Table Of ContentRecent Research in Psychology
Clyde Coombs (1912-1988)
Donald R. Brown J.E. Keith Smith
Editors
Frontiers of
Mathematical Psychology
Essays in Honor of Clyde Coombs
With 36 Illustrations
Springer-Verlag
New York Berlin Heidelberg London
Paris Tokyo Hong Kong Barcelona
Donald R. Brown J.E. Keith Smith
Center for Research on Learning Department of Psychology
and Teaching University of Michigan
University of Michigan Ann Arbor, Michigan 48109
Ann Arbor, Michigan 48109 USA
USA
Library of Congress Cataloging-in-Publication Data
Frontiers of mathematical psychology: essays in honor of Clyde Coombs
/ Donald R. Brown, J.E. Keith Smith, editors.
p. cm. - (Recent research in psychology)
Includes bibliographical references.
ISBN-13:978-0-387-97451-4 e-ISBN-13:978-1-4612-3088-5
001:10.1007/978-1-4612-3088-5
1. Psychology - Mathematical models. 2. Psychometrics.
I. Coombs, Clyde Hamilton, 1912- II. Brown, Donald R., 1925-
. III. Smith, J. E. Keith. IV. Series.
BF39.F76 1991
150'.1'51-dc20 90-48269
CIP
Printed on acid-free paper.
© 1991 Springer-Verlag New York Inc.
All rights reserved. This work may not be translated or copied in whole or in part without the
written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New
York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly
analysis. Use in connection with any form of information storage and retrieval, electronic
adaptation, computer software, or by similar or dissimilar methodology now known or hereaf
ter developed is forbidden.
The use of general descriptive names, trade names, trademarks, etc., in this publication, even if
the former are not especially identified, is not to be taken as a sign that such names, as
understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by
anyone.
Camera-ready copy provided by the editors.
9 8 7 6 5 4 3 2 1
ISBN-13:978-0-387-9745 1-4
Preface
The papers in this volume were prepared after a preliminary
symposium held at The University of Michigan in honor of Clyde
Coombs. Following the symposium, each paper was extensively
revised and in many instances completely rewritten to provide a
timely and provocative survey of current works in mathematical
psychology in the style of Clyde Coombs. All of the authors were
students or colleagues who were closely influenced by Coombs and
our intention was not to cover all approaches to the field, but rather to
illustrate the continuing influence of Coombs's work and approach
to the application of mathematics to basic psychological phenomena.
If we are successful, it is because of his influence on the
contributors.
v
Acknowledgements
The preparation of this volume in memory of Clyde Coombs owes
much to the many friends, students, and colleagues of Clyde Coombs
who generously provided their support and encouragement.
Funding was provided by Dean John D'Arms of the Horace H.
Rackham School of Graduate Studies at The University of
Michigan. Thanks are also due to Professor Albert Cain, Chair of
the Psychology Department, for financial aid and moral support
and to the Center for Research on Learning and Teaching for
numerous kinds of help. Dr. Susan Nelson and Ms. Nancy Bates of
the Psychology Department provided constant administrative
backup along with Ms. Susan Bareis of the Center for Research on
Learning and Teaching. The editorial staff of Springer-Verlag
was always understanding with our numerous problems and we
thank them. Lolagene Coombs, June Brown and Greta Smith all
pitched in whenever needed. A very special thanks is given to Ms.
Maria Huntley who prepared and reprepared the whole manuscript
with patience, perseverance, dedication, skill, and good humor.
Her efforts kept this project going on schedule and with uniformly
high quality.
Donald R. Brown
J. E. Keith Smith
vii
Contents
Preface ................................................................... v
Acknowledgements .................................................. vii
Contributors ............................................................ xi
Introduction .......................................................... xiii
1
From Indices to Mappings: The Representational
.Approac1l to Measurement ............................................. 1
David H. Krantz
2
Social Dilemmas, Economic Self-Interest,
and Evolutionary Theory ............................................ 53
Robyn M. Dawes
3
Probabilistic Dimensionality:
A Study of Confidence and Intention. ............................... 80
Gordon G. Bechtel
4
Judgments of Relative Importance in Decision Making:
The Importance of Interpretation and
the Interpretation oflmportance .................................... 110
William M. Goldstein and Jane Beattie
5
Validating the Dimensional Structure of Psychological
Spaces: Applications to Personality and Emotions .............. 138
Richard J. Gerrig, Laurence T. Maloney, and
Amos Tversky
ix
6
The Disparity Between Willingness-to-Pay Versus
Willingness-to-Accept as a Framing Effect ...................... 166
Gary H. McClelland and William D. Schulze
7
Rapid Aimed Movements and the Speed-Accuracy
Trade Off: Optimal Strategies ..................................... 193
J. E. Keith Smith
x
Contributors
Jane Beattie William M. Goldstein
Center for Decision Research Department of Psychology
Graduate School of Business University of Chicago
University of Chicago 5848 South University Avenue
11 01 East 58th Street Chicago, Illinois 60637
Chicago, Illinois 60637
David H. Krantz
Gordon G. Bechtel Department of Psychology
College of Business Columbia University
Administration 116th and Broadway
Marketing Department New York, New York 10027
University of Florida
Gainesville, FL 32611 Laurence T. Maloney
Department of Psychology
Robyn M. Dawes 6 Washington Place
Department of Social and 8th Floor
Decision Science New York University
Carnegie Mellon University New York, New York 10003
Pittsburgh, Pennsylvania 15213
Gary H. McClelland
Richard J. Gerrig Department of Psychology
Department of Psychology University of Colorado
Yale University Boulder, Colorado 80309
P. O. Box llA Yale Station
New Haven, Connecticut 06520 William D. Schulze
Department of Economics
University of Colorado
Boulder, Colorado 80309
Xl
J. E. Keith Smith Amos Tversky
Department of Psychology Department of Psychology
106B Perry Building Stanford University
University of Michigan Stanford, California 94305
Ann Arbor, Michigan 48109
xii
