Game theory and Canadian politics

201 Pages·1998·9.15 MB·English

by  Thomas Flanagan

GAME THEORY AND CANADIAN POLITICS
This is the first book-length application of game theory to Canadian
politics. It uses a series of case studies to illustrate fundamental con-
cepts of game theory such as two-person and n-person games, the
Nash equilibrium, zero-sum and variable-sum games, the paradox of
voting, the Condorcet winner, the Condorcet extension, the Banzhaf
power index, and spatial models of competition. No mathematics more
complex than simple algebra is required to follow the exposition.
The case studies are not just contrived illustrations of abstract
models but intensively researched studies of important episodes in
Canadian politics. Topics include the Lubicon Lake land claim stale-
mate, the formation of national political coalitions, the adoption of the
metric system, nomination of party leaders, the importance of proce-
dural rules in Parliament, and the entry of the Reform Party into the
political system. In each case, utilization of game-theory models
produces new and often surprising conclusions.
Game theory, and the rational-choice paradigm of which it is a part,
are an increasingly important addition to the conventional modes of
political analysis. This book is intended to show what game theory can
add to the philosophical, institutional, and behavioural approaches
that have dominated previous works on Canadian politics.
THOMAS FLANAGAN is Professor of Political Science, University of
Calgary. He is the author of several books, including Louis 'David' Riel:
'Prophet of the New World. '
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THOMAS FLANAGAN
Game Theory
and Canadian Politics
UNIVERSITY OF TORONTO PRESS
Toronto Buffalo London
www.utppublishing.com
University of Toronto Press Incorporated 1998
Toronto Buffalo London
Printed in Canada
ISBN 0-8020-4094-2 (cloth)
ISBN 0-8020-7946-6 (paper)
Printed on acid-free paper
Canadian Cataloguing in Publication Data
Flanagan, Thomas, 1944-
Game theory and Canadian politics
Includes bibliographical references and index.
ISBN 0-8020-4094-2 (bound) ISBN 0-8020-7946-6 (pbk. )
1. Political science - Methodology. 2. Game theory.
3. Canada - Politics and government. I. Title.
JA72. 5. F531998 320. 010971 C98-931661-0
An earlier version of part of Chapter 3 appeared in Ken Coates, ed., Aboriginal
Land Claims in Canada: A Regional Perspective (Toronto: Copp Clark Pitman,
1992). Used by permission Addison Wesley Longman Publishers. An earlier
version of part of Chapter 6 appeared as 'Amending the Canadian Constitu-
tion: A Mathematical Analysis/ Constitutional Forum 7, 2-3 (1996): 97-101.
Used by permission. An earlier version of part of Chapter 8 appeared as 'The
Staying Power of the Legislative Status Quo: Collective Choice in Canada's
Parliament after Morgentaler, ' Canadian Journal of Political Science 30, 1 (March
1997): 31-53. Used by permission.
University of Toronto Press acknowledges the financial assistance to its
publishing program of the Canada Council for the Arts and the Ontario Arts
Council.
Contents
PREFACE Vll
1 Rational Choice 3
2 Game Theory 20
3 Stalemate at Lubicon Lake 37
4 Models of Metrication 55
5 How Many Are Too Many? The Size of Coalitions 74
6 Who's Got the Power? Amending the Canadian Constitution 93
7 The 'Right Stuff: Choosing a Party Leader 105
8 The Staying Power of the Status Quo 120
9 Invasion from the Right: The Reform Party in the 1993 Election 140
10 What Have We Learned? 164
NOTES 173
INDEX 187
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Preface
The invention and elaboration of game theory is one of the great intel-
lectual achievements of the second half of the twentieth century. Al-
though there was some crucial earlier work, the founding event was the
publication in 1944 of The Theory of Games and Economic Behavior, by
John von Neumann and Oskar Morgenstern.1 Von Neumann was one
of the mathematical giants of our century, for whom game theory was
an intellectual diversion; Morgenstern was an economist with an inter-
est in mathematics.
The half century following their original book saw a profusion of
literature on game theory, particularly in mathematics and economics,
but increasingly also in other disciplines, such as political science, psy-
chology, sociology, and biology. The maturity of game theory was rec-
ognized in 1994 by the award of the Nobel prize in economics to three
eminent scholars in the field. In fact, the award would have come years
earlier except that one of the three, John Nash, whose creative contribu-
tions came in the early 1950s, fell prey to schizophrenia late in that
decade and did not recover until the mid-1980s. An award that did not
include Nash was unthinkable, and the Nobel committee did not want
to make the award until they were certain that Nash was in a proper
state to receive it. 2
Economists played a pioneering role in applying game theory to the
traditional concerns of political science. The first game theory article in
a political science journal, published in the American Political Science
