Decision Science and Technology Reflections on the Contributions of
Decision Science and Technology is a compilation of chapters written in honor of a remarkable man, Ward Edwards. Among Ward's many contributions are two significant accomplishments, either of which would have been enough for a very distinguished career. F
- PDF / 52,961,128 Bytes
- 425 Pages / 439.37 x 666.142 pts Page_size
- 2 Downloads / 171 Views
DECISION SCIENCE ANO TECHNOLOGY:
Reflections on the Contributions of Ward Edwards
Edited by James Shanteau Kansas State University 8arbara A. Mellers Ohio State University David A. Schum George Mason University
Springer Science+Business Media, LLC
ISBN 978-1-4613-7315-5 ISBN 978-1-4615-5089-1 (eBook) DOI 10.1007/978-1-4615-5089-1 Library of Congress Cataloging-in-Publication Data A C.I.P. Catalogue record for this book is available from the Library ofCongress.
Copyright © 1999 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers, New York in 1999 Softcover reprint of the hardcover 1st edition 1999 AII rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, LLC. Printed an acid-free paper.
PREFACE
When a small group of us (Shanteau, Mellers, and Schum) first contemplated putting a Festschrift volume together in tribute ,to War-, ;:$, -- e, y >- e and C ~ E E e, (x,Cje) EBy '" (xEBy,CjY).
(4)
We see that the two sides amount to the same thing, and so it is indeed a highly rational axiomS. It has been studied empirically in two papers, Cho and Luce (1995) and Cho, Luce, and von Wmterfeldt (1994), and it appears to be sustained within the noise level of their methods. The introduction of EB allows one to define a concept of "subtraction" in the usual
way:
Defmition 2.
For all !,g,h E (i, (5)
Note that if EB is additive over money, i.e., Eq. (1) holds, then for x and yboth money gains or money losses xey=x-y,
(6)
which with segregation is exactly the property invoked above in the analysis of the Allais paradox and invoked by Kahneman and Tversky (1979) as pre-editing. The Negative Exponential Representation-I will not attempt to give a precise statementofthe resultaboutF, but only the gist ofit (for details see Luce, 1996, 1997, Luce & Fishburn, 1991, 1995); Suppose that U is the simplest rank-dependent representation of biruuy gambles, i.e., for x t y >- e, U(x,Cjy) = U(x)W(C) + U(y)[l- W(C)],
(7)
that U is weakly subadditive 9 in the sense that U(x EBx)
< 2U(x),
(8)
and that segregation holds. Then one can show mathematically that for some constants 8> 0, a > 0, (9)
17
whence (10) Thus, U and V are related through a negative exponential transformation. Clearly, .6. and U have the same unit and U is bounded from above by .6., which intuitively seems somewhat plausible. From Theorem 1, Eq. (10), and the additivity of V, it is easy to show for gains X, Y that
U(X (By) = U(x) + U(y) _ U(x~(y).
(11)
ObseIVe that U is unique up to multiplication by a positive constant. These transformations, it should be noted, are completely distinct lO from the ratio scale transformations of V. The above result has a converse, but I will omit it here because it is somewhat complex (Luce, 1996). A Parallel in Physics-So, despite the fact that the operati
