ACTING UNDER UNCERTAINTY: MULTIDISCIPLINARY CONCEPTIONS

THEORY AND DECISION LIBRARY

General Editors: W. Leinfellner and G. Eberlein

Series A: Philosophy and Methodology of the Social Sciences

Editors: W. Leinfellner (Technical University of Vienna) G. Eberlein (Technical University of Munich)

Series B: Mathematical and Statistical Methods

Editor: H. Skala (University of Paderborn)

Series C: Game Theory Mathematical Programming and Mathematical Economics

Editor: S. Tijs (University of Nijmegen)

Series D: System Theory, Knowledge Engineering and Problem Solving

Editor: W. Janko (University of Vienna)

SERIES A: PHILOSOPHY AND METHODOLOGY OF THE SOCIAL SCIENCES

Editors: W. Leinfellner (Technical University of Vienna) G. Eberlein (Technical University of Munich)

Editorial Board

M. Bunge (Montreal), J. S. Coleman (Chicago), M. Dogan (Paris), J. Elster (Oslo), L. Kern (Munich), I. Levi (New York), R. Mattessich (Vancouver), A. Rapoport (Toronto), A. Sen (Oxford), R. Tuomela (Helsinki), A. Tversky (Stanford).

Scope

This series deals with the foundations, the general methodology and the criteria, goals and purpose of the social sciences. The emphasis in the new Series A will be on well-argued, thoroughly analytical rather than advanced mathematical treatments. In this context, particular attention will be paid to game and decision theory and general philosophical topics from mathematics, psychology and economics, such as game theory, voting and welfare

theory, with applications to political science, sociology, law and ethics.

George M. von Furstenberg Rudy Professor of Economics

Indiana University

Bloomington, Indiana, U.S.A.

ACTING UNDER UNCERTAINTY:

MULTIDISCIPLINARY CONCEPTIONS

Springer-Science+Business Media, B.V.

Library of Congress Cataloging-in-Publication Data

Von Furstenberg, George M., 1941-Acting under uncertainty: multidisciplinary conceptions / George

M. von Furstenberg. p. cm. - (Theory and decision library. Series A.,

Philosophy and methodology of the social science) ISBN 978-90-481-5785-3 ISBN 978-94-015-7873-8 (eBook) DOI 10.1007/978-94-015-7873-8

I. Uncertainty. 2. Decision-making. 3. Risk. 4. Microeconomics. I. Title. II. Series. HB615.V66 1990 658.4 '03-dc20

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Copyright © 1990 by Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1990.

Softcover reprint of the hardcover I st edition 1990

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recording, or otherwise, without the prior written permission of the publisher, Kluwer Academic Publishers, 101 Philip Drive, Assinippi Park,

Norwell, Massachusetts 02061.

Table of Contents

List of Contributors...................................................................... vu

Preface.......................................................................................... xi

Acknowledgments......................................................................... xvu

I.

II.

The Evolution of Scientific Conceptions of Uncertainty and Their Social Underpinnings ........................................ . 1

1. Coping with Uncertainty in Natural Science: 1200-1700 A. George MoHand...................................................... 3

2. Political, Moral, and Economic Decisions and the Origins of the Mathematical Theory of Probability: The Case of Jacob Bernoulli's The Art of Conjecturing Edith SyHa................................................................... 19

3. The Quantification of Uncertainty After 1700: Statistics SociaHy Constructed? Theodore M. Porter..................................................... 45

4. Uncertainty and the Conditioning of Beliefs Henry E. Kyburg, Jr.................................................... 77

5. The Unity of Probability Glenn Shafer............................................................... 95

6. Necessity, Chance, and Freedom Gernot M. R. Winkler.................................................. 127

Risk Analysis and Social Responsibility ............................ . 159

7. Risk in Cultural Perspective Steve Rayner............................................................... 161

8. Statistical Hypothesis Tests and Statistical Power in Pure and Applied Science David F. Parkhurst................ ........................ ......... ..... 181

9. Uncertainty in Environmental Risk Assessment Glenn W. Suter 11......... ................ ..................... .......... 203