Review in 1954, was co-authored by a mathematician and an economist.3
William Riker, already a well-known authority on American govern-
ment, read that article and became the first political scientist to promote
game theory within the discipline.4 For 40 years thereafter, Riker, his
viii Preface
students, and an ever-growing number of colleagues have worked to
bring game theory into political science.
A simple statistic illustrates their success. In 1995, the American Politi-
cal Science Review (APSR), generally considered the discipline's most
prestigious journal, published 50 articles. Of those 50, 16, or 32 per cent,
were based wholly or partially on game theory.5 Of course, this statistic
from one journal does not describe the discipline as a whole; the per-
centage of game-theory articles would undoubtedly be lower in most
journals, in the United States as well as in other countries. But to the
extent that the APSR publishes trend-setting articles, it shows the direc-
tion in which the discipline may be moving.
In Canada, however, the influence of game theory has not been nearly
as great. The 1995 issues of the Canadian Journal of Political Science con-
tained 22 articles, of which only one (4. 5 per cent) had any connection
to game theory, and that was rather remote. We are still in the very
early stages of the application of game theory to the study of Canadian
politics.
This book is written in full awareness of being virtually at the begin-
ning. Many books on game theory claim to be simple or nontechnical,
requiring only a clear mind and high-school algebra; yet I know from
reading such books and trying to teach them to intelligent students that
their promise of simplicity is seldom fulfilled. 6 This book, in contrast to
existing works, is meant to be understood by political scientists and
political science students who have no special gift for mathematics. It
could be assigned as supplementary reading in a course in Canadian
politics or as one of the texts in an elementary course in game theory. I
don't claim that it will teach game theory in a systematic way, but I
believe it will impart some of the flavour and show what game theory
can do. If it inspires some students to go further, it will have achieved
its purpose.
I hope that Game Theory and Canadian Politics will be read not only by
students taking courses but also by others with a serious interest in
Canadian politics, for the case studies assembled here present interest-
ing and nonobvious results. These case studies are not just potted illus-
trations of how to apply techniques; they incorporate considerable re-
search and are meant to convey new knowledge. The use of game-
theory models provides a framework for insights that might arise from
intuition but that, without such a framework, would remain scattered
and fragmented rather than becoming part of a systematic body of
knowledge.
Preface ix
Chapters 1 and 2 present the basic ideas of rational choice and game
theory. Chapter 3 develops a two-person ordinal game in which the
Nash equilibrium is the appropriate solution concept. Chapter 4 uses
Schelling curves to make two-person models applicable to society at
large. Then come five chapters dealing with topics in n-person game
theory. Chapter 5 discusses coalition theory, including William Riker's
size principle. Chapter 6 presents the Banzhaf power index as a way of
measuring power in minimum winning coalitions. Chapters 7 and 8
both deal with the phenomenon of cycles in n-person voting games.
And chapter 9 uses spatial models as a way of representing games with
continuous choices. Finally, Chapter 10 reviews the findings of the case
studies to show how they complement the philosophical, institutional,
and behavioural approaches that dominate the contemporary study of
Canadian politics.
The case studies are admittedly eclectic: the Lubicon Lake land claim
stalemate; adoption of the metric system; national political coalitions;
the distribution of power under various constitutional amending for-
mulas; the nomination of party leaders; the importance of procedural
rules in Parliament; and the Reform Party's political breakthrough in
the 1993 election. The topics were chosen because each one lends itself
to analysis through a different game-theory model. Taken together, they
illustrate some of the most important concepts of elementary game
theory: zero-sum and variable-sum games, the Nash equilibrium, two-
person and n-person games, cooperative and noncooperative games,
the Banzhaf Power Index, the paradox of voting, the Condorcet winner,
the Condorcet extension, and spatial models of competition. Anyone
who works through the variety of illustrations will start to gain some
appreciation of what game theory can (and cannot) do for the study of
Canadian politics.
I would like to thank Dan Liebman for his careful copy-editing, espe-
cially for his painstaking work on the many tables and figures in the
manuscript. I am also grateful for various contributions from other staff
members of the University of Toronto Press; their professionalism con-
tinues to uphold the Press's reputation as the leading academic pub-
lisher in Canada.