reliable. If it shows high demand, the firm builds. If it shows low demand, the firm does not build and earns nothing further. Not building without a survey also earns nothing. Should the firm commission the survey?

Show the solution

Net payoff of building if demand is high = 100 − 40 = ₹60 crore.
Net payoff of building if demand is low = 30 − 40 = −₹10 crore.
Build now without survey: EV = 0.6 × 60 + 0.4 × (−10) = 36 − 4 = ₹32 crore.
Not building gives 0, so without a survey the best choice is to build, worth ₹32 crore.
With the survey: if high (0.6) build for 60. If low (0.4) do not build for 0. EV before the survey cost = 0.6 × 60 + 0.4 × 0 = ₹36 crore.
Subtract the survey cost: 36 − 3 = ₹33 crore.
Compare: 33 is greater than 32. EVPI = 36 − 32 = ₹4 crore, which exceeds the ₹3 crore fee.

Answer: Commission the survey. It has an expected value of ₹33 crore against ₹32 crore for building immediately. The survey is worth up to ₹4 crore, so a ₹3 crore fee is justified. This assumes the firm is risk neutral and the probabilities are reliable.

Exam tips

Read whether the table shows profits or costs before you apply any rule. Say which you assume if the question is unclear.
Show the regret table in full. Even if you slip on the final step, method marks are available for correct regret values.
In written questions, always add a short comment on what each criterion assumes. Expected value suits risk-neutral, repeated decisions. Maximin suits cautious decision makers.
For trees, draw the diagram neatly with node values written on it. Mark rejected branches with a double stroke.
In multiple-choice questions, work the numbers quickly and double-check the direction of best and worst before you answer.

Practice questions from Decision-making process, attitude to risk and competition

Decision Criteria and Decision Trees in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Decision Criteria and Decision Trees: frequently asked questions

What is the difference between expected value and maximin?

Expected value uses probabilities and chooses the best average payoff. Maximin ignores probabilities and chooses the option with the best worst-case payoff. Expected value suits risk-neutral decisions, while maximin suits cautious ones.

How is minimax regret different from maximin?

Maximin looks at raw payoffs and protects against the worst outcome. Minimax regret looks at the gap between your payoff and the best you could have had in each state. It aims to limit how much you would regret the decision afterwards.

How do I solve a decision tree expected value problem?

Draw the tree, then work from right to left. At chance nodes take the probability-weighted average. At decision nodes take the best branch. Subtract costs on the branches where they are paid, and then state the recommended path.

Can the criteria give different answers?

Yes, and this is common. Each criterion reflects a different attitude to risk and use of information. In an exam, show each result and explain why they differ before you recommend an option.