Additive Representations of Preferences A New Foundation of Decision
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THEORY AND DECISION LIBRARY General Editors: W. Leinfellner and G. Eberlein Series A: Philosophy and Methodology of the Social Sciences Editors: W. Leinfellner (Technical Universtiy 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 Operations Research Editor: S. H. Tijs (University ofNijmegen) Series D: System Theory, Knowledge Engineering and Problem Solving Editor: W. Janko (University of Vienna)
SERIES C: GAME THEORY, MATHEMATICAL PROGRAMMING AND OPER4-TIONS RESEARCH Editor: S. H. Tijs (University of Nijmegen)
Editorial Board H. Keiding (Copenhagen), J.-F. Mertens (Louvain-Ia-Neuve), H. Moulin (Blacksburg), B. Peleg (Jerusalem), T. E. S. Raghavan (Chicago), J. Rosenmuller (Bielefeld), A. Roth (Pittsburgh), D. Schmeidler (Tel-Aviv), R. Selten (Bonn). Scope Particular attention is paid in this series to game theory and operations research, their formal aspects and their applications to economic, political and social sciences as well as to socio-biology. It will encourage high standards in the application of game theoretical methods to individual and social decision making.
For a list of titles in this series, see final page.
ADDITIVE REPRESENTATIONS OF PREFERENCES A New Foundation ofDecision Analysis
by PETER P. WAKKER Department ofMathematical Psychology, University ofNijmegen, The Netherlands
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
Library of Congress Cataloging in Publication Data
Wakker. Pete~ P. Additive representations of preferences : a new foundation of decision analysis I Peter P. Wakker. p. cm. -- (Theory and decision library. Series C. Game theory. mathematical programmlng. and operations research) "Rewritten version of the author's Ph.D. dissertation at the Department of Economics of the University of Brabant"--P. Bibliography: p. Inc I udes i nde x. ISBN 978-90-481-4036-7 ISBN 978-94-015-7815-8 (eBook) DOI 10.1007/978-94-015-7815-8
1. Declsion-making--Mathematical models. QA402.5.W325 1989 658.4'03·3--dc19
I. Title.
11. Series. 88-26783
CIP
ISBN 978-90-481-4036-7
All Rights Reserved
© 1989 by Spritlger Sciencet-Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1989 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, eiectronic or mechanical inc1uding photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner
CONTENTS Acknowledgements
IX
PREFACE, PREVIEW, AND GUIDE LINES FOR USE 1
Preface Preview Guide lines for use
2
CHAPTER O. ELEMENTARY DEFINITIONS
8
0.1. 0.2.
Nontopological preliminaries Topological preliminaries
CHAPTER I. FROM CHOICE FUNCTIONS TO BINARY RELATIONS 1.1.
1.2.
1.3.
Choice functions, their use, and interpretational complications 1.1.1. Example 1.1.2. Elementary formalizations and some assumptions 1.1.3. Thought experiments 1.1.4. Normative and descr
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