Vi Table of Contents

10. Uncertainty in Morals and Politics Hector-Neri Castaneda............................................... 231

III. Learning and Acting Under Uncertainty............................. 265

11. Re-Modeling Risk Aversion: A Comparison of Bernoullian and Rank Dependent Value Approaches Lola L. Lopes.............................................................. 267

12. Neither Gullible Nor Unteachable Be: Signal Extraction and the Optimal Speed of Learning from Uncertain News George M. von Furstenberg......................................... 301

13. Rethinking Rational Expectations James Bullard.............................................................. 325

14. Multiattribute Decision Models: Task Order and Group Effects N. John Castellan, Jr. and Teresa A. Sawyer............... 355

IV. Coping With Extreme Forms of Uncertainty...................... 375

15. Measuring Vague Uncertainties and Understanding Their Use in Decision Making Thomas S. Wallsten..................................................... 377

16. Quantifying Vagueness and Possibility: New Trends in Knowledge Representation Didier Dubois and Henri Prade.................................. 399

17. Chaos and Complexity in Economic and Financial Science William A. Brock......................................................... 423

18. Information H. L. Resnikoff and Madan L. Puri.............................. 451

Index............................................................................................. 471

Contributing Authors

William A. Brock (Ph.D. Applied Mathematics)* F. P. Ramsey Professor of Economics University of Wisconsin, Madison, WI 53706, USA

James B. Bullard (Ph.D. Economics) 3133 Adams Mill Road, NW, Washington, DC 20010, USA

Hector-Neri Castaneda (Ph.D. Philosophy)* The Mahlon Powell Professor of Philosophy and Editor, Nous Indiana University, Bloomington, IN 47405, USA

N. John Castell an, Jr. (Ph.D. Psychology)* Professor of Psychology and Editor, Judgment/Decision Making

Newsletter Indiana University, Bloomington, IN 47405, USA

Didier Dubois (Drs. of Engineering and Science) Research Scientist, National Center foiScientific Research

(C.N.R.S.) Langages et Systemes Informatiques Institut de Recherche en Inf ormatique de Toulouse, Universite

Paul-Sabatier; 118, route de Narbonne, F-31062 Toulouse Cedex, France

Henry E. Kyburg, Jr. (Ph.D. Philosophy)* Burbank Professor of Moral and Intellectual Philosophy University of Rochester, Rochester, NY 14627, USA

Lola L. Lopes (Ph.D. Psychology)* Professor and Chair, Department of Psychology, and Professor

of Industrial Engineering University of Wisconsin, Madison, WI 53706, USA

viii Contributing Authors

A. George MoHand (Ph.D. History of Science) Senior Lecturer and Head, Department of History and

Philosophy of Science King's College, University of Aberdeen, Aberdeen AB9 2UB,

Scotland

David F. Parkhurst (Ph.D. Botany)** Professor, Environmental and Science Policy Program, School

of Public and Environmental Affairs Indiana University, Bloomington, IN 47405, USA

Theodore M. Porter (Ph.D. History) Assistant Professor of History University of Virginia, Charlottesville, VA 22903, USA

Henri Prade (Dr. of Engineering and Doctorat d'Etat) Research Scientist, National Center for Scientific Research

(C.N.R.S.) Langages et Systemes Informatiques Institut de Recherche en Informatique de Toulouse, Universite

Paul-Sabatier; 118, route de Narbonne, F-31062 Toulouse Cedex, France

Madan L. Puri (Ph.D. Statistics)* Professor of Mathematics and Editor, Journal of Statistical

Planning and Inference Indiana University, Bloomington, IN 47405, USA

Steve Rayner (Ph.D. Anthropology) Research Scientist, Energy Division Oak Ridge National Laboratory, Oak Ridge, TN 37831-6206,

USA

Howard L. Resnikoff (Ph.D. Mathematics)** President, Aware Inc. One Cambridge Center, Cambridge, MA 02142, USA

Contributing Authors

Teresa A. Sawyer (Ph.D. Psychology) Coordinator of Social Sciences, Health, and Human Services Carroll Community College, Westminster, MD 21157, USA

