Introduction to Choice Theory
Jonathan Levin and Paul Milgrom∗
September 2004
1 Individual Decision-Making
Individual decision-making forms the basis for nearly all of microeconomic analysis.
These notes outline the standard economic model of rational choice in decision-
making. In the standard view, rational choice is defined to mean the process of
determining what options are available and then choosing the most preferred one
according to some consistent criterion. In a certain sense, this rational choice
model is already an optimization-based approach. We will find that by adding
one empirically unrestrictive assumption, the problem of rational choice can be
represented as one of maximizing a real-valued utility function.
The utility maximization approach grew out of a remarkable intellectual con-
vergence that began during the 19th century. On one hand, utilitarian philosophers
were seeking an objective criterion for a science of government. If policies were to
be decided based on attaining the “greatest good for the greatest number,” they
would need to find a utility index that could measure of how beneficial different
policies were to different people. On the other hand, thinkers following Adam
Smith were trying to refine his ideas about how an economic system based on
individual self-interest would work. Perhaps that project, too, could be advanced
by developing an index of self-interest, assessing how beneficial various outcomes
∗
These notes are an evolving, collaborative product. The first version was by Antonio Rangel
in Fall 2000. Those original notes were edited and expanded by Jon Levin in Fall 2001 and 2004,
and by Paul Milgrom in Fall 2002 and 2003.
1
,are to any individual person. Some of the greatest thinkers of the era were both
philosophers and economists.
Could the utilitarian and economic approaches be combined? That question
suggests several others. How can we tell if the Smithian model of choice is right,
that is, that individuals make choices in their own interests? What does that mean,
precisely? How can we use data to tell whether the proposition is true? What are
all the empirical implications of rational choice? What kind of data do we need
to make the test? Even if the Smithian model is true, can the utility function we
need for policy-making be recovered from choice data? If we can recover utilities,
is simply adding up utilities really the best way to use that information for public
decisions? What is the best way to use that information?
The utility-maximization approach to choice has several characteristics that
help account for its long and continuing dominance in economic analysis. First,
from its earliest development, it has been deeply attached to principles of govern-
ment policy making. The original utilitarian program proved to be too ambitious,
but the idea that welfare criteria could be derived from choice data has proved
to be workable in practice. Moreover, because this approach incorporates the
principle that people’s own choices should determine the government’s welfare cri-
terion, it is well-aligned with modern democratic values. Second, many of the
comparative statics predictions of the choice theory – the qualitative predictions
concerning the ways in which choices change as people’s environments change –
tend to be confirmed in empirical studies. Third, the optimization approach (in-
cluding utility maximization and profit maximization) has a spectacularly wide
scope. It has been used to analyze not only personal and household choices about
traditional economic matters like consumption and savings, but also choices about
education, marriage, child-bearing, migration, crime and so on, as well as business
decisions about output, investment, hiring, entry, exit, etc. Fourth, the optimiza-
tion approach provides a compact theory that makes empirical predictions from a
relatively sparse model of the choice problem – just a description of the chooser’s
objectives and constraints. In contrast, for example, psychological theories (with
strong support from laboratory experiments) predict that many choices depend
systematically on a much wider array of factors, such as the way information is
2
, presented to the subjects, the noise level in the laboratory and other variables that
might influence the subject’s psychological state.
Despite the attractions of the rational choice approach, its empirical failings in
economics and psychology experiments have promoted an intense interest in new
approaches. A wide range of alternative models have been advocated. Learning
models, in which individuals make choices like those that have worked well for
them in the past, have attracted particular attention from economic theorists and
experimenters. Bounded rationality models in which decision makers adopt rules
that evolve slowly have had some empirical successes. For example, a model in
which department stores use standard mark-ups to set retail prices appears to give
a better account of those prices than does a simple profit maximization model,
according to which mark-ups vary sensitively according to price elasticities. Other
models assume that people seek acceptance by imitating their peers, rely on in-
tuition on heuristics, or make choices that are heavily influenced by their current
emotional state. Recent research try to identify parts of the brain involved in
decision-making and model how brain processes affect decisions. Still others give
up on modeling choice mechanisms at all and simply concentrate on measuring
and describing what people choose.
Although these various alternatives appear to have advantages for some pur-
poses, in this class we will focus on the decidedly useful and still-dominant model
of rational choice.
2 Preferences and Choice
Rational choice theory starts with the idea that individuals have preferences and
choose according to those. Our first task is to formalize what that means and
precisely what it implies about the pattern of decisions we should observe.
Let X be a set of possible choices. In consumer choice models, one might
specify that X ⊂ Rn , meaning for instance that there are n different goods (beer,
tortilla chips, salsa, etc..) and if x ∈ X, then x = (x1 , ..., xn ) specifies quantities of
each type of good. In general, however, the abstractness of the choice set X allows
enormous flexibility in adapting the model to various applications. Some of the
3
Jonathan Levin and Paul Milgrom∗
September 2004
1 Individual Decision-Making
Individual decision-making forms the basis for nearly all of microeconomic analysis.
