Table Of ContentDECISION THEORY AND DECISION BEHAVIOUR
THEORY AND DECISION LmRARY
General Editors: W. Leinfellner and G. Ebedein
Series A: Philosophy and Methodology of the Social Sciences
Editors: W. Leinfellner (Technical Universtiy of Vienna)
G. Ehedein (Technical University of Munich)
Series B: Mathematical and Statistical Methods
Editor: H. Skala (University of Paderborn)
Series C: Game Theory, Mathematical Prograrnrning and
Operations Research
Editor: S. H. Tijs (University ofNijmegen)
Series D: System Theory, Knowledge Engineering and Problem
Solving
Editor: W. Janko (University of Economics, Vienna)
SERIES B: MATHEMAT ICAL AND STATISTICAL METHODS
Volume 15
Editor: H. Skala (Paderbom)
Editorial Board
J. Aczel (Waterloo), G. Bamberg (Augsburg), H. Drygas (Kassel), W. Eichhorn
(Karlsruhe), P. Fishbum (New Jersey), D. Fraser (Toronto), W. Janko (Vienna),
T. Kariya (Tokyo), P. de Jong (Vancouver), M. Machina (San Diego), A. Rapoport
(Toronto), M. Richter (Kaiserslautern), B. K. Sinha (Cattonsville), D. Sprott (Waterloo),
P. Suppes (Stanford), H. Theil (Florida), E. Trillas (Madrid), L. Zadeh (Berkeley).
Scope
The series focuses on the application of methods and ideas of logic, mathematics and
statistics to the social sciences. In particular, formal treatment of social phenomena, the
analysis of decision making, information theory and problems of inference will be
central themes of this part of the library. Besides theoretical results, empirical investiga
tions and the testing of theoretical models of real world problems will be subjects of
interest. In addition to emphasizing interdisciplinary communication, the series will
seek to support the rapid dissemination of recent results.
For a list of titles published in this series, see final page.
DECISION THEORY AND
DECISION BEHA VIOUR
Normative and Descriptive Approaches
AN A TOL RAPOPOR T
University ofToronto, Canada
SPRINGER-SCIENCE+BUSINESS MEDIA B.Y.
Library of Congress Cataloging-in-Publication Oata
Rapoport, Anatol, 1911-
Decision theory and decision behaviour: normative and descriptive
approachesjA natol Rapoport.
p. cm.-(Theory and decision library. Series B,
Mathematical and statistical methods)
BibJiography: p.
Includes index.
ISBN 978-90-481-4047-3 ISBN 978-94-015-7840-0 (eBook)
DOI 10.1007/978-94-015-7840-0
1. Decision-making. 2. Game theory. I. Title. 11. Series.
T57.95.R36 1989
658.4'03-dc20 89-33204
printed on acid/ree paper
All Rights Reserved
© 1989 by Springer Science+Business Media Oordrecht
Origina1ly published by Kluwer Academic Publishers in 1989
Softcover reprint of the hardcover 1s t edition 1989
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
TABLE OF CONTENTS
PREFACE vii
INTRODUCTION 1
PART I: DECISIONS INVOLVING A SINGLE ACTOR
CHAPTER 1 Orders and Scales 11
CHAPTER 2 Optimization 25
CHAPTER 3 Decisions under Uncertainty 55
CHAPTER 4 Decisions under Risk 68
CHAPTER 5 Subjective Aspects of Risk 97
CHAPTER 6 Multi-objective Decisions 122
CHAPTER 7 Theory of Social Choice 143
CHAPTER 8 Individual Psychology of Decision-making 159
PART 11: NON-COOPERATIVE GAMES
CHAPTER 9 Two-person Constant Sum Games 177
CHAPTER 10 Some Topics in Continuous Games 197
CHAPTER 11 Two-person Non-constant Sum Games 216
CHAPTER 12 Psychological Pressures in Non-cooperative Games 237
CHAPTER 13 Theory of Voting 252
CHAPTER 14 Social Traps 270
PART 111: COLLECTIVE DECISIONS
CHAPTER 15 Two-person Coo perative Games 291
CHAPTER 16 N-person Cooperative Games 317
CHAPTER 17 The Allocation Problem 336
CHAPTER 18 Indices of Power 350
CHAPTER 19 Theories of Coalition Formation 369
v
vi CONTENTS
CHAPTER 20 Psychology of Collective Decision-making 382
CONCLUDING REMARKS 400
APPENDIX A Glossary of Symbols and Terms 409
REFERENCES 416
INDEX 421
PREFACE
This book presents the content of a year's course in decision processes for
third and fourth year students given at the University of Toronto.