Glenn Shafer (Ph.D. Statistics) Ronald G. Harper Distinguished Professor of Business University of Kansas, Lawrence, KS 66045, USA

Glenn W. Suter, II (Ph.D. Ecology) * * Senior Research Scientist, Environmental Sciences Division Oak Ridge National Laboratory, Oak Ridge, TN 37831-6038,

USA

Edith D. Sylla (Ph.D. History of Science)

ix

Professor of History and Assistant Dean, College of Humanities and Social Sciences

North Carolina State University, Raleigh, NC 27695-8101, USA

George M. von Furstenberg (Ph.D. Economics)* Rudy Professor of Economics Indiana University, Bloomington, IN 47405, USA

Thomas S. Wallsten (Ph.D. Experimental Psychology) Professor of Psychology and Editor, Journal of Mathematical

Psychology University of North Carolina, Chapel Hill, NC 27514, USA

Gernot M. R. Winkler (Ph.D. Physics and Astronomy) Director, Time Service Department U.S. Naval Observatory, 34th and Massachusetts Avenue, NW,

Washington, DC 20390-5100, USA

Biographical information may be found in:

• Marquis Who's Who in America, 46th Ed., 1989-90, and/or earlier editions .

•• American Men & Women of Science. Physical and Biological Sciences, 17th Ed., 1989-90, and/or earlier editions.

Preface

Uncertainty could be associated with wisdom, enterprise, and discovery. In ordinary speech, however, it has mostly negative connotations. There is "fear of the unknown" and "ignorance is bliss;" there are maxims to the effect that "what you don't know doesn't hurt you" (or: "bother you") in several languages. This volume suggests that we need be bothered by the excessive confidence with which scientists, particularly social scientists, present some of their conclusions and overstate their range of application. Otherwise many of the questions that should be raised about all the major uncertainties attending a particular issue routinely may continue to be thwarted or suppressed. Down playing uncertainty does not lead to more responsible or surer action, it sidetracks research agendas, and leaves the decision makers exposed to nasty surprise.

This volume demonstrates that recognizing the many forms of uncertainty that enter into the development of any particular subject matter is a precondition for more responsible choice and deeper knowledge. Our purpose is to contribute to a broader appreciation of uncertainty than regularly accorded in any of the numerous disciplines represented here. The seventeenth-century French philosopher Descartes, quoted in this volume, wrote that "whoever is searching after truth must, once in his life, doubt all things; insofar as this is possible." White areas left on maps of the world in past centuries were a much more productive challenge than marking the end of the known world with the pillars of Hercules. Similarly, if one can think of only one possibility where there are several, much too high a probability, or degree of belief, will tend to be assigned to the one eventuality conceived of. Treating it as as good as certain would imply that there is nothing further to consider or to guard against.

False certainty is bad science, and it can be dangerous if it stunts the articulation of critical choices. It is a statement of fact that research leads to the discovery of contradictions, but these are not to be blamed as if they caused cumulative science to take regrettable detours. Rather, the more account is taken in any discipline of uncertainty in concepts, measures, processes, organization, and models, the more complete and thought-out the inventory of conditions becomes on which any

xu Preface

conclusion must rest. By the same token, taking such a careful inventory can help identify priority areas in which uncertainty can most usefully be reduced so as to justify increased confidence in a decision.

However, not all forms of uncertainty are reducible either in practice or in principle: The progress of science has ceased to be measured in this century by the degree to which uncertainty has been replaced by supposedly final scientific knowledge. Instead, research creates uncertainty. As a quote introducing the last paper in this volume puts it more accurately, "An addition to knowledge is won at the expense of an addition to ignorance." Research not only leads to the discovery of new uncertainties, but the application of its results can also provoke system disturbances (say, "greenhouse effects") that generate uncertainties where none had previously appeared.

The notion of progressive reduction of uncertainties is especially problematic in the social sciences. We may get progressively better insights into how a flood of gold from the New World explained the great inflation in Europe in the second half of the sixteenth century, but it would be a mistake to conclude that we have had better or surer control over inflation since the invention of government fiat paper money. To give another example: Perhaps research can also narrow the question of what precipitated the French Revolution and raise, in time, the degree to which this event can be explained "with necessity." But the notion is not tenable that our understanding of the forces of culture, politics, and economics clearly has improved prospectively or when these forces are first felt. Societies never hold still for research in the social sciences to catch up, but keep changing some of their dynamics. They do so partly as a result of ongoing research and attempts at "scientific" manipulation which individuals react to knowingly.