These notes outline the standard economic model of rational choice in decision-
making. In the standard view, rational choice is defined to mean the process of
determining what options are available and then choosing the most preferred one
according to some consistent criterion. In a certain sense, this rational choice
model is already an optimization-based approach. We will find that by adding
one empirically unrestrictive assumption, the problem of rational choice can be
represented as one of maximizing a real-valued utility function.
The utility maximization approach grew out of a remarkable intellectual con-
vergence that began during the 19th century. On one hand, utilitarian philosophers
were seeking an objective criterion for a science of government. If policies were to
be decided based on attaining the “greatest good for the greatest number,” they
would need to find a utility index that could measure of how beneficial different
policies were to different people. On the other hand, thinkers following Adam
Smith were trying to refine his ideas about how an economic system based on
individual self-interest would work. Perhaps that project, too, could be advanced
by developing an index of self-interest, assessing how beneficial various outcomes
∗
These notes are an evolving, collaborative product. The first version was by Antonio Rangel
in Fall 2000. Those original notes were edited and expanded by Jon Levin in Fall 2001 and 2004,
and by Paul Milgrom in Fall 2002 and 2003.
1
,are to any individual person. Some of the greatest thinkers of the era were both
philosophers and economists.
Could the utilitarian and economic approaches be combined? That question
suggests several others. How can we tell if the Smithian model of choice is right,
that is, that individuals make choices in their own interests? What does that mean,
precisely? How can we use data to tell whether the proposition is true? What are
all the empirical implications of rational choice? What kind of data do we need
to make the test? Even if the Smithian model is true, can the utility function we
need for policy-making be recovered from choice data? If we can recover utilities,
is simply adding up utilities really the best way to use that information for public
decisions? What is the best way to use that information?
The utility-maximization approach to choice has several characteristics that
help account for its long and continuing dominance in economic analysis. First,
from its earliest development, it has been deeply attached to principles of govern-
ment policy making. The original utilitarian program proved to be too ambitious,
but the idea that welfare criteria could be derived from choice data has proved
to be workable in practice. Moreover, because this approach incorporates the
principle that people’s own choices should determine the government’s welfare cri-
terion, it is well-aligned with modern democratic values. Second, many of the
comparative statics predictions of the choice theory – the qualitative predictions
concerning the ways in which choices change as people’s environments change –
tend to be confirmed in empirical studies. Third, the optimization approach (in-
cluding utility maximization and profit maximization) has a spectacularly wide
scope. It has been used to analyze not only personal and household choices about
traditional economic matters like consumption and savings, but also choices about
education, marriage, child-bearing, migration, crime and so on, as well as business
decisions about output, investment, hiring, entry, exit, etc. Fourth, the optimiza-
tion approach provides a compact theory that makes empirical predictions from a
relatively sparse model of the choice problem – just a description of the chooser’s
objectives and constraints. In contrast, for example, psychological theories (with
strong support from laboratory experiments) predict that many choices depend
systematically on a much wider array of factors, such as the way information is
2
, presented to the subjects, the noise level in the laboratory and other variables that
might influence the subject’s psychological state.
Despite the attractions of the rational choice approach, its empirical failings in
economics and psychology experiments have promoted an intense interest in new
approaches. A wide range of alternative models have been advocated. Learning
models, in which individuals make choices like those that have worked well for
them in the past, have attracted particular attention from economic theorists and
experimenters. Bounded rationality models in which decision makers adopt rules
that evolve slowly have had some empirical successes. For example, a model in
which department stores use standard mark-ups to set retail prices appears to give
a better account of those prices than does a simple profit maximization model,
according to which mark-ups vary sensitively according to price elasticities. Other
models assume that people seek acceptance by imitating their peers, rely on in-
tuition on heuristics, or make choices that are heavily influenced by their current
emotional state. Recent research try to identify parts of the brain involved in
decision-making and model how brain processes affect decisions. Still others give
up on modeling choice mechanisms at all and simply concentrate on measuring
and describing what people choose.
Although these various alternatives appear to have advantages for some pur-
poses, in this class we will focus on the decidedly useful and still-dominant model
of rational choice.
2 Preferences and Choice
Rational choice theory starts with the idea that individuals have preferences and
choose according to those. Our first task is to formalize what that means and
precisely what it implies about the pattern of decisions we should observe.
Let X be a set of possible choices. In consumer choice models, one might
specify that X ⊂ Rn , meaning for instance that there are n different goods (beer,
tortilla chips, salsa, etc..) and if x ∈ X, then x = (x1 , ..., xn ) specifies quantities of
each type of good. In general, however, the abstractness of the choice set X allows
enormous flexibility in adapting the model to various applications. Some of the
3
