1 Introduction
1.1 Economics: Neoclassical and behavioural
Descriptive theory -> how people in fact make decisions.
Normative theory -> how people should make decisions.
Theories of rational choice -> rational decisions are those that are in accordance with the theory:
irrational decisions are those that are not. A theory of rational choice can be thought of as descriptive
or normative (or both). To say that is its descriptive, is to say that people in fact act rationally. To say
that it is normative, is to say that people should at rationally.
- Typically, the term rational-choice theory is reserved for theories that are normatively correct,
whether or not they are simultaneously descriptively adequate.
Neoclassical (/standard) economics -> characterized by its commitment to a theory of rational
choice that is simultaneously presented as descriptively adequate and normatively correct. This
approach presupposes that people by and large act in the manner that they should. Neoclassical
economists do not need to assume that all people act rationally all the time, but they insist that
deviations from perfect rationality are so small or so unsystematic as to be negligible.
- Behavioural economics share neoclassical economists’ conception of economics as the study of
people’s decisions under conditions of scarcity and of the results of those decisions for society.
But they reject the idea that people by and large behave in the manner they should.
- While behavioral economists certainly do not deny that some people act rationally some of the
time, they believe that the deviations from rationality are large enough, systematic enough, and
consequently predictable enough, to warrant the development of new descriptive theories of
decision. If this is right, a descriptively adequate theory cannot at the same time be normatively
correct, and a normatively correct theory cannot at the same time be descriptively adequate.
1.2 The origins of behavioural economics
Hedonic psychology -> an account of individual behavior according to which individuals seek to
maximize pleasure and minimize pain.
Then they focused on what people actually did, their preferences.
Cognitive science -> sceptical of the theories and methods of the early neoclassical period –
comfortable talking about beliefs, desires, rules of thumb, and other things “in the head”.
2 Rational Choice under Certainty
2.1 Introduction
Axiomatic theory -> The theory consists of a set of axioms: basic propositions that can not be proven
using the resources offered by the theory, and which will simply have to be taken for granted.
2.2 Preferences
Formally speaking, a preference is a relation (between two or more entities).
- Binary, when it is between two entities. Ternary, when it involves three different entities.
- We often use small letters to denote entities or individuals and capital letters to denote relations.
,We define a universe U. The universe is the set of all things that can be related to one another.
Donald Duck’s nephews Huey, Dewey, and Louie. If so, that is our universe. The convention is to list
all members of the universe separated by commas and enclosed in curly brackets, like so: {Huey,
Dewey, Louie}. Here, the order doesn’t matter.
- A universe may have infinitely many members, in which case simple enumeration is
inconvenient. This is true, for instance, when you consider the time at which you entered the
space where you are reading this.
(Weak) preference relation -> “Is at least as good as”, and can be denoted: ≥
2.3 Rational preferences
A rational preference relation is a preference relation that is transitive and complete.
- Transitive when the following condition holds: for all x, y, and z in the universe, if x bears relation
R to y, and if y bears relation R to z, than x must bear relation R to z.
o Intransitive could be “is in love with”.
-
A
relation is complete when the following condition holds: for any x and y in the universe, either x
bears relation R to y, or y bears relation R to x (or both).
o Incomplete could be “is in love with”. For any two randomly selected people it is not
necessarily the case that either one is in love with the other.
o A thing even stands in a relationship to itself (it is reflexive).
-
The
choice of a universe might determine whether a relation is
transitive or intransitive, complete or incomplete.
2.4 Indifference and strict preference
As the previous section showed, the (weak) preference relation
admits ties. When two options are tied, we say that the first
option is as goods as the second or that the agent is indifferent
between the two options: we use ~ to denote indifference.
- It is reflexive and transitive, it is also symmetric: if x is as good as y then y is as good as x.
When a first option is at least as good as a second, but the second is not at least as good at the first,
we say that the first option is better than the second or that the agent strictly or strongly prefers the
first over the second: we use the symbol >.
,All these have proofs or indirect proofs (proof by contradiction).
Morgan’s law: ¬ (p & q) is logically equivalent to ¬ p ∨ ¬ q.
2.5 Preference orderings
The preference relation is often referred to as a preference ordering. This is so because a
rational preference relation allows us to order all alternatives in a list, with the best at the
top and the worst at the bottom.
2.6 Choice under certainty
To make a choice under certainty is to face a menu. A menu is a set of options such that you have to
choose exactly one option from the set. This is to say that the menu has two properties. First, the
items in the menu are mutually exclusive; that is, you can choose at most one of them at any given
time. Second, the items in the menu are exhaustive; that is, you have to choose at least one of them.
, In economics, the menu is often referred to as the budget set: this is simply that part of the set of
alternatives that you can afford given your budget, that is, your resources at hand. The line
separating the items in your budget from the items outside of it is called the budget line.
To be rational, or to make rational choices, means (i) that you
have a rational preference ordering, and (ii) that whenever you
are faced with a menu, you choose the most preferred item, or
(in the case of ties) one of the most preferred items. The
second condition can also be expressed as follows: (ii’) that …
you choose an item such that no other item in the menu is
strictly preferred to it. Or like this: (ii”) that … you do not
choose an item that is strictly less preferred to another item in
the menu.
It is important to note what the theory of rationality does not
say. The theory does not say why people prefer certain things to others, or why they choose so as to
satisfy their preferences. This theory says nothing about feelings, emotions, moods, or any other
subjectively experienced state.
Moreover, the theory does not say that people are selfish, in the sense that they care only about
themselves; or that they are materialistic, in the sense that they care only about material goods; or
that they are greedy, in the sense that they care only about money. The definition of rationality
implies that a rational person is self-interested, in the sense that her choices reflect her own
preference ordering rather than somebody else’s. But this is not the same as being selfish: the
rational individual may, for example, prefer dying for a just cause over getting rich by defrauding
others. The theory in itself specifies only some formal properties of the preference relation; it does
not say anything about the things people prefer. Rational people cannot have preferences that are
intransitive or incomplete, and they cannot make choices that fail to reflect those preferences.
2.7 Utility
One way of preference ordering: The preference ordering has three “steps.” In order to represent
these preferences by numbers, we assign one number to each step, in such a way that higher steps
are associated with higher numbers. A utility function associates a number with each member of the
set of alternatives. We say that the utility function u(·) represents the preference relationship ≥.
- (1) It must be a function from the set of alternatives into the set of real numbers. This means that
every alternative gets assigned exactly one number. It is acceptable to assign the same number
to several alternatives; (2) for something to be a utility function, it must assign larger numbers to
more preferred alternatives.
- A function that satisfied this condition can be said to be an index or a measure of preference
relation ≥
- Given a rational preference relation, you may ask whether it is always possible to find a utility
function that represents it. When the set of alternatives is finite, the answer is yes. The question
is answered by means of a so-called representation theorem.
