Recent Developments in the Foundations of Utility and Risk Theory

401 Pages·1986·9.78 MB·English

by  Amartya Sen (auth.)

RECENT DEVELOPMENTS IN
THE FOUNDATIONS OF UTILITY AND RISK THEORY
THEORY AND DECISION LIBRARY
AN INTERNATIONAL SERIES
IN THE PHILOSOPHY AND METHODOLOGY OF THE
SOCIAL AND BEHAVIORAL SCIENCES
Editors
GERALD EBERLEIN, University of Technology, Munich
WERNER LEINFELLNER, University of Nebraska
Editorial Advisory Board:
K. BORCH, Norwegian School of Economics and Business Administration
M. BUNGE, McGill University
J. S. COLEMAN, University of Chicago
w. KROEBER-RIEL, University of Saarland
A. RAPOPORT, University of Toronto
A. SEN, Oxford Univer:sity
w. STEGMULLER, University of Munich
K. SZANIAWSKI, University of Warsaw
L. TONDL, Prague
A. TVERSKY, Stanford University
VOLUME 47
RECENT DEVELOPMENTS IN
THE FOUNDATIONS OF
UTILITY AND RISK THEORY
Edited by
L. DABONI
Institute of Finance Mathematics, University of Trieste, Italy
A. MONTESANO
Faculty of Political Science, University of Milan, Italy
and
M. LINES
Faculty of Business and Economics, University of Venice, Italy
D. REIDEL PUBLISHING COMPANY
A MEMBER OF THE KLUWER ACADEMIC PUBLISHERS GROUP
DORDRECHT/BOSTON/LANCASTER/TOKYO
library of Congress Cataloging in Publication Data
Recent developments in the foundations of utility and risk theory.
(Theory and decision library; v. 47)
Papers delivered at the Second International Conference on Foundations of
Utility and Risk Theory, Venice, June 1984.
Includes index.
1. Utility theory-Congresses. 2. Risk-Congresses. I. Daboni, Luciano.
II. Montesano; Aldo. III. Lines, M. (Marji) IV. International Conference
on Foundations of Utility and Risk Theory (2nd; 1984 : Venice, Italy) V.
Series.
HB201.R35 1986 330.15'7 86-594
ISBN-13: 978-94-010-8551-9 e-ISBN-13: 978-94-009-4616-3
001: 10 .1 007/978-94-009-4616-3
Published by D. Reidel Publishing Company,
P.O. Box 17,3300 AA Dordrecht, Holland.
Sold and distributed in the U.S.A. and Canada
by Kluwer Academic Publishers,
190 Old Derby Street, Hingham, MA 02043, U.S.A.
In all other countries, sold and distributed
by Kluwer Academic Publishers Group,
P.O. Box 322, 3300 AH Dordrecht, Holland.
All Rights Reserved
© 1986 by D. Reidel Publishing Company, Dordrecht, Holland
Reprint of the original edition 1986
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner
CONTENTS
PREFACE vii
PART I. RATIONALITY AND UNCERTAINTY IN DECISION THEORY
RATIONALITY AND UNCERTAINTY 3
Amartya Sen
¥RACTICAL CERTAINTY AND THE ACCEPTANCE OF EMPIRICAL
STATEMENTS 27
John C. Harsanyi
A NEW BASIS FOR DECISION THEORY 43
Donald Davidson
SOME QUESTIONS ABOUT BAYESIAN DECISION THEORY 57
Max Black
REGRET, RECRIMINATION AND RATIONALITY 67
Robert Sugden
PART II. UTILITY AND UNCERTAINTY
DETERMINATION OF CARDINAL UTILITY ACCORDING TO AN
INTRINSIC INVARIANT MODEL 83
Maurice Allais
THE PRESENT STATE OF UTILITY THEORY 121
Georges Bernard
A CHARACTERIZATION OF DECISION MATRICES THAT YIELD
INSTRUMENTAL EXPECTED UTILITY 139
Allan Gibbard
ASSOCIATIVE MEANS AND UTILITY THEORY 149
Luciano Daboni
ON UTILITY FUNCTIONS IN A FINANCIAL CONTEXT 153
Guido A. Rossi
THE GENERALIZED MEANS MODEL (GMM) FOR NON-
DETERMINISTIC DECISION MAKING 161
Hector A. Munera
INDIVIDUAL CARDINAL UTILITY, INTERPERSONAL
COMPARISONS, AND SOCIAL CHOICE 185
Antonio Camacho
CONTENTS
PART II. UTILITY AND UNCERTAINTY continued
SURVIVING IMPLICATIONS OF EXPECTED UTILITY THEORY 201
Ole Hagen
CONSISTENCY AND EXPECTED UTILITY THEORY 215
