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Introduction to Decision Theory
Introduction
Professor L. Blume
Cornell University
What is Decision Theory About?
Decision Theory is about making choices.
Normative Decision Theory — What rational people should
do.
Positive Decision Theory — What rational people will do.
Behavioral Decision Theory — What irrational people will do.
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What Do We Want From DT?
Economists:
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What Do We Want From DT?
Economists: Descriptive models for positive analysis of economic
systems, normative analysis for welfare economics
and mechanism design.
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What Do We Want From DT?
Economists: Descriptive models for positive analysis of economic
systems, normative analysis for welfare economics
and mechanism design.
Statisticians: A normative theory for deriving sensible statistical
procedures.
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What Do We Want From DT?
Economists: Descriptive models for positive analysis of economic
systems, normative analysis for welfare economics
and mechanism design.
Statisticians: A normative theory for deriving sensible statistical
procedures.
Computer Scientists: A normative theory for desiging software
agents and expert systems.
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Modelling Approaches
Axiomatic DT
List axioms which characterize “rational decisionmaking. Then
show that these axioms characterize a particular approach to
decisiomaking; e.g. Savage’s axioms and expected utility.
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Modelling Approaches
Axiomatic DT
List axioms which characterize “rational decisionmaking. Then
show that these axioms characterize a particular approach to
decisiomaking; e.g. Savage’s axioms and expected utility.
Descriptive DT
List a collection of problems and a rule for choice.
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Origins
Nature has placed mankind under the governance of two sovereign
masters, pain and pleasure. It is for them alone to point out what
we ought to do, as well as to determine what we shall do. On the
one hand the standard of right and wrong, on the other the chain
of causes and effects, are fastened to their throne.
Jeremy Bentham
An Introduction to the Principle
of Morals and Legislations, 1789
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Ordinalism
Mill already understood that utility was not a hedonic
measure.
Jevons, Menger, Walras, wanted a theory of value, and did
not care about the psychological origin of utility.
Fisher and Pareto were the first to understand that demand
depended only on the shapes of indifference curves.
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Mere Internal Consistency
The shift in emphasis away from the physiological and
psychological hedonistic, introspective aspects of utility led to the
purging out of objectionable, and sometimes unnecessary,
connotations . . . of the Bentham . . . variety.
Paul Samuelson
Foundations of Economic
Analysis, 1947.
The purpose of revealed preference theory is . . . to develop the
theory of consumers behavior freed from any vestigial traces of the
utility concept.
Paul Samuelson
“A Note on the Pure Theory of
Consumers’ Behavior”, 1938.
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Samuelson’s Psychology of Choice
Radical behaviorism asserts that two mental states are
distinguishable only to the extent that some observable
behavior distinguishes them.
Samuelson writes, ‘of a steady tendency toward the removal
of moral, utilitarian, welfare connotations . . . ’ and of ‘the
rejection of hedonistic, introspective, psychological elements.’
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Samuelson’s Psychology of Choice
Radical behaviorism asserts that two mental states are
distinguishable only to the extent that some observable
behavior distinguishes them.
Samuelson writes, ‘of a steady tendency toward the removal
of moral, utilitarian, welfare connotations . . . ’ and of ‘the
rejection of hedonistic, introspective, psychological elements.’
MWG on revealed preference: ‘Perhaps most importantly, it
makes clear that the theory of individual decision making need
not be based on a process of introspection but can be given
an entirely behavioral foundation.’
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Rational Choice as Folk Psychology
In our everyday transactions we use the language of beliefs
and desires to interpret and forecast the behavior of others.
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Rational Choice as Folk Psychology
In our everyday transactions we use the language of beliefs
and desires to interpret and forecast the behavior of others.
Economists too: The investor believes that the asset price will
be higher tomorrow. She wants greater wealth tomorrow. So
she purchases the asset.
Belief and desire describe mental states and the folk
psychology is a theory of mind which is both adequate for the
psychology of decision and accurate in its predictions.
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Characteristics of Economic Rationality
Rationality is instrumental. Its concern is the efficient
pursuing of ends by available means; not the sensibility of the
ends. The preference orders of a mass murderer and a saint
are treated equally.
Desire is not anchored by any other aspect of the decision
problem; either the feasible set nor the context of choice.
Formally, desires are captured by a preference ordering on
possible objects of choice whose existence is independent of
the feasible set or the context of choice. This is the content
of GCT.
There is no distinction between choice and judgement.
Choosing from among a set of objects, and ranking or valuing
the objects in some fashion, are regarded as equivalent tasks.
There is no distinction between degree of belief and relative
likelihood.
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Criticisms I: What is Explained?
Suppose we seek to explain an observation that in some market
with fixed supply, buyers’ incomes have increased and the price of
the good has increased.
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Criticisms I: What is Explained?
Suppose we seek to explain an observation that in some market
with fixed supply, buyers’ incomes have increased and the price of
the good has increased.
Behaviorist The market demand curve has shifted outward.
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Criticisms I: What is Explained?
Suppose we seek to explain an observation that in some market
with fixed supply, buyers’ incomes have increased and the price of
the good has increased.
Behaviorist The market demand curve has shifted outward.
Intentional Change in the budget set and the nature of those
preferences which could create such a shift.
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Criticisms II: The Content of Consistency
Anyone whose definition of rationality is only the internal
consistency implied by the revealed preference axioms must be
prepared to accept any complete and transitive preference order.
These would include, for instance preference orders whose
maximization implies consumption of unsustainable amounts of,
say, food, when consumption bundles that would sustain life are
affordable. The fear of slipping any ‘values’ into a descriptive
analysis leads to taking serious preference orders which are
inconsistent with any sensible notion of the rationality principle.
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Criticisms III: The Impossibility of Welfare Economics
Suppose an obsessive, exacting, driven individual with a preference
order wakes up on the wrong side of bed one day, and at every step
makes the worst rather than the best possible choices pursuant to
his goals. He is perfectly consistent; his choice satisfies all the
revealed preference axioms. Should welfare calculations be made
with his revealed preference order? If one does not believe that
choice expresses individuals’ values, then there is no point to using
derived utlity functions to ajudicate among social states.
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