The Art of Decision-Making

The Art of Decision-Making

Morton Davis The Art of Decision-Making With 20 Illustrations Springer Science+Business Media, LLC

Monon Davis Department of Mathematics CUNY. City College N\!w York. New York 10031 U.5.A. AMS Classification: 00 01. OO A06 Library of Congress Cataloging in Publication Data Davis. Morton D.. 1930- The art of decision-making. Bibliography: p. Includes index. 1. Decision-making. I. Title. HD30.1.3.D372 1985 658.4'03 85-25118 o 1986 Springer Science+Busincss Media New York Origina!1y published by Springer-Vcrlag New York in 1986 Softcover reprint of the hardcover 1st edition 1986 All rights reserved. No pan of this book may be translated or reproduced in any form without written permission from Springer-Science+Business Media, LLC 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 frecly by anyone. Typeset by Asco Trade Typesetting Lld., Hong Kong. 9 8 7 6 5 4 3 2 I ISBN 978-1-4612-7004-1 ISBN 978-1-4612-1074-0 (ebook) DOI 10.1007/978-1-4612-1074-0

Contents Introduction Vll The Bottom Line: Decisions in Business and Economics Practical Problem-Solving 31 Game Theory: The Art of Making Joint Decisions 45 Decision-Making in the Boardroom: Problems of Voting 66 A Mixture of Wit and Whimsy 82

Introduction Suppose you had the chance to invest in a venture that succeeds half the time. When you fail you lose your investment; when you succeed you make a profit of $1.60 for every $1.00 you invest. The odds are 8 to 5 in your favor and you should do well-casinos and insurance companies thrive under less favorable conditions. If you can invest as much as you like, as often as you like, using a betting system that guarantees you can't go broke, common sense suggests you will almost certainly make a profit after you make a large number of investments. In response to your request for a hot stock your astrologer tells you ABC Inc. will triple in a year (she's really a fraud and picked the stock at random). But since such stocks are rare (one in a thousand) you consultan expert and, strangely enough, he confirms the astrologer. From experience you know that the expert diagnoses all stocks, good and bad, correctly, 90% of the time. Common sense suggests you have an excellent chance of tripling your money. You are chairman of a committee ofthree. Decisions are made by majority rule but if there is no majority your vote as chairman breaks ties. Common sense suggests you will inevitably have more power to determine the outcome than the other members. In each case common sense is wrong! Common sense is an unreliable guide. Toprove it, we pose a numberof"easy" questions with "obvious" answers, obvious answers that tum out to be wrong. Clearly something more than intuition and common sense is needed to be an effective problem-solver. This book is divided into five sections. The first section

Vlll Introduction contains general business problems while the second section emphasizes a few specific problem-solving techniques. The third section introduces game theory: the art of decisionmaking in a competitive environment. The fourth sectiondecision-making in the boardroom-deals with voting problems and paradoxes, and the fifth section is a potpourri of problems in logic and probability. The subject matter varies from section to section but there is a common themeunaided intuition often goes astray. Our purpose is to spot potential pitfalls and avoid them, and you can acquire this skill in more than one way. One approach is to master specific techniques such as linear programming, mixed strategies, or Bayes' theorom (or at least learn they exist and where to find them). But you can also take a more relaxed view and consider these questions as a diversion and a test of your insight. By repeatedly observing how and where your intuition falls short in a variety of situations, you stretch your imagination painlessly. The flexibility you gain in this last approach is probably as important as the technical proficiency you gain in the other. Most of the mathematics and notations in this book are rather informal, and require no special explanation. However, we do use the notation 43 +, for example, to denote a number greater than or equal to 43. As you work through these problems you will gain a surer hand but you will still look foolish at times; there are too many potential hazards and you can't know them all. Still, you do best to get any edge that you can, for, as Damon Runyon said, "It may be that the race is not always to the swift nor the battle to the strong but that's the way to bet." One final thought-it is generally believed that good things don't happen unless you suffera bit; here, I think, the reverse is true. You do best if you respond as a child responds to a riddle-with delight. Morton Davis