Cost-Minimizing Choice Behavior in Transportation Planning A Theoret
In the Administration building at Linkopi ¨ ng University we have one of Oscar Reutersvard’ ¨ s “Impossible Figures” in three dimensions. I call it “Perspectives of Science”. When viewed from a speci c point in space there is order and structure in the 3-
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Sven Erlander
Cost-Minimizing Choice Behavior in Transportation Planning A Theoretical Framework for Logit Models
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Professor Sven Erlander Department of Mathematics Linköping University 581 83 Linköping Sweden [email protected]
ISSN 1430-9602 ISBN 978-3-642-11910-1 e-ISBN 978-3-642-11911-8 DOI: 10.1007/978-3-642-11911-8 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010927685 © Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: eStudio Calamar, Spain Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Front view Staircase to second floor, Administration Building, Linköping University
Painting by Oscar Reutersvärd transformed into 3-dimensional sculpture by Björn Kruse and Tomas Ohlsson Side view Perspectives of Science
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Preface
In the Administration building at Link¨oping University we have one of Oscar Reutersv¨ard’s “Impossible Figures” in three dimensions. I call it “Perspectives of Science”. When viewed from a specific point in space there is order and structure in the 3-dimensional figure. When viewed from other points there is disorder and no structure. If a specific scientific paradigm is used, there is order and structure; otherwise there is disorder and no structure. My perspective in Transportation Science has focused on understanding the mathematical structure and the logic underlying the choice probability models in common use. My book with N. F. Stewart on the Gravity model (Erlander and Stewart 1990), was written in this perspective. The present book stems from the same desire to understand underlying assumptions and structure. It investigates how far a new way of defining Cost-Minimizing Behavior can take us. It turns out that all commonly used choice probability distributions of logit type – log linear probability functions – follow from cost-minimizing behavior defined in the new way. In addition some new nested models appear. The new way of defining cost-minimizing behavior is the following: Cost-minimizing behavior obtains if the likelihood (probability) of any independent N-sample of observations
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