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Verminotic pneumonia in South American fur seal (Arctocephalus australis) in Southern Brazil
- Yasmin Daoualibi, Renata F. Moreira, Marcele B. Bandinelli, Joanna V. Z. Echenique, Paulo G. C. Wagner, João F. Soares, Saulo P. Pavarini
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- Parasitology / Volume 150 / Issue 2 / February 2023
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- 01 November 2022, pp. 150-156
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Verminotic pneumonia caused by Parafilaroides spp. nematodes is an underreported disease in beached South American fur seals, with scant literature available on the characteristics of parafilaroidiasis, the nematode itself, as well as its occurrence in pinnipeds in Brazil. The present work aims to identify, describe and detail the histological features of the infection and molecular characteristics of verminotic pneumonia in the South American fur seal. Twenty-six specimens of Arctocephalus australis, found dead on the northern coast of Rio Grande do Sul in 2021, were analysed. These animals were identified and submitted to necropsy and histology. For the molecular identification of metastrongylids, lung fragments were subjected to DNA extraction, polymerase chain reaction targeting the Internal transcribed spacer 2 (ITS-2) gene and subsequent sequencing. In total, 12 animals presented with parasites in the lung parenchyma on histological evaluation, and only 1 showed a granulomatous lung lesion at necropsy. Microscopically, the nematodes were found mainly in the alveoli, associated with little or no inflammatory response, and they had morphological characteristics compatible with metastrongylids. Six ITS-2 gene quality sequences were obtained; after comparative analysis via BLAST, they showed similarity with sequences obtained from Parafilaroides sp. Therefore, verminotic pneumonia caused by Parafilaroides represents an important differential diagnosis of lung disease in South American fur seals found on the northern coast of Rio Grande do Sul.
7 - Stochastic Choice
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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- Revealed Preference Theory
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- 05 January 2016
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- 05 January 2016, pp 95-113
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Summary
We now study the empirical content of individual rational choice when choice is stochastic. There are two possible interpretations of this exercise.
The first is that we lack data on individual choices. There is instead a population of agents, and we observe the distribution of choices in the population. For example we may know how many people purchased Italian wine in a wine store, and how many purchased French cheese in a cheese store, but we do not know if those who bought the French product in one store are the same people who bought Italian in the other. The theory to be tested is that of rational agents with stable preferences. Thus we want to know when an observed distribution of choices is consistent with a population of rational agents with potentially different, but stable, preferences.
The second interpretation is that we observe an individual who literally randomizes among different alternatives. We might observe this individual agent over time, enough to infer a stochastic rule that he uses to select an element at random when faced with a given set of available choices.
STOCHASTIC RATIONALITY
The model of stochastic choice can be described as follows. A system of choice probabilities is a pair (X,P), where X is a finite set of alternatives and P is a function with domain contained in 2X\﹛∅﹜ × X, where P(A,x) = PA(x) is a non-negative number for each nonempty A ⊆ X and x ∈ A, and such that ∑x∈A PA(x) = 1. In other words, PA(x) defines a probability distribution over the set A.
In our first interpretation of stochastic choice, there would be an underlying large population of agents: PA(x) is the fraction of agents who choose x when the set A of possible alternatives is available. In the second interpretation of stochastic choice, an individual agent's choices really are random, and we know that PA(x) is her probability of choosing x from A.
1 - Mathematical Preliminaries
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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We begin by reviewing basic mathematical facts and notation that we shall use repeatedly in the book. The basic results we need relate to binary relations and their extensions and representations, and to solutions to systems of inequalities.
BASIC DEFINITIONS AND NOTATIONAL CONVENTIONS
Relations
Let X be a set. An n-ary relation on X is a subset of Xn. A binary relation on X is a subset of X ×X. When R is a binary relation on X, we write (x, y) ∈ R as x R y. When R is an n-ary relation, we also write R(x1, …, xn) instead of (x1, …, xn) ∈ R.
Given a binary relation R, define its strict part, or asymmetric part, PR by (x, y) ∈ PR iff (x, y) ∈ R and (y, x) ∉ R. Define its symmetric part, or indifference relation, IR by (x, y) ∈ IR iff (x, y) ∈ R and (y, x) ∈ R. Two elements x, y ∈ X are unordered by R if (x, y) ∈ R and (y,x) ∈ R.
Two elements are ordered by R when they are not unordered by R. We say that a binary relation B is an extension of R if R ⊆ B and PR ⊆ PB. A binary relation B is a strict extension of R if it is an extension, and in addition there is a pair that is unordered by R but ordered by B. Finally, a binary relation is complete if it leaves no pair of elements unordered. That is, R is complete if for all x and y, x R y or y R x (or both).