A principal theme of the book is the relationship between normative and
descriptive decision theory. The distinction between the two approaches is not
clear to everyone, yet it is of great importance. Normative decision theory
addresses itself to the question of how people ought to make decisions in
various types of situations, if they wish to be regarded (or to regard
themselves) as 'rational'. Descriptive decision theory purports to describe how
people actually make decisions in a variety of situations.
Normative decision theory is much more formalized than descriptive
theory. Especially in its advanced branches, normative theory makes use of
mathematicallanguage, mode of discourse, and concepts. For this reason, the
definitions of terms encountered in normative decision theory are precise, and
its deductions are rigorous. Like the terms and assertions of other branches of
mathematics, those of mathematically formalized decision theory need not
refer to anything in the 'real', i.e. the observable, world. The terms and
assertions can be interpreted in the context of models of real li fe situations, but
the verisimilitude of the models is not important. They are meant to capture
only the essentials of adecision situation, which in reallife may be obscured
by complex details and ambiguities. It is these details and ambiguities,
however, that may be crucial in determining the outcomes of the decisions.
Their omission from the models may lead to the deduced consequences of
decisions being entirely different from the actual outcomes. For this reason,
the assertions of normative decision theory, generated by rigorous deduction
from assumed idealized conditions, cannot be interpreted as predictions of
actual human decisions or of their consequences. Thus, the objective of
normative decision theory is not to predict decisions or their consequences
but to disclose the logical essence of an idealized decision problem.
In contrast, descriptive decision theory does deal with reallife situations (or
laboratory simulations of such situations). For this reason, its terms cannot be
defined with absolute precision. At most, in experimental approaches, the
expected observations are defined in ways that make them recognizable; for
example, which of severallabeled alternatives a subject in an experiment will
choose on a given occasion under given labeled (rather than precisely defined)
conditions. When the descriptive approach becomes 'theoretical', i.e., seeks to
establish causes and effects of observed events, especially if the causes or
effects refer to psychological states (motivations, preferences, satisfactions,
disappointments, etc.) rigour becomes an ideal rather than a standard.
VB
Vlll PREFACE
The distinction between the normative and the descriptive approaches
should make clear why it is futile to demand 'predictive power' from
normative decision theory (as we demand from a theory developed in a
natural science) and equally futile to demand mathematical rigour from
descriptive theory. Sometimes descriptive theory is not in a position to make
predictions of people's decisions. It must often content itself with a classifi
cation of decision processes or of social phenomena governed by decisions, for
example a taxonomy of political coalitions and the like. Here descriptive
decision theory finds itself on a level analogous to that of early biology, when
it was in the 'natural history', specimen-collecting stage.
Ordinarily, the two directions of decision theory are pursued separately.
Formal normative theory is typically studied in the context of economics,
especially microeconomics, or of management science, disciplines recently
enriched by the infusion of the theory of games, the most thoroughly
developed branch of normative decision theory. Students of political science
are also sometimes introduced to some topics in the theory of games. When
this theory first appeared on the intellectual horizon, much was expected from
it in military circles. Whether these expectations were justified is hard to say,
since the sort of situations that would put applications of the theory to a test
(e.g., decision situations in a war conducted on an appropriate level of
sophistication) have not yet occurred, and it is a moot question whether such
a war would create opportunities for on-line application of game-theoretic
analysis. At any rate, except for abrief mention in Chapter 10 of so-called
games ofpursuit and evasion (in which considerable interest has been aroused
in military circles) no contact is made in this book between formal decision
theory and problems of interest to military professionals.
Treatments of descriptive decision theory can now be found in books and
courses in psychology, especially social psychology. To the extent that
psychology deals with concepts relevant to choices, e.g., with motivations,
preferences, problem solving, etc., it deals with subject matter to which
descriptive decision theories (note the plural) are relevant.
In this book roughly equal emphasis is placed on both approaches and their
different concerns. I was motivated to take this 'two-track' approach because I
feel that both are important but each is neglected when the other is presented.
