The Spatial Model of Politics

Norman Schofield

• Publisher: Taylor & Francis
• Year: 2007
• Print ISBN: 9780415569408
• eBook ISBN: 9781134357383
• Edition: 1
• Topic: Business
• Subtopic: Business General
• Index: Business

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.

Chapter 1
Introduction

1.1 Representative Democracy

A fundamental question that may be asked about a political, economic or social system is whether it is responsive to the wishes or opinions of the members of the society and, if so, whether it can aggregate the conflicting notions of these individuals in a way which is somehow rational. More particularly, is it the case, for the kind of configuration of preferences that one might expect, that the underlying decision process gives rise to a set of outcomes which is natural and stable, and more importantly, “small” with respect to the set of all possible outcomes? If so, then it may be possible to develop a theoretical or “causal” account of the relationship between the nature of the decision process, along with the pattern of preferences, and the behavior of the social and political system. For example, microeconomic theory is concerned with the analysis of a method of preference aggregation through the market. Under certain conditions this results in a particular distribution of prices for commodities and labor, and thus income. The motivation for this endeavor is to match the ability of some disciplines in natural science to develop causal models, tying initial conditions of the physical system to a small set of predicted outcomes. The theory of democracy is to a large extent based on the assumption that the initial conditions of the political system are causally related to the essential properties of the system. That is to say it is assumed that the interaction of cross-cutting interest groups in a democracy leads to an “equilibrium” outcome that is natural in the sense of balancing the divergent interests of the members of the society. One aspect of course of this theoretical assumption is that it provides a method of legitimating the consequences of political decision making.

The present work directs attention to those conditions under which this assumption may be regarded as reasonable. For the purposes of analysis it is assumed that individuals may be represented in a formal fashion by preferences which are “rational” in some sense. The political system in turn is represented by a social choice mechanism, such as, for example, a voting rule. The purpose is to determine whether such a formal political system is likely to exhibit an equilibrium. It turns out that a stable social equilibrium in a pure (or direct) democracy is a rare phenomenon. This seems to suggest that if the political system is in fact in equilibrium, then it is due to the nature of the method of representation.

As Madison argued in Federalist X,

[I]t may be concluded that a pure democracy…can admit of no cure for the mischiefs of faction…. Hence it is that such democracies have ever been spectacles of turbulence and contention; have ever been found incompatible with personal security…and have in general been as short in their lives, as they have been violent in their deaths

A republic, by which I mean a government in which the scheme of representation takes place, opens a different prospect… [I]f the proportion of fit characters be not less in the large than in the small republic, the former will present a greater option, and consequently a greater probability of a fit choice.¹

Social choice is a theory of direct or pure democracy which seeks to understand the connection between individual preferences, institutional rules and outcomes. The theory suggests that Madison’s intuition was largely correct. In any direct democracy, if there is no great concentration of power, in the form of an oligarchy or dictator, then decision making can be incoherent. Madison, in Federalist LXII, commented on the “mischievous effects of mutable government”:

It will be of little avail to the people that the laws are made by men of their own choice, if laws be so…incoherent that they cannot be understood; if they be repealed or revised before they are promulgated, or undergo such incessant changes that no man who knows what the law is today can guess what it will be tomorrow²

The opposite of chaos is equilibrium, or rationality, what Madison called “stability in government” in Federalist XXXVII::

Stability in government, is essential to national character, and to …that repose and confidence in the minds of the people… An irregular and mutable legislation is not more an evil in itself, than it is odious to the people[.]³

This volume may be regarded as a contribution to the development of Madison’s intuition. Chapters 2 to 5 present a self-contained exposition of social choice theory on the possibility of aggregating individual preferences into a social preference in a direct democracy. Chapter 6 considers legislative bargaining in polities based on proportional representation, while Chapters 7 to 9 present a theory of elections-the selection of the representatives in an indirect democracy, what Madison called a republic. A brief concluding Chapter 10 attempts to relate social choice theory, the models of election and Madison’s theory of the Republic in terms of the aggregation of preferences and beliefs.

In a sense, Chapter 6 combines elements of social choice theory with the theory of elections that is to follow in the later chapters. It applies the theoretical notions developed in the early chapters to examine bargaining in a legislature. In particular, it assumes that the representatives have policy preferences, induced from the preferences of their constituents and the activists for the various parties. The party leaders must bargain among themselves in order to form a governing coalition, in the situation most common under proportional representation, that the election has led to a number of parties, none of which commands a majority.

Social choice theory suggests that there are two fundamentally different bargaining situations in such a multiparty legislature. The first is where there is a large, centrally located party in the policy space. Such a party is located at what is known as the “core.” No combination of other parties can agree to overturn the position of this “core” party. Consequently the “core” party can, if it so chooses, form a minority government, one without a majority of the seats in the legislature. This property of the core provides an explanation for what has appeared to be a puzzle. The data set collected by Laver and Schofield (1990) dealing with coalition governments in 12 European countries in the period 1945–1987 shows that about one-third of the governments were minority. About one-third were minimal winning, with