Introduction

Preference

Choice

Preference-Maximizing Choice

EC4407 & EC4607 Behavioural Economics Lectures 1–2 Georgios Gerasimou University of St Andrews

Semester 2, 2015-16

Please do not circulate these notes without permission

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Introduction

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Preference-Maximizing Choice

Contact Info

Office hours:

Monday 2-4pm

(additional hours before/after class test & before final exam)

Office:

Room G4W in Castlecliffe

Email address:

[email protected]

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Module Basic Info Lectures: EC4407: 2–4pm every Tuesday in School VI for 10 weeks EC4607: 2–4pm every Tuesday in School VI for 9 weeks Tutorials: EC4407 (group 1): Weeks 3, 5, 7, 9 and 11 EC4607 (group 2): Weeks 3, 5, 7 and 9 (details to be confirmed) Assessment: EC4407 & EC4607: Class test in Week 7 (details to be confirmed) EC4407 only: 1500-word project to be submitted by 22 April EC4407 & EC4607: Final exam in May Final grade: EC4407: 25% Test + 25% Project + 50% Exam EC4607: 40% Test + 60% Exam

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Syllabus 1. Introduction. Preference, choice and rational choice. 2. Status quo bias and the endowment effect. Choice deferral and choice overload. 3. Context effects and explanations. Salience theory of consumer choice. 4. Choice under risk, expected utility theory and some of its paradoxes. Prospect theory and applications. 5. Choice under ambiguity and the Ellsberg paradox. Maxmin expected utility and applications. 6. Choice over time. Time-(in)consistent preferences. Exponential & quasi-hyperbolic discounting. Procrastination. 7. Behavioral game theory: Ultimatum games, dictator games and social preferences. 8. Biases in probability judgements. Overconfidence. (EC4407 only)

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Textbooks

E. Angner, A Course in Behavioral Economics, Palgrave Macmillan, 2012 D. Just, An Introduction to Behavioral Economics, Wiley, 2014 N. Wilkinson and M. Klaes, An Introduction to Behavioral Economics, 2nd edition, Palgrave Macmillan, 2012

E. Shafir (ed.), The Behavioral Foundations of Public Policy, Princeton, 2013

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Readings for Lectures 1–2

Many concepts in today’s lectures are standard but others are collected from many sources and do not appear compactly in any single text

The most relevant sources for further reading are: Chapters 1–3 in Angner Chapter 1 in: A. Mas-Collel, M. Whinston and J. Green (1995) “Microeconomic Theory”, Oxford University Press

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Behavioural Economics

Economics is the field that studies the allocation of scarce resources As such, it pertains to a wide range of situations such as consumer decision making, voting, partner selection or policy decisions To analyse such situations, economics relies on theories that aim to help us better understand the world we live in Every theory builds on a number of assumptions, from which certain logical conclusions follow When the conclusions of a theory are not supported by the empirical evidence, then if one aims to improve the theory’s descriptive relevance one must revisit the theory’s assumptions

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Behavioural Economics

Many of the core assumptions in economics are related to the behaviour of the individual decision maker Behavioural economics increases the explanatory power of economics by providing it with more realistic psychological foundations (Camerer & Loewenstein, 2004)

The behavioural economics approach extends rational choice and equilibrium models; it does not advocate abandoning these models entirely (Ho et al, 2006)

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Behavioural Economics The role of experiments is imperative in behavioural economics While the ultimate goal is to propose a new theory that is better at explaining what we observe, this cannot be done without relevant evidence from carefully designed experiments However, once such evidence is available, there is often disagreement about the underlying cause But even if there is no such disagreement, there may be a large number of possible ways to extend the standard model in a way that accounts for this commonly agreed cause This non-uniqueness of modelling approaches is to be contrasted to that of models of rational choice for which, typically, there is consensus about what the right approach is This plethora of alternative explanations in behavioural economic

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Neoclassical Consumer Theory

In the textbook theory, the consumer is portrayed as making a utility-maximizing choice from his budget set His budget set in turn is an infinite set determined by the exogenously given prices of the goods and his income Although useful for theoretical and pedagogic purposes, this is a major simplification of both the decision problem and of the consumer’s choice procedure We will consider different choice environments and alternative formulations of consumer decision making

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Finite Menus of Choice Alternatives