The following are standard properties of binary relations. A binary relation R is:
• transitive if, for all x, y, and z, x R y and y R z imply that x R z;
• quasitransitive if, for all x, y, and z, xPR y and yPR z imply that xPR z;
• reflexive if x R x for all x;
• irreflexive if (x, x) ∉ R for all x;
• symmetric if, for all x and y, (x, y) ∈ R implies that (y, x) ∈ R;
11 - Social Choice and Political Science
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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This chapter deals with models of collective choice in which individual agents’ preferences are aggregated into collective behavior. The first class of models use some fixed method to aggregate preferences. We assume that collective choices can be observed, but that individual agents’ preferences are unobserved. The second class of models are more structured models of voting in political economy and political science. A common idea in political science is that voters' preferences are “Euclidean”; we present the testable implications of this notion. Finally, we consider models of individual voter behavior and work out the corresponding observable implications.
TESTABLE IMPLICATIONS OF PREFERENCE AGGREGATION FUNCTIONS
The main questions in this section take the following form. Suppose that a group preference (or choice) is observable. Is this group preference consistent with a collection of rational agents whose preferences are aggregated according to some rule? We may, for example, wonder when a group's collective behavior is consistent with majority rule.
There are three ways to interpret the material that we are about to present. First, if we know the aggregation rule that the agents use, we may want to test the hypothesis that a society of agents behave rationally as individuals, when the only observable data come in the form of aggregate preference. Second, when the aggregation rule is unknown, we may want to test the joint hypotheses that a group of agents use a certain aggregation rule, and that they each behave rationally as individuals. Finally, a different interpretation of these results is that we might want to characterize all possible “paradoxes” that we might expect from using a given aggregation rule. Condorcet's paradox (a cycle on three alternatives) illustrates the problems that can arise from using majority rule. The results in this section describe all possible paradoxes of this type.
The model is as follows. Let X be a set of possible alternatives. We shall assume that we observe all possible binary comparisons of elements in X; that is, we observe a complete binary relation on X.
Frontmatter
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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References
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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12 - Revealed Preference and Systems of Polynomial Inequalities
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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It should be apparent by now that systems of linear inequalities emerge naturally in revealed preference theory. They constitute the essence of Afriat's Theorem, for example; and we formulated revealed preference problems using systems of linear inequalities in Chapters 3, 6, 7, and 8. In this chapter, we describe how revealed preference problems can generally be understood as a system of inequalities. From a purely computational perspective, one can very often solve a revealed preference problem by algorithmically solving the corresponding system of inequalities.
When the system of inequalities is linear, the problem is easy to solve both computationally and analytically. Here we develop a GARP-like acyclicity test (similar to the ones in Chapters 2 and 3). The test will follow from the linearity of the system of inequalities embodied in the revealed preference question.
We shall discuss an extension of the linear theory to systems of polynomial inequalities. The theory of polynomial inequalities will be seen to be very relevant for revealed preference theory (but harder to work with compared to the theory of linear inequalities).
LINEAR INEQUALITIES: THE THEOREM OF THE ALTERNATIVE AND REVEALED PREFERENCE
We start by revisiting the Theorem of the Alternative, or Farkas’ Lemma from Chapter 1. It is easy to see why it is useful in revealed preference theory. We then discuss some sources of linear systems for popular models in economics. The following is a bit weaker than Lemma 1.13. It is written so as to emphasize that the lemma can be used to “remove existential quantifiers;” it states that an existential statement (one that start with “there is… ”) is equivalent to a universal statement (one that starts with “for all… ”). Note that the discussion of the Tarski–Seidenberg Theorem in Chapter 9 is also about removing existential quantifiers.
Lemma 1.13'(Integer–Real Farkas) Let ﹛Ai﹜i=1M be a finite collection of vectors inQK. The following statements are equivalent:
I) There exists y ∈ RK such that for all i = 1, …, M, Ai. y > 0.
II) For all z ∈ Z+M \ ﹛0﹜, it holds that.
6 - Production
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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Production theory is another classical environment in which revealed preference theory is applied. The case of production is simpler than the case of demand treated in the previous chapters, mainly because firm output is a cardinally measurable and observable concept, whereas utility is not. In the case of production, we shall assume that firm output and prices are both observed, while the set of all feasible production vectors, that is the firm's technology, is not.