While the subjective experience of uncertainty is as old as human kind, scientific representations of uncertainty and of degrees of belief needed to be discovered. Part I of this book details how this scientific process evolved. Many of the conceptual breakthroughs in prior centuries initially came almost as a by-product of attempts to understand, interpret, and perhaps manipulate distributions of physical and behavioral characteristics observed in society. Scientific hypotheses began to be understood as not about how things are but about how they could be viewed for some advantage, such as the ability to predict interaction and behavior. The question of what the law of large numbers meant for individual exercise of free will and the foundation

Preface xiii

of social order occupied social scientists as the eighteenth century progressed. Subsequently, how to represent the formation and adjustment of beliefs about individual characteristics or events posed problems beyond frequentist assignments of probability values. Belief that is warranted by knowledge of the long run is only one of several possible starting points for grounding a theory of probability, none of which is, by itself, sufficient.

These issues are brought into contemporary focus toward the end of Part I. It is not just that there is epistemic uncertainty, or that there are limitations in obtaining information which one day might be overcome. Rather, there is an unbridgeable remaining difference between intellectual imaging and the reality of the unknown object or process it attempts to picture. Respecting this difference by using concepts that are mutually irreducible, like chance and necessity, to model an infinitely rich reality allows both subjectivist and objectivist elements to contribute to perception of the world.

The question of how one should morally, or responsibly, act here and now in the face of various risks is central to Part II. In some ways how to act responsibly depends on whom one feels responsible to. For instance, acting within organized hierarchies, people take it as their duty to see to it that the correct rules are applied and that the normal processes of their institution are followed. By contrast, public-interest groups, which tend to be egalitarian-collectivist rather than hierarchical institutions, do not find that following rules, regulations, and due­process is necessarily sufficient to meet their concerns. Because of their broad cultural and ethical claims and self-seeking, such groups are least respectful of expert renditions of technical evidence which hierarchical institutions accept as input into the risk management systems they apply.

And indeed, expert advice rendered by scientists trained in statistical hypothesis testing can easily miss the point. The conventions of such testing are designed to protect the stock of existing knowledge from being undermined by anything less than conclusive evidence to the contrary. Such conventions do not necessarily reflect the benefit/cost calculations appropriate to the situation. H, for instance, the alleged toxicity of a licensed chemical, if true, would be a major public health concern, while the cost of banning it needlessly would be small because substitutes are readily available, a needless ban (a type I error) is obviously far less bad than wrongly failing to ban the chemical (a type II error) if it should, in fact, be highly toxic. Hence one should require

xiv Preface

a high confidence level that the chemical is not toxic by use of tests that have the power to address t his issue, and not be relying on test results that are directly concerned only with not erring on the side of falsely blaming a chemical that is, in fact, harmless. Even quantitative uncertainty, that is distinguished from other kinds of uncertainty by being readily estimated by conventional techniques, thus poses far more difficult problems of criterion selection and interpretation than normally admitted.

An analogous conclusion has been drawn in the last paper in Part II about a probabilistic morality that is based on the expected utility of actions that may impinge on others. No simple decision calculus can represent the ideal of morality and do justice to both the interpersonal and meta-institutional character of morality in all instances. Yet, in choosing to act under uncertainty, the possibility of moral action is preserved.

Finding parsimonious psychological principles of behavior towards risky choices and exploring where plausible rules of learning and of decision making may lead are the subjects of Part III. Psychologically, individuals appear to be disproportionately concerned with best and worst possible outcomes which indicate the maximum gain or loss potential they f ace. They also tend to have aspiration levels for reasonable gains and for limiting losses. Hence they are concerned with more than security even if they are risk averse as a general rule. By contrast, the functions that are widely used to predict the maximization of expected utility have utility increase with the size of payoffs continuously at a decreasing rate. They yield solutions which are unaffected by changes in scale or by the addition of constants and theref ore not adequate to represent the three f actors--security, potential, and aspiration--that can explain the stylized facts of individual choice.

