Norman Schofield

Originally published in 1984. Since the logic underlying economic theory can only be grasped fully by a thorough understanding of the mathematics, this book will be invaluable to economists wishing to understand vast areas of important research. It provides a basic introduction to the fundamental mathematical ideas of topology and calculus, and uses these to present modern singularity theory and recent results on the generic existence of isolated price equilibria in exchange economies.

Originally published in 1984. Since the logic underlying economic theory can only be grasped fully by a thorough understanding of the mathematics, this book will be invaluable to economists wishing to understand vast areas of important research. It provides a basic introduction to the fundamental mathematical ideas of topology and calculus, and uses these to present modern singularity theory and recent results on the generic existence of isolated price equilibria in exchange economies.

In recent years, the usual optimization techniques, which have proved so useful in microeconomic theory, have been extended to incorporate more powerful topological and differential methods, and these methods have led to new results on the qualitative behavior of general economic and political systems. These developments have necessarily resulted in an increase in the degree of formalism in the publications in the academic journals. This formalism can often deter graduate students. The progression of ideas presented in this book will familiarize the student with the geometric concepts underlying these topological methods, and, as a result, make mathematical economics, general equilibrium theory, and social choice theory more accessible.

Combining elements of economic reasoning and political science has proven to be very useful for understanding the broad variation in economic development around the world. In a sense research in this field goes back to the Scottish Enlightenment and Adam Smith’s original plan in his Theory of Moral Sentiments and Wealth of Nations. Leadership or Chaos by Norman Schofield and Maria Gallego is intended as an advanced, self-contained text in political economy dealing with social choice. The theory and empirical analysis are used to examine democratic institutions and elections in the developed world, and the success or failure of moves to democratization in the less developed world. The book closes with a consideration of current quandaries with regard to political and economic stability and climate change and a discussion of the moral foundations of our society.

In recent years, the usual optimization techniques, which have proved so useful in microeconomic theory, have been extended to incorporate more powerful topological and differential methods, and these methods have led to new results on the qualitative behavior of general economic and political systems. These developments have necessarily resulted in an increase in the degree of formalism in the publications in the academic journals. This formalism can often deter graduate students. The progression of ideas presented in this book will familiarize the student with the geometric concepts underlying these topological methods, and, as a result, make mathematical economics, general equilibrium theory, and social choice theory more accessible.

The mathematical theory of voting has intellectual roots extending back two centuries to the writings of Borda and Condorcet. Yet it has only been in the last forty years that general theorems have begun to emerge. With the publication of this volume, Norman Schofield brings the results together in a ,common framework. SOCIAL CHOICE AND DEMOCRACY, however, is not merely a synthetic exercise, for Schofield's own work over the last decade has constituted a major initiative in deepening and' broadening our general understanding of voting arrangements. At last the results of his research, bits and pieces of which have been reported in a number of journals of international standing and in various collections, are coherently and systematically presented as an entirety. For students of democracy -- chiefly philosophers and political scientists, but increasingly economists as well -- the insights of this volume are profound. From it I infer the following.

Combining elements of economic reasoning and political science has proven to be very useful for understanding the broad variation in economic development around the world. In a sense research in this field goes back to the Scottish Enlightenment and Adam Smith’s original plan in his Theory of Moral Sentiments and Wealth of Nations. Leadership or Chaos by Norman Schofield and Maria Gallego is intended as an advanced, self-contained text in political economy dealing with social choice. The theory and empirical analysis are used to examine democratic institutions and elections in the developed world, and the success or failure of moves to democratization in the less developed world. The book closes with a consideration of current quandaries with regard to political and economic stability and climate change and a discussion of the moral foundations of our society.

Using unique and cutting-edge research, Schofield a prominent author in the US for a number of years, explores the growth area of positive political economy within economics and politics. The first book to explain the spatial model of voting from a mathematical, economics and game-theory perspective it is essential reading for all those studying positive political economy.

One theme that has emerged from the recent literature on political economy concerns the transition to democracy: why would dominant elites give up oligarchic power? This book addresses the fundamental question of democratic stability and the collapse of tyranny by considering a formal model of democracy and tyranny. The formal model is used to study elections in developed polities such as the United States, the United Kingdom, the Netherlands, Canada, and Israel, as well as complex developing polities such as Turkey. The key idea is that activist groups may offer resources to political candidates if they in turn adjust their polities in favor of the interest group. In polities that use a "first past the post" electoral system, such as the US, the bargaining between interest groups and candidates creates a tendency for activist groups to coalesce; in polities such as Israel and the Netherlands, where the electoral system is very proportional, there may be little tendency for activist coalescence. A further feature of the model is that candidates, or political leaders, like Barack Obama, with high intrinsic charisma, or valence, will be attracted to the electoral center, while less charismatic leaders will move to the electoral periphery. This aspect of the model is used to compare the position taking and exercise of power of authoritarian leaders in Portugal, Argentina and the Soviet Union. The final chapter of the book suggests that the chaos that may be induced by climate change and rapid population growth can only be addressed by concerted action directed by a charismatic leader of the Atlantic democracies.