We will consider two approaches to production theory: the cost minimization model and the profit maximization model. In the first model, factor prices and factor demands are observed, and (single-dimensional) output is observed as well. This environment is very similar to the consumer case, but, as we have noted, simpler. We want to know whether the model is consistent with the cost minimization hypothesis, meaning that the cost of production is minimized for a given level of output.
In the second model, the model of profit maximization, we want to test the hypothesis that producers maximize profit. This model is in a sense “dual” to the consumer case. In the consumer case, we needed to solve for the function being maximized, but we know the budget set. In contrast, in the producer case, we know the function being maximized: it is a linear profit function; but we do not necessarily know the available technology (the constraint set faced by the firm).
COST MINIMIZATION
We take as primitive a dataset comprising the input–output decisions of a firm. The firm uses n factors, and produces a single good. An input–output dataset D consists of a collection (yk, xk,pk), k = 1, …, K, where yk ∈ R, xk ∈ Rn+, and pk ∈ Rn++. Each observation k consists of a quantity of output yk, a vector of factor demands xk, and factor prices pk. Note that output can be negative, but inputs are always positive.
5 - Practical Issues in Revealed Preference Analysis
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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The tests in Chapters 3 and 4 are meant to be applicable to actual datasets, and many researchers have investigated these applications using experiments, consumption surveys, and other sources of data. Naturally, there are complications that arise when one tries to carry out the tests we have described. We shall focus on the basic application of GARP (or SARP) to data on consumption expenditures. The difficulties in applying GARP can be summarized as follows:
First, GARP is an “all or nothing” notion. A dataset either falsifies the theory of a rational consumer or it does not. One may, however, want to distinguish a grayscale of degrees of violation of the theory. It is possible that some violations can be attributed to simple mistakes on the part of a fully rational consumer. We develop concepts along these lines in 5.1.
Second, the nature of budget sets introduces problems with the power of testing for GARP. When two observed budget sets are nested, then there are no choices that can indicate a violation of GARP (actually ofWARP in that case). More generally, any dataset in which budget sets have substantial overlap is biased towards the satisfaction of GARP. The problem of budget overlap is very real because often data contain more individual-level variation in expenditure levels than variation in relative prices. As we explain below (Section 5.2), these features cause budget sets to have substantial overlap.
Third, many studies do not track the identities of individual consumers.With such cross-sectional datasets, two observations (x1,p1) and (x2,p2) actually correspond to different individuals (or households), but they are identified as having the same preferences based on their observable characteristics. The procedure of identifying individuals based on their observable characteristics is called “matching” in statistics and econometrics. The basic problem is how to carry out this identification, or matching: when can we treat two individuals as the same for the purposes of revealed preference tests.
Moreover, certain cross-sectional datasets exacerbate the problem of power. The observations (x1,p1) and (x2,p2) in the data are of two different individuals (treated as the same agent) at similar points in time. Prices p1 and p2 are then bound to be similar, because even prices in different locations are similar at the same point in time.
Index
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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Miscellaneous Endmatter
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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3 - Rational Demand
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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Revealed preference theory started out as an exploration into the testable implications of neoclassical demand theory, and while it has expanded in many different directions, the analysis of rational demand is the most actively researched area in revealed preference theory. In this chapter, we present an exposition of the basic results in the revealed preference theory of rational demand.
We suppose here that we have observations on the purchasing decisions of a single consumer. The consumer makes a sequence of independent choices at different price vectors. The data consists of the consumer's choices, and we seek to understand the implications of rational consumption behavior for such data.
The material on rational demand is divided into three chapters. In Chapter 3 we discuss the basic results on weak and strong rationalization, including Afriat's Theorem, the main result in the revealed preference theory of rational demand. In Chapter 4 we turn to specific properties of demand functions; and in Chapter 5 to some of the practical issues that arise when applying the results of revealed preference theory to empirical research.
WEAK RATIONALIZATION
Consider an agent choosing a bundle of n goods to purchase. Consumption space is X ⊆ Rn+, meaning that the consumer chooses x ∈ X. We assume that for any x ∈ X and ε >0, there is ε’ with 0<ε’ <ε and x+ε’1 ∈ X; this means that it is possible to add more of every good to any bundle in X and still remain in X.
Given a preference relation on X, let d : Rn++ ×R+→2X be the demand correspondence associated to ; it is defined as
We refer to d as a demand function if d(p,m) is always a singleton.