Robin Pope
AGGREGATE REVEALED PREFERENCES AND RANDOM
UTILITY THEORY 231
G. Leonardi, E. F. Arcangeli, A. Reggiani
CONCAVE ADDITIVELY DECOMPOSABLE REPRESENTING
FUNCTIONS AND RISK AVERSION 249
Peter Wakker
PART III. INFORMATION AND UTILITY
CONCEPTS OF INFORMATION BASED ON UTILITY 265
Morris H. DeGroot
INFORMATION UTILITY - STATISTICAL AND SEMANTICAL
FEATURES 277
Anio O. Arigoni
PART IV. RISK PROPENSITY AND DECISION
ASSESSING RISK PROPENSITY 291
K. R. MacCrimmon, D. A. Wehrung
WHAT NAIVE DECISION MAKERS CAN TELL US ABOUT RISK 311
Lola Lopes
A MEASURE OF RISK AVERSION IN TERMS OF PREFERENCES 327
Aldo Montesano
STATE-DEPENDENT UTILITY AND RISK AVERSION 337
Gerald L. Nordquist
PART V. DECISION MAKING UNDER UNCERTAINTY
THE IMPACT OF UNCERTAINTY ON THE OPTIMAL DECISION
OF RISK NEUTRAL FIRMS 355
Karl Aiginger
STRATEGIC PLANNING MODELS AND RISK MANAGEMENT 375
J~nos ~cs
INDEX 393
PREFACE
The Second International Conference on Foundations of
Utility and Risk Theory was held in Venice, June 1984. This
volume presents some of the papers delivered at FUR-84.
(The First International Conference, FUR-82, was held in
Oslo and some of the papers presented on that occasion
were published by Reidel in the volume Foundations of
Utility and Risk Theory with Applications, edited by
Bernt P. Stigum and Fred Wenst~p). The theory of choice
under uncertainty involves a vast range of controversial
issues in many fields like economics, philosophy,
psychology, mathematics and statistics. The idea of
discussing these problems in international conferences has
been successful: two conferences have been held and others
will follow. The climate of the debate has changed in the
meantime, partly as a result of these conferences. It is no
more only a question of attacking or defending the
neo-Bernoullian assumptions, but also of proposing wider
generalizations and including new elements in the analysis
of the decision process.
For instance Amartya Sen - comparing the two current
notions of rationality, internal consistency and
self-interest pursuit introduces the concept of
reasoning and considers the irrationality which may result
from the failure of a positive correspondence between
reasoning and choice or from a limited capacity of
reasoning. Rationality is also considered with respect to
the controversial axiom of strong independence. John C.
Harsanyi introduces the concept of practical certainty,
i.e. the instrumental decision of accepting some empirical
statements as true based on the judgement that the loss
which the agent may incur in using the policy determined
by that acceptance is smaller than the gain obtained by
simplifying the decision problem. Donald Davidson expands
on Ramsey's original problem of discovering probabilities
and values, considering also the meaning of sentences
whose interpretation is not predetermined. Thus decision
theory is combined with interpretation in an analysis
which adheres to Jeffrey's theory. Max Black argues
viii PREFACE
against the tendency to view any departure from the
standard model of expected utility maximization as a
manifestation of inconsistency and shows some sensible
reasons for what might look like a perverse choice, Robert
Sugden points out that regret theory concerns the
decisions of people in difficult situations, when they do
not have a complete master plan for choosing the best
action, and he laments the fact that the lack of such a
plan is considered irrational.