The consumer here is assumed to choose from finite sets of alternatives The finite set of all possible alternatives that the consumer might be presented with is denoted X The analog of a budget set in this context will be referred to as a menu A menu describes what is feasible to the consumer at a given point in time (feasibility here should not be tight with affordability) Formally, a menu is a nonempty subset A ⊆ X

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Weak Preferences

When the individual thinks x is at least as good as y for some options x and y in X, we write x%y The relation % captures the agent’s weak preferences on X Whenever x % y and y 6% x holds we write x  y and understand that x is strictly preferred to y Whenever x % y and y % x holds we write x ∼ y and understand that x and y are equally good, or that the consumer is indifferent between them

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Fundamental Axiom 1: Transitivity The consumer’s weak preferences % are transitive if, for any three alternatives x, y and z in X x % y and y % z together imply x % z This axiom postulates that preferences are ordered, hence internally consistent Clearly, however, it does not restrict their shape The following are implications of transitivity of %: xy & yz ⇒ xz xy & y∼z ⇒ xz x∼y & yz ⇒ xz x∼y & y∼z ⇒ x∼z

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The “Money Pump” Argument in Favour of Transitivity Consider an individual with cyclic preferences x  y, y  z and z  x Suppose he is initially endowed with x Since z  x, he would be willing to pay a small ez > 0 to get z Since y  z, he would then be willing to pay a small ey > 0 to get y And since x  y, he would be willing to pay a small ex > 0 to get x In theory, therefore, he would end up with his original endowment x, poorer by an amount equal to ez + ey + ex

−→ This theoretical exploitation scheme is known as a money pump −→ It provides an argument why preferences should be transitive Original reference: D. Davidson, J. McKinsey and P. Suppes (1955) “Outlines of a Formal Theory of Value, I”, Philosophy of Science, 22, 140-160 (argument attributed to Norman Dalkey)

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An Argument Against Transitivity of Strict Preference When choice alternatives are multi-attribute the consumer may resort to majority rule to compare them However, majority rule can lead to cyclic preferences

Attribute 1 Attribute 2 Attribute 3

x Good Medium Bad

y Medium Bad Good

z Bad Good Medium

x dominates y in attributes 1 and 2 y dominates z in attributes 1 and 3 z dominates x in attributes 2 and 3 Hence, majority rule implies x  y  z  x

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Another Argument Against Transitivity of Strict Preference

Violations of strict-preference transitivity have also been detected when some information is missing from the products’ description

Processor Storage Memory

PC 1 Bad Good

PC 2 Good Bad

PC 3 Bad Good -

Here a significant fraction of consumers expressed PC1  PC2  PC3  PC1 by relying on the single attribute where information was available for both products

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An Argument Against Transitivity of Indifference Consider a consumer who likes coffee Let xi be a cup of coffee with i grains of sugar Given the negligible sweetening effect of just one grain of sugar, we expect xi ∼ xi+1 for i = 1, 2, . . . because xi and xi+1 are very similar Transitivity of indifference then implies x1 ∼ x1000 The latter prediction, however, is unrealistic Depending on the consumer’s tastes, we would expect either x1  x1000

or

x1000  x1

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Fundamental Axiom 2: Completeness A weak preference relation % is complete if for any two alternatives x and y it holds that x % y or y % x Completeness postulates that any two alternatives can be compared Under this assumption the consumer is not allowed to be indecisive This is obviously wrong from an empirical point of view Importantly, unlike transitivity, completeness is not defensible as an objective “rationality” property either

Note that in some models we take strict preferences  as a primitive (i.e. we assume no indifference)

In such cases completeness means x  y or y  x for all distinct x and y

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Relaxing Completeness Suppose we want to relax completeness in order to allow for the possibility of consumer indecisiveness If completeness does not hold there exist alternatives x and y such that x 6% y and y 6% x

(1)

Condition (1) defines the consumer’s incomparability/indecisiveness relation Importantly, unlike the case of indifference, transitivity of % does not imply transitivity of incomparability Indeed, the latter relation is generally intransitive (which is intuitive)

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Utility Representation of Complete and Transitive Preferences

Proposition Given a finite choice set X: 1. A preference relation % on X is complete and transitive if and only if 2. There exists a utility function u on X which represents % in the sense that, for all x and y x % y ⇐⇒ u(x) ≥ u(y) (2)

