Jack Douglas Stecher

Generating Ambiguity in the Laboratory

This article develops a method for drawing samples from a distribution with no finite quantiles or moments. The method provides researchers with a way to give subjects the experience of ambiguity. In any experiment, learning the distribution from experience is impossible for the subjects, essentially because it is impossible for the experimenter. We characterize our method, illustrate it in simulations, and then test it in a laboratory experiment. Our method does not withhold sampling information, does not assume that the subject is incapable of making statistical inferences, is replicable across experiments, and requires no special apparatus. We compare our method to the techniques used in related experiments that attempt to produce an ambiguous experience for the subjects. This paper was accepted by Peter Wakker, decision analysis.

Existence of approximate social welfare

This paper presents weak requirements on incomplete social preferences, and illustrates how such preferences can be derived from a choice rule. While the requirements do not guarantee the existence of a social welfare function, they do suffice for social preferences to be mapped faithfully to neighborhoods on the real line. That is, whenever consistent social choices are possible between given alternatives, the associated welfare intervals do not overlap.

Subjective Information in Decision Making and Communication

Luce’s purpose was to argue for intransitive indifference. In what follows, I pursue a differentapproach.Rather than treating thisstudentashaving intransitive indifference, with preferences defined over objective cups of coffee, I view the student has having preferences defined over the coffee as he subjectively perceives it. To make this rigorous, Iprovideanaxiomaticmodelof thestudent’sperceptions,allowingthereader of this article to know which coffee cup the student is tasting, in order to clarify the relationship between the subjective decision problem and the objective alternatives. The discussion so far looks at the problem in one direction, namely, that a given decision maker can see distinct objects as indistinguishable. The issue in the other direction – that the way a given decision maker perceives a given object may not be unique – is discussed in Husserl (1913), Sect. 41. In describing his view of a table in front of him, Husserl writes

A Zero Effect Explains Deviations from Expected Utility in Allais-type Tasks

This article tests the predictions of expected utility theory and of several of its most prominent alternatives and assesses their ability to explain behavior in Allais-type tasks. We nd that, given a transparent presentation, expected utility theory performs surprisingly well, and that the alternative theories perform poorly except inasmuch as they make the same predictions as expected utility theory. We also contribute to methodology, and study the consequences of using hypothetical versus real incentives. Although hypothetical incentives do not aect compliance with expected utility, they have a large eect on attitude toward risk.This article tests the predictions of expected utility theory and of several of its most prominent alternatives and assesses their ability to explain behavior in Allais-type tasks. We find that, given a transparent presentation, expected utility theory performs surprisingly well, and that the alternative theories perform poorly except inasmuch as they make the same predictions as expected utility theory. We also contribute to methodology, and study the consequences of using hypothetical versus real incentives. Although hypothetical incentives do not affect compliance with expected utility, they have a large effect on attitude toward risk.

The Choice of Standards for a Reporting Language

The problem of information exchange arises in many contexts, ranging from computer science to linguistics to financial accounting. One aspect of this problem is the choice of whether to use a single standard for all users of information or whether to use different languages for different audiences; this has been of particular interest in international accounting contexts. This paper creates a framework (specifically, a mathematical category) for studying this issue. Topological spaces are used to model how an agents understanding of the world is translated into a local reporting language, and a certain class of continuous functions captures when a local reporting environment can be translated into a standardized language. In general, standardization comes at the cost of allowing less information to be transmitted. The category presented here provides a method for studying settings where agents are not aware of the same objects and also for settings where agents need their standards to be not only mutually agreeable but also acceptable to outside parties. Thus, unawareness and incomplete contracting have natural interpretations in the framework presented here.

Competitive equilibrium with intuitionistic agents

This paper studies an economy whose agents perceive their consumption possibilities subjectively, and whose preferences are defined on what they subjectively experience, rather than on those alternatives that are objectively present. The model of agents’ perceptions is based on intuitionistic logic. Roughly, this means that agents reason constructively: a solution to a problem exists only if there is a construction by which the problem can be solved. The theorems that can be proved determine how an agent perceives a set of alternatives. A dual model relates perceived alternatives to a shared language, which the agents use in trading. So perceptions relate objective alternatives to an agent’s subjective view of them, and reporting dually relates an agent’s subjective world to a shared language. It turns out that an appropriately modified notion of competitive equilibrium always exists. However, in contrast with standard results in economic theory, competitive equilibrium need not be efficient.

Lending, Lying, and Costly Auditing

In this paper, we describe a bankruptcy game played in a pure-exchange, perfectly competitive economy, and establish the existence of competitive equilibria. The game admits of lying by borrowers and costly auditing by lenders. The equilibria are characterized by (endogenously determined) equilibrium probabilities of default, loan quantities, interest rates, and default risk premia, and by equilibria simultaneously determined in risk-free debt markets. We find that the optimal debt contract is the standard debt contract, and that the risk-free debt market may be inactive, as all parties may strictly prefer risky debt contracts to risk-free debt.

A Category for Studying the Standardization of Reporting Languages

The problem of information exchange among agents who see the world subjectively arises in many contexts. One aspect of this problem is the choice of whether to use a standardized terminology among all agents or to use different languages for different audiences; this has been of particular interest in international accounting contexts. We develop a formal structure for studying this issue. An agents reporting environment is modeled as a topological space, where the open neighborhoods represent ways that the agent can report (approximately) what he wishes to convey. We then develop a category of reporting environments, called Rep, and model the translation of one reporting environment to another as a homomorphism in this category. We show that reporting in a standardized language is different from using information in that language; this is because homomorphisms may only exist in one direction. Potential future applications are studying settings where agents are not aware of the same things (modeled as pullbacks) or where reports concern parties in addition to the reporting entity and the end user (modeled as pushouts).

Using Brouwer’s continuity principle to pick stocks

Accounting theory treats a wide class of equity valuation approaches as equivalent. For example, under clean surplus accounting, the earnings approach is viewed as identical to the discounted dividends approach. Empirical research, however, typically finds that the two valuation approaches do not predict market prices equally well. This paper offers a theoretical explanation for this apparent anomaly: expectations of discounted infinite sums (incomes, cash flows, or dividends) are undefined unless some restrictive probabilistic conditions hold. Without the usual stationarity and ergodicity assumptions, it may still be possible to estimate upper and lower bounds on such sums, but these bounds need not coincide. In such a setting, earnings and discounted dividends yield intervals of justifiable valuations, which intersect but need not coincide. Depending on the extent to which a firm is held by insiders, differences in the valuations that different formulae justify may not show up in market prices. This provides an explanation for two additional empirical puzzles. First, empirical studies detecting little incremental information in dividends over earnings may be predisposed toward this finding. Second, stronger apparent reactions to dividend omissions than to initiations may be an illusion.

Expected Utility and Equilibrium with Subjective Choice Sets and Strategic Reporting

This paper studies an economy where agents trade using a shared language, so that they do not need to meet in person with goods physically present. Agents provide vague descriptions of proposed net trades, which we interpret as arising either from inherent limitations in what the agents can describe or from strategic presentations of information. We construct a family of orders over terms in the language, arising from an individuals preferences over consumption as subjectively perceived, illustrate the induced orders properties, and show the constructive existence of competitive equilibrium. Finally, we illustrate the relationship between the existence of a competitive equilibrium obtained in the language and the one that would result from an interaction involving perceived consumption sets.