While the papers we have mentioned above discuss the
rationale behind decision making, those that follow are
concerned with people's value, i.e. with utility. Maurice
Allais determines an invariant cardinal utility function
which agrees with empirical data of his 1952 and 1975
tests. This function is loglinear on a large domain and is
the same for all agents up to only one parameter. Georges
Bernard shows that it is necessary to abandon the
independence axiom in order to establish a general utility
function, non-linear in probabilities, of uncertain
prospects. Three approaches are considered, the last of
which, proposed by the author, is examined mainly with
regard to the principle of dominance. Allan Gibbard
outlines the conditions under which decision matrices
(introduced by Savage) yield the instrumental expected
utility, which is a general kind of expected utility.
Luciano Daboni and Guido A. Rossi in their papers use de
Finetti's original approach in order to determine a
utility function for uncertain situations. Hector A.
Munera proposes a generalized means model of which the
expected utility model and the linearized moments model
are particular cases. Munera also uses the concept of
mean introduced by de Finetti and Kolmogoroff. After
recapitulating his measure of the intensity of preference
which considers the choice situation among sequences of
elementary alternatives, Antonio Camacho shows how these
cardinal utilities could be used for determining social
choice in special cases. Ole Hagen analyzes some
inplications among them utility dominance of the
expected utility theory which survive in competing
theories. Robin Pope considers Savage's explanation of his
error in answering Allais's test and goes on to indicate a
timing inconsistency in von Neumann-Morgenstern's set of
axioms. Giorgio Leonardi, E. Fabio Arcangeli and Aura
Reggiani give a new axiomatic reconstruction of random
utility models (already considered by Luce and Mc Fadden)
PREFACE
and use the resulting theory in order to analyze
observations of aggregate choice with respect to the
standard ordinal utility and revealed preference theories.
Peter Wakker specifies the properties of the preference
relations necessary and sufficient to guarantee the
existence of continuous concave functions of utility.
The connection between information and utility is
considered in two papers. Morris H. DeGroot, following a
Bayesian approach, analyzes the measure of information with
respect to the probability distribution and the utility
function of a decision maker. He introduces the notion of
expected information and of retrospective information
presenting their properties and role. Anio O. Arigoni
treats the evaluation of the informational utility of
linguistic variables in descriptions of facts for which
statistical and semantic features are considered jointly.
The attitude of decision makers towards risk is the
focus of the following papers. Kenneth R. MacCrimmon and
Donald A. Wehrung have undertaken a large-scale study to
assess the risk propensity of practicing decision makers.
The results have the important characteristic of being
obtained by considering many different situations and
attitutes. Lola L. Lopes gives four propositions about how
people process risks and explains the gap between
behavioural phenomena and neo-Bernoullian theory using
explanations provided by the subjects. Aldo Montesano
introduces a measure of risk aversion which does not
require the existence of the neo-Bernoullian utility
function but only the existence of a certainty equivalent
for every action. Gerald L. Nordquist considers the
problem of how to measure risk aversion in the case of a
utility function dependent on the state of nature.
The last part of the volume discusses some problems of
economic activity deriving from uncertainty. Karl Aiginger
examines the conditions that make firms produce more (or
less) under uncertainty than they would under certainty.
Janos ~cs evaluates the application of risk management in
strategic planning.
ACKNOWLEDGEMENTS
The University of Venice, Cal Foscari hosted the
Second International Conference on the Foundations of
Utility and Risk Theory. The Program Committee consisted
of Werner Leir.fellner, Ole Hagen and Aldo Montesano. Marji
x PREFACE
Lines served as Conference Secretariat. Many thanks to
Lucia Dal Mistro and Roberta Nordio for their help in the
preparation of this volume.
Financial support for the conference was given by the
following organizations:
Consiglio Nazionale delle Ricerche (National Council
of Research).
Regione Veneto (Regional Administration of Veneto).
Comune di Venezia (municipality of Venice).
Provincia di Venezia (Provincial Administration of
Venice).
Banca Nazionale del Lavoro.
Assicurazioni Generali.
Istituto Nazionale delle Assicurazioni
and the University of Nebraska.
We also wish to thank all of the participants at the
conference for contributing to the remarkable atmosphere of
friendly critique and finally, for making these FUR
conferences a recurrent source of reference in the field
of utility and risk theory.
Venice, October 30, 1985
Luciano Daboni
Aldo Montesano
Marji Lines.