MGMT20005 Chap.1 Decision Analysis Without Probabilities
Decision Analysis Without Probabilities
Week 1 builds the decision before it applies a rule. A complete model names the objective, the alternatives under management control, the uncertain states of nature, and one consequence for every alternative-state combination. Those consequences form a payoff table.
When probabilities are unavailable, the table can be read through different management attitudes: maximax searches for the largest possible profit, maximin protects the largest worst-case profit, and minimax regret limits the largest missed opportunity. Cost tables require the direction logic to be rebuilt because smaller numbers are better.
The chapter also distinguishes an influence diagram, a payoff table and a decision tree. Each representation has a different job, and using the wrong one can hide timing or compare unlike consequences.
What this chapter covers
- 01
Objective, alternatives, states of nature and consequences
- 02
Influence diagrams, payoff tables and decision trees
- 03
Optimistic maximax decisions for profit tables
- 04
Conservative maximin decisions for profit tables
- 05
Opportunity-loss matrices and minimax regret
- 06
Direction changes when a table contains costs
Worked example · free
Choose a launch scale three ways
- 2Maximax row maxima are 56, 92 and 138, so the optimistic rule selects National.
- 2Maximin row minima are 42, 18 and minus 34, so the conservative rule selects Pilot with a protected payoff of 42.
- 2Weak-demand regrets are 0, 24 and 76 because 42 is the state benchmark. Strong-demand regrets are 82, 46 and 0 because 138 is the benchmark.
- 2Maximum row regrets are 82, 46 and 76, so minimax regret selects Regional with the smallest worst regret, 46.
Key terms
- Decision alternative
- An action available to the decision maker and therefore under managerial control.
- State of nature
- An uncertain external condition that affects the consequence but is not chosen by management.
- Payoff table
- A matrix of consequences for every combination of decision alternative and state of nature.
- Maximin criterion
- A conservative profit rule that selects the alternative with the largest worst payoff.
- Opportunity loss
- The difference between an alternative's payoff and the best payoff available in the same state.
- Minimax regret
- A rule that selects the alternative whose largest opportunity loss is smallest.
Decision Analysis Without Probabilities FAQ
Why can three decision rules recommend different alternatives?
They optimise different summaries of the same payoff table. Maximax focuses on the best possible outcome, maximin focuses on the protected worst outcome, and minimax regret focuses on the largest missed opportunity. A disagreement is not an arithmetic contradiction. It reveals how the preferred action changes with the management attitude built into the criterion.
How does a cost table change the method?
The objective direction changes because smaller costs are better. Do not copy profit shortcuts mechanically. For an optimistic cost view, compare each alternative's best low-cost outcome; for a protective cost view, compare worst high-cost outcomes and choose the smallest. Regret is measured above the cheapest state-specific cost rather than below the largest profit.
Why is regret calculated by state rather than by alternative?
Regret asks how much an action gives up compared with the best action that could have been chosen in the same future. The benchmark therefore belongs to a state column. A row comparison would mix different futures and would no longer represent a missed opportunity under one realised state.
When should a decision tree replace a payoff table?
Use a tree when timing matters, later choices depend on earlier events, or probabilities sit on sequential branches. A table is efficient when one decision is compared across a common set of states. Both can represent the same basic elements, but the tree makes chronological information and contingent decisions visible.
Exam move
Build every Week 1 answer from the same visible routine. First name the objective and write whether larger or smaller is better. Second confirm that every alternative is assessed against the same states and that each consequence uses the same unit and time horizon. Third compute the row summary required by the named rule. For regret, pause before subtraction and write the state benchmark above each column.
Finally state the selected alternative, the criterion and its decisive value in one sentence. Practise both profit and cost tables because the mathematics is simple enough that most lost marks come from direction. Avoid inventing equal probabilities when none are supplied; these rules are designed precisely for decisions without a probability distribution.
A useful final drill is to invent a two-row, three-state table and solve it under all three rules. Change one consequence and predict which summaries will move before recalculating. This exposes whether you understand the criterion or are only copying a sequence. Finish by explaining why a different criterion could legitimately select another alternative from exactly the same evidence.
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