Students of economics and of management science often remain insulated
from the psychology of decision-making, while students of psychology have
no opportunity to appreciate the intricacies of formal decision models and of
the part these intricacies can play in influencing choices. Thus, the alternation
between the formal and descriptive modes is one way in which the exposition
was organized.
The other basis of organization sterns from distinguishing the relationships
of the decision-makers, who will usually be called 'actors', to their environ
ment and to each other. Part I deals with decision situations involving a single
actor. He need not be an individual. 'He' may be a firm, a political party, or a
PREFACE IX
nation. The identity of the actor is determined by a set of interests. Thus, in
situations involving a single actor, the problems need to be considered only
from 'his' point of view. The relationship of the actor to the environment will
depend on whether the environment is deterministic or not. In the former
case, a one-to-one correspondence will be supposed between the actor's
choices among alternatives and the associated outcomes. These situations will
be called decisions under certainty. Ifthe environment is not deterministic, we
shall be dealing with decisions under risk or decisions under uncertainty,
according to wh ether probabilities can or cannot be assigned to the 'states of
nature' which, together with the actor's choices, determine the outcomes.
Part II treats non-cooperative games. These are decision situations involv
ing two or more ac tors with ge,nerally non-coincident interests and with no
opportunities for the actors to cooperate with each other. The principal theme
in this branch of decision theory is the problem of choosing strategies (courses
of action conditional on the outcomes of intermediate steps) which can in
some sense be regarded as 'optimal'. Making the meaning of'optimal' clear in
these contexts is itself an important problem raised in the theory of decision.
Part III deals with collective decisions. Here two or more actors have some
common interests and are able to co ordinate their strategies so as to achieve
outcomes which, in some way, benefit both or all of them. The problem
remaining is typically that of distributing the benefits attained by this sort of
cooperation among the actors concerned.
The assumed level of mathematical maturity varies with the topics treated.
Familiarity with differential equations is required to follow the arguments in
the sections on control theory in Chapter 2 and on continuous games in
Chapter 10. These topics can be omitted without disturbing continuity. In
some discussions, multiplication of vectors and matrices is involved. On two
occasions, the eigenvalues of a matrix are mentioned.
For the rest, familiarity with the ideas of elementary citlculus and
elementary probability theory should suffice. These topics are introduced in
Grade 13 of Ontario public schools and are listed as the only prerequisites for
the course on which this book is based.
I have found that, in general, discussion of mathematical methods in the
context of decision problems motivates students to familiarize themselves
with the uses of mathematics. An instructor in an introductory course in
decision theory should be likewise motivated to help students acquire some
mathematicalliteracy in the context of applications. Increasingly, mathemat
ics is seen (or ought to be seen) as a powerful aid to rigorous thinking. This is
especially true ofthe role mathematics plays in decision theory, as is evidenced
by the natural way in which the fundamental concepts of decision theory are
cleady and cogently expressed in set-theoretic and functional notation.
Familiarity with this language is more important for a deep understanding of
formal decision theory than facility in techniques of 'classical' mathematics.
Although mathematical notation and mathematical arguments are used
x PREFACE
throughout this book, recourse to genuine mathematical rigour is minimal.
Emphasis is on intuitive understanding of the arguments rather than on
formal proofs. This comparative laxity is consistent with the attempt to bring
together students interested in the technical side of decision theory and those
interested in its implications for psychology and the social sciences.
The scope of the book, offered primarily as a survey of the subject, reftects
breadth rather than depth. Many topics are only 'savoured', as it were. Thus,
treatments of linear programming, control theory, statistical decisions, and
games in characteristic function form barely scratch the surface of these now
extensiveiy developed fields. On the social science side, the large bodies of
literat ure on the formation of political coalitions, allocations of costs and
benefits in public works, and on the psychology of individual and collective
decision-making are barely tapped. The variety of topics touched upon was
meant to stimulate the reader or student to pursue whatever directions are
found to be especially interesting to any desired depth.
In combining the normative and descriptive approaches to decision
processes, I hoped to enable the reader to reap the fruits ofthis union, namely,
the rich philosophical implications ofthe apparently straightforward concept
of 'rationality'. In view of the growing realization of the paramount import
ance of decisions with global consequences, these philosophical implications
should be taken very seriously.
ANATOL RAPOPORT
Toronto, February, 1989