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Choice Correspondence Let M be the collection of all menus that can be generated from X We model the consumer’s choices from different elements of M with a choice correspondence This is a possibly multi-valued function C that associates each menu A in M with a subset of A (possibly the entire menu), i.e. C(A) ⊆ A

for all A ∈ M

Although behaviourally restrictive, it is typically assumed that C(A) 6= ∅ for all A ∈ M

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Weak Axiom of Revealed Preference

Notational remark: If A is a menu and S ⊂ A, then x ∈ A \ S means “x in A & x not in S” Weak Axiom of Revealed Preference (WARP) If x in C(A), y in A \ C(A) and y in C(B), then x not in B In words: If x is chosen over y in some menu, then y is not choosable in the presence of x in some other menu

−→ WARP precludes weak choice reversals

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Rational Choice & Utility Maximization

Proposition Given a finite choice set X: 1. A choice correspondence C takes nonempty values and satisfies WARP if and only if 2. There exists a complete and transitive preference relation % on X that rationalizes C in the sense that, for each menu A x in C(A) ⇐⇒ x % y for all y ∈ A

(3)

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Rational Choice & Utility Maximization The first implication, 1 ⇒ 2, tells us that choosing something from every menu and in a WARP-consistent way implies that choices are as if they’ve been generated by utility maximization

The second implication, 2 ⇒ 1, tells us that utility-maximizing behavior implies that choices have been made from all menus and in a WARP-consistent way

The proposition characterizes rational choice as choice that is derived from maximization of complete and transitive preferences that are defined on the entire set X

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Rational Choice & Utility Maximization

Modelling a decision maker in this way has two aims: Positive/descriptive: To explain his actual behaviour Normative/prescriptive: To suggest an objectively rational way of decision-making

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Preference (In)Stability and Context (In)Dependence In reality, a consumer’s preferences may depend on which menu is being considered or which alternative acts as a reference point for him We can capture menu dependence by writing %A , %B for two menus A and B, and we can write %r , %s for two reference points r and s to capture reference dependence, respectively Menu- and reference-dependence allow for preference reversals like x %A y and y B x or x %r y and y s x If %A = %B for all menus A and B, and if %r = %s for all reference points r and s, then preferences will be called stable or context-independent Otherwise they will be called unstable or context-dependent

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Preference (In)Stability and Context (In)Dependence Menu-Dependent Preferences

Suppose, for example, that X = {w, x, y, z} and that the elements of X represent pizza slices Suppose also that w and x are equal in size, and bigger than both y and z Let menus A and B be defined by A = {w, x, y}

and

B = {w, y}

A “hungry but righteous” consumer might prefer large to small when at least two large slices are available, and prefer the smaller slice otherwise His preferences can be modelled as w ∼A x, x A y and w A y y B w so that C(A) = {w, x} and C(B) = {y}

(WARP violation)

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Preference (In)Stability and Context (In)Dependence Reference-Dependent Preferences

Now suppose X = {iPhone, Android, Windows} are smartphone platforms Consider Consumer A who is inversely influenced by which platform is chosen by Consumer B When A hears that B is planning to buy an iPhone his preferences are Android iPhone iPhone iPhone Windows But once it is known that B has purchased an Android device instead, his preferences become iPhone Android Android Android Windows

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Preference (In)Stability and Context (In)Dependence Incomplete Preferences

Consider, finally, an example with X = {w, x, y, z} and let A = {w, x, y}

and

B = {x, y, z}

Suppose the consumer’s preferences are such that w  y, z  x and no other comparisons are possible due to the consumer’s indecisiveness Preferences here are incomplete and context-independent (i.e. stable) (Moreover, there is no indifference between distinct alternatives in X)

Suppose that the consumer must choose something from both A and B There is no most-preferred option in either of these menus The next best thing would be to choose something that is not worse than anything else feasible (i.e. an undominated option) This would result in C(A) = {w, x} & C(B) = {y, z}

(WARP violation)

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Preference (In)Stability and Context (In)Dependence The first two examples illustrate that a consumer’s preferences can be unstable but at the same time both complete and transitive within a menu or for a given reference point When this is the case he behaves as a utility maximizer within a given context but not across contexts In the next few lectures we will discuss some empirical phenomena that cannot be explained by rational choice but can be explained by models of context-dependent utility maximization and/or models of context-independent preferences that are not complete or transitive

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