A consumption dataset D is a collection (xk,pk), k = 1, …K, with K ≥ 1 an integer, xk ∈ X and pk ∈ Rn ++. For each k, xk is the consumption bundle purchased by the consumer at prices pk. We shall assume that the consumer exhausts all his income, so that the expenditure pk · xk is also the total income devoted to consumption at the time at which the purchases were made.
Preface
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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WHAT IS REVEALED PREFERENCE THEORY?
“Revealed preference” is a term with several interpretations in economic theory, all closely related but possessing subtle philosophical differences. The central theme common to all interpretations is that of understanding what economic models say about the observable world. Most practitioners of revealed preference theory recognize that an economic model is useful for organizing data and making predictions, but they would not go so far as to admit that the model is, or represents, “reality.” Economic models usually consist of multiple interacting parts. Some parts are theoretical in nature, and are not meant to be observed. These unobservable parts are then tied to objects which could potentially be observed and measured.
Let us begin with the canonical example of revealed preference theory. Economists often view individuals as making decisions consistent with some objective function, usually interpreted as “utility.” So, the theory posits that an individual chooses that option which gives her the highest utility among all feasible options. This has proved to be a useful and tractable model in many branches of economics; in fact, the concept is ubiquitous. But it has been recognized at least since Pareto (1906) that, even if an individual optimizes a utility, the cardinal structure of said utility function (that is, the numerical values assigned to potential choices by the utility) cannot be inferred from choice behavior. Utility is a “theoretical” concept. The only empirically meaningful statements that can be gleaned from data relate to whether one option exhibits a higher utility than another. Once this is recognized, it is natural to ask: what are the predictions of the utility maximization model for observable choice behavior? Obviously, the predictions will have to be made across different choice situations. A theory that claims an individual chooses the best available option from those in front of her will have little to say without imposing constraints on the notion of “best.” So, the next step was to understand what these predictions are. These questions form the first few chapters of this book.
The revealed preference approach seeks to understand what a given model says about data. Observable economic data are either consistent with a given model or not.
2 - Classical Abstract Choice Theory
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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We start our development of revealed preference theory by discussing the abstract model of choice. All revealed preference problems have two components: data, and theory. Given a family of possible data, and a particular theory, a revealed preference exercise seeks to describe the particular instances of data that are compatible with the theory. We shall illustrate the role of each component for the case of abstract choice. The data consist of observed choices made by an economic agent. A theory describes a criterion, or a mechanism, for making choices.
Given is a set X of objects that can possibly be chosen. In principle, X can be anything; we do not place any structure on X. A collection of subsets ∑ ⊆ 2X\﹛∅﹜ is given, called the budget sets. Budget sets are potential sets of elements from which an economic agent might choose. A choice function is a mapping c : ∑→2X\﹛∅﹜ such that for all B ∈∑, c(B)⊆B. Importantly, choice from each budget is nonempty.
For the present chapter, choice functions are going to be our notion of data. The interpretation of a choice function c is that we have access to the choices made by an individual agent when facing different sets of feasible alternatives. A particular choice function, then, embodies multiple observations.
The main theory is that of the maximization of some binary relation on X. The theory postulates that the agent makes choices that are “better” than other feasible choices, where the notion of better is captured by a binary relation. The theory will be refined by imposing assumptions on the binary relation: for example that the relation is a preference relation (i.e. a weak order).
Given notions of data and theory, the problem is to understand when the former are consistent with the latter. We are mainly going to explore two ways of formulating this notion of consistency.
Dedication
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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Revealed Preference Theory
- Christopher P. Chambers, Federico Echenique
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Pioneered by American economist Paul Samuelson, revealed preference theory is based on the idea that the preferences of consumers are revealed in their purchasing behavior. Researchers in this field have developed complex and sophisticated mathematical models to capture the preferences that are 'revealed' through consumer choice behavior. This study of consumer demand and behavior is closely tied up with econometrics (especially nonparametric econometrics), where testing the validity of different theoretical models is an important aspect of research. The theory of revealed preference has a very long and distinguished tradition in economics, but there was no systematic presentation of the theory until now. This book deals with basic questions in economic theory, such as the relation between theory and data, and studies the situations in which empirical observations are consistent or inconsistent with some of the best known theories in economics.
Contents
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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13 - Revealed Preference and Model Theory
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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Summary
In this book, we have studied the concept of empirical content in disparate environments. To conclude our study, we wish to suggest that there is a unifying theme behind these exercises. The idea of the empirical content of a theory as the set of all falsifiable predictions of the theory is generally applicable, and subject to formal study.