Using unique and cutting-edge research, Schofield a prominent author in the US for a number of years, explores the growth area of positive political economy within economics and politics. The first book to explain the spatial model of voting from a mathematical, economics and game-theory perspective it is essential reading for all those studying positive political economy.

This book adapts a formal model of elections and legislative politics to study party politics in Israel, Italy, the Netherlands, Britain, and the United States. The approach uses the idea of valence, that is, the party leader's non-policy electoral popularity, and employs survey data to model these elections. The analysis explains why small parties in Israel and Italy keep to the electoral periphery. In the Netherlands, Britain, and the US, the electoral model is extended to include the behavior of activists. In the case of Britain, it is shown that there will be contests between activists for the two main parties over who controls policy. For the recent 2005 election, it is argued that the losses of the Labour party were due to Blair's falling valence. For the US, the model gives an account of the rotation of the locations of the two major parties over the last century.

This book adapts a formal model of elections and legislative politics to study party politics in Israel, Italy, the Netherlands, Britain, and the United States. The approach uses the idea of valence, that is, the party leader's non-policy electoral popularity, and employs survey data to model these elections. The analysis explains why small parties in Israel and Italy keep to the electoral periphery. In the Netherlands, Britain, and the US, the electoral model is extended to include the behavior of activists. In the case of Britain, it is shown that there will be contests between activists for the two main parties over who controls policy. For the recent 2005 election, it is argued that the losses of the Labour party were due to Blair's falling valence. For the US, the model gives an account of the rotation of the locations of the two major parties over the last century.

This work offers a set of extended interpretations of Madison's argument in Federalist X of 1787, using ideas from social choice theory and from the work of Douglass North, Mancur Olson, and William Riker. Its focus is not on rational choice theory itself, but on the use of this theory as a heuristic device to better understand democratic institutions. The treatment adapts a formal model of elections to consider rapid constitutional change at periods when societies face quandaries. The topics explored in the book include Britain's reorganization of its fiscal system in the eighteenth century to prosecute its wars with France; the Colonies' decision to declare independence in 1776; Madison's argument about the 'probability of fit choice' during the Ratification period of 1787-88; the argument between Hamilton and Jefferson in 1798–1800 over the long run organization of the US economy and the election of Lincoln in 1860.

This work offers a set of extended interpretations of Madison's argument in Federalist X of 1787, using ideas from social choice theory and from the work of Douglass North, Mancur Olson, and William Riker. Its focus is not on rational choice theory itself, but on the use of this theory as a heuristic device to better understand democratic institutions. The treatment adapts a formal model of elections to consider rapid constitutional change at periods when societies face quandaries. The topics explored in the book include Britain's reorganization of its fiscal system in the eighteenth century to prosecute its wars with France; the Colonies' decision to declare independence in 1776; Madison's argument about the 'probability of fit choice' during the Ratification period of 1787-88; the argument between Hamilton and Jefferson in 1798–1800 over the long run organization of the US economy and the election of Lincoln in 1860.

In recent years, the usual optimization techniques, which have proved so useful in microeconomic theory, have been extended to incorporate more powerful topological and differential methods, and these methods have led to new results on the qualitative behavior of general economic and political systems. These developments have necessarily resulted in an increase in the degree of formalism in the publications in the academic journals. This formalism can often deter graduate students. The progression of ideas presented in this book will familiarize the student with the geometric concepts underlying these topological methods, and, as a result, make mathematical economics, general equilibrium theory, and social choice theory more accessible.

The politics of coalition--the very heart of the political process in most European countries--can be analyzed either theoretically or empirically. Multiparty Government reconciles these approaches. It gives students of European politics access to the insights of contemporary theory while applying it to an analysis of real-world coalition politics.Michael Laver and Norman Schofield examine five basic themes: the identity and motivation of the actors in the coalition game; the eventual membership of the coalitions they form; their durability; the payoffs that are shared out by coalition members; and the impact of constitutional bargaining, behavioral, and historical constraints on the process of coalition bargaining. They illustrate their discussion of theory with a range of detailed case studies.Multiparty Government offers an accessible approach that bridges the gap between the "European politics" and "game theory" traditions of political science, and puts the systematic study of the politics of coalition on the broader political science map."Laver and Schofield's book is at the same time accessible, pithy, down-to-earth, insightful, and yes, even captivating. In its scope and quality, it has no rival in the literature of party coalitions . . . all students of political parties or legislative behavior should allow themselves the privilege of being educated and entertained by Laver and Schofield's fine book." --American Political Science ReviewMichael Laver is Professor of Political Science and Sociology, University College, Galway. His books include Playing Politics; Private Desires, Political Action: An Invitation to the Politics of Rational Choice; The Crime Game; and Social Choice and Public Policy. Norman Schofield is Professor and Director, Center in Political Economy, Washington University. He is the author of Statistics: Theory & Practice in the Social Sciences; Mathematical Methods in Economics; and Social Choice and Democracy.