Aspiration levels in gambles can be determined from the protocols of subjects experimentally, and expectations of specific future events, such as changes in the general price level, can be documented through surveys. In both cases, however, the question remains how these aspirations and expectations are formed and how they square with the actual outcomes, at least on average. In economics, empirical models that have attempted to allow for expectations that are consistent with the actual outcomes in the aggregate have met with little success. As a result, economists have begun to question the

Preface xv

usefulness of treating economic agents as endowed with knowledge which no plausible learning process could lead them to acquire. If agents do not know the correct model beforehand, the learning mechanism or discovery process selected is itself capable of affecting the outcome during transitions since beliefs about the future are important to what is happening now. Indeed, beliefs may not only affect the transition but even the endpoint one moves to.

Beyond the question of external consistency of beliefs, psychologists at the end of Part III have also examined internal consistency of complex decisions and how it may be affected, for instance, by group discussion. Whether the preference rating of alternative outcomes is established directly, or indirectly via the assignment of weights in a multiattribute weighting function appears to make little difference. Interestingingly, however, the linear multiattribute decision model is more acurate in predicting group judgments when the individual members performed individual ratings before, rather than after, group ratings. Hence the information sharing associated with group discussion did not help improve consistency in the experiments reported. There are questions also of the relative efficiency of verbal versus quantitative communication.

Modeling the combination of many attributes to a single choice is in some ways the reverse process from taking a vague concept and assigning it to partial membership in various precise concepts. Instead of a phrase either agreeing with a precise concept or not, it can agree with it to varying degrees ranging from 0 ("not at all") to 1 ("entirely"). In fuzzy set theory, which deals with extreme forms of uncertainty discussed in Part IV, this degree of membership of the elements thus is expressed by any number from 0 to 1, rather than just by the limiting extremes. While degrees of this kind appear commensurate with the probability of discrete events, their interpretation is quite different. Mathematical measures of possibility and of degrees of necessity have been devised to be more respectful of information and its normal imperfections than traditional, frequentist approaches can be when information is either incomplete or vague.

Returning to processes that are characterized by numbers, though not necessarily by data that are completely precise, leads to further uncertainty about traditional representations. Economic and financial processes often appear stochastic; if they are subject to laws, these laws seem to allow considerable play. But could it be that the appearance of

xvi Preface

randomness is deceptive? There are certain dynamic equations that generate numbers that may pass as random under conventional tests even though, mathematically, there is no uncertainty at all how one value follows from its predecessors, provided each can be measured without error. Such equations give rise to deterministic chaos; their solutions are highly sensitive to initial conditions, making all but very short-term forecasting impossible. Tiny measurement errors blow up very fast under positive feedback, and tiny errors are practically inescapable. For instance, already the seventh decimal place in the expression for n/4, the last paper in Part IV reports, is still in doubt when the expansion of the alternating series representing it, or [1-(1/3) + (1/5)-(1/7) ... ], has been carried to 1.5 million terms. With the cost of additional accuracy rising at a steeply increasing rate, complete accuracy is an endpoint that is not practical even for digital computers.

It should not seem paradoxical that to attain lowered expectations for what can be known have ushered in the period of greatest expansion and precision of what is known in mathematics and science. The social sciences would stand to benefit from following the example of first reducing their claims to conclusive knowledge.

Acknowledgements

A multidisciplinary research program is difficult to carry forward without financial support that allows experts from different areas and institutions to come together and to interact with the core group in a central place. At Indiana University, seed money for this process was provided in 1987 -88 by the Multidisciplinary Seminars Program initiated by Anya P. Royce, Professor of Anthropology and Dean of the Faculties. Ideas were exchanged and discussed and the resulting papers were then refined in 1988-89 until they spoke clearly of difficult and essential matters having to do with the conception of uncertainty and how one might act under its conditions. Numerous cross-references between the papers written for this volume show the mutual enrichment and intellectual friendships that arose from the central concern uniting us.