A student finalising the Decision Analysis course is expected
to. . .
Below you will find in 3 pages a detailed overview of what you are expected to know, understand
and able to do for the written exam of the Decision Analysis course.
You should be able to understand and apply the following criteria:
• maximin, maximax, minimax regret
• deterministic dominance in the absence of (explicit) uncertainty (transparencies)
• stochastic/probabilistic dominance
• deterministic dominance under risk (special case of stochastic dominance, in textbook)
• Bayes’ criterion
You should be able to identify and/or distinguish between different elements of a decision problem
and its representation:
• decision variable with its alternatives
• chance variable, its outcomes and (possibly various conditional) probability distribution(s)
• goal, objective
• attribute and its values
• consequence and its value/utility
• (expected) reward vs (expected) utility
• chance tree vs decision tree
• scenario vs strategy
• optimal decision vs optimal strategy
• reduced vs non-reduced decision tree
• expected utility vs certainty equivalent of a lottery
You should have only superficial knowledge of the different assessment methods for probabilities, utilities and scaling constants. You should, however, be familiar with the lottery assessment
method for scaling constants and you should know how to interpret scaling constants.
You should understand and use the following definitions, concepts or formulas, but you are not
required to reproduce them:
• distribution of rewards
• certain/simple/compound lottery
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• (rational) preference ordering
• the axioms and main theorem underlying utility theory
• certainty equivalent and probability equivalent
• definitions of different risk attitudes; you should know the relation between risk attitude and
shape of the utility function
• discounting (money, or lifetime)
• risk premium, degree of risk averseness/proneness, risk-aversion function
• the two-attribute utility functions that hold under X UI Y, but don’t require MUI (forms
with 3 subutility functions, or using isopreference curves)
• the seemingly weaker assumptions implying standard forms of the utility function (slides
194, 196, 210)
• the two-attribute multiplicative utility function and its strategic equivalence to the twoattribute multilinear form
• the differences between the n > 2 attribute multi-linear and multiplicative form
• the n > 2 attribute utility functions, and how the two-attribute situation is a special case
• the n > 2 independence properties, and how the two-attribute situation is a special case
• iso-preference curves (you should be able to describe their meaning and how they can be
used for constructing utility functions)
• the exponential survival function and life expectancy
• the time-tradeoff method
• the DEALE method
• the QALY model
You should understand how the independence assumptions relate to the functional forms of the
utility functions discussed, and how different choices with respect to, for example, choosing the
origin and unit for the function may change its apparant form. That is, you should understand
the proofs, but you are not required to reproduce them.
You should know the standard independence assumptions underlying the n > 2 attribute utility
functions (especially the difference between various UI properties for the multilinear form and
MUI for the multiplicative form)
You should be able to describe how to go about verifying independence assumptions in practice
(see also the examples in the M.C. Airport case study), and understand and describe the relation
between the different independence assumptions.
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You should understand and be able to reproduce the following definitions, concepts or formulas
that are repeatedly and extensively used in the course:
• strategic equivalence: definition and associated theorem
• preference independence for 2 attributes
• additive independence for 2 attributes
• utility independence for 2 attributes: definition and associated equivalence proposition (slides
186 and 189)
• the standard form of the two attribute additive utility function (u(X, Y ) = kX · uX (X) +
kY · uY (Y )), together with its normalisations, and under what standard assumption (AI) it
can be used
• the standard form of the two attribute multilinear utility function (u(X, Y ) = kX · uX (X) +
kY ·uY (Y )+kXY ·uX (X)·uY (Y )), together with its normalisations, and under what standard
assumption (MUI) it can be used
You should know and understand how the following algorithms work, you are able to apply them,
understand why they work (correctness) and/or under which assumptions they work:
• inverting a chance tree and what the meaning of that is
• reducing a decision tree
• foldback analysis
• sensitivity analysis and threshold analysis: all variations discussed and associated graphical
representations (sensitivity graphs, iso-utility curves, tornado diagrams)
• value of (im)perfect information analysis
• analytic hierarchy process
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