A theory can make predictions which are non-falsifiable. A case in point is the theory of representation by a utility function. Recall Theorem 1.1. The theorem implies that if a preference relation over R+n possesses a utility representation, then there is a countable set Z ⊆ R+n such that for all x, y ∈ X for which, there exists z ∈ Z for which. This implication of the theory of utility is not falsifiable. To demonstrate that the theory has been falsified, one would need to establish the non-existence of such a set Z. Doing so involves checking, one-by-one, every possible countable subset Z of R+n, a task which can never be completed.
A first and basic issue in understanding empirical content has to do with universal vs. existential axiomatizations. The idea was already introduced in Chapters 9 and 12, where we saw the removal of existential quantifiers as a source of testable implications. The issue of universal and existential axioms goes back to Popper (1959), who thought that a theory with a universal description is falsifiable, while an existential theory is not.
Popper offers the example of the theory that claims “all swans are white.” This theory is universal, in the sense that it states a property of all swans, or “universally quantifies over swans.” It is easy to see that, in principle, such a theory can be falsified by finding a single swan that is not white. Contrast with Popper's example of an existential theory: that “there exists a black swan.” The existential theory cannot be falsified. Falsifying the theory would involve collecting all possible swans and verifying that each one is not black.We could only do this if we could somehow be sure to have exhaustively checked all the swans in the universe.
9 - General Equilibrium Theory
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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The previous chapters deal with theories of individual agents’ behavior. In the rest of the book, we turn to economic theories that predict group or societal outcomes. We first turn our attention to general equilibrium theory.
General equilibrium theory can often be studied through a reduced-form model, the excess demand function of an economy. The equilibrium outcomes of the economy are given as zeroes of the excess demand function. There are two immediate questions about the scope of the model: What is the class of excess demand functions that can arise from a well-behaved economy? And which sets of prices can be equilibrium prices?
The answers to these questions carry a largely negative message about general equilibrium theory. The Sonnenschein–Mantel–Debreu Theorem (as we shall refer to it) shows that, roughly speaking, any continuous function that satisfies Walras’ law can be the aggregate excess demand function of a very well-behaved economy. The result implies that any compact set of strictly positive prices can be the set of Walrasian equilibrium prices of a well-behaved economy. No additional constraints are obtained by insisting on basic regularity properties of the equilibria.
Considered as data on an economy, an excess demand function, or a set of putative equilibrium prices, may seem odd. The next set of questions under study is much more similar to the approach in Chapter 3. If we assume that we can observe equilibria for different vectors of endowments (in a sense, we can sample from the “equilibrium manifold”), then the theory of general equilibrium can be refuted: There are nonrationalizable datasets. The theory is testable if we can observe prices from different endowment vectors. The nature of the testable implications follow from a very general principle, the Tarski–Seidenberg Theorem, which we shall also review here.
We focus on a model of an economy where all economic activity takes the form of exchange.
8 - Choice Under Uncertainty
- Christopher P. Chambers, University of California, San Diego, Federico Echenique, California Institute of Technology
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Summary
In this chapter we turn to models of choice under uncertainty. We consider an agent who makes choices without fully knowing the consequences of those choices, and focus on models in which uncertainty can be quantified and formulated probabilistically. The most important such model is, of course, expected utility.
OBJECTIVE PROBABILITY
There are times when probabilities can be thought to be objective and known, or observable. This is the case, for example, when outcomes are randomized according to some known physical device—such as a game in a casino, or a randomization device used by an experimenter in the laboratory.
We consider two basic environments. In one the primitive objects of choice are lotteries. In the other, the objects of choice are state-contingent consumption.
Notation
Let X be a finite set. We denote by Δ(X) = ﹛p ∈ RX : p ≥ 0; ∑x∈X p(x) =1﹜ the set of all probability distributions over X.
Choice over lotteries
Given is a finite set X of possible prizes. Δ(X) is the set of all lotteries over X. We imagine an agent who chooses a lottery. The agent understands that there is uncertainty over the realization of the lottery: over which prize the lottery will result in. But the probabilities specified in the lottery are accurate (or at least useful) representations of that uncertainty.
We investigate a very basic result on revealed preference in this environment.
An expected utility preference is a binary relation for which there exists u : X→R such that for all p,q ∈ Δ(X),
The classical axiomatization of expected utility preferences relies on the independence axiom of decision theory; namely, that for all p,q, r ∈ Δ(X) and all.
Most experimental studies refuting the expected utility model are direct refutations of the independence axiom. The best-known such refutation is through a thought experiment, known as the Allais paradox. Instead of setting up a thought experiment, we are going to assume that we are given data on choices among pairs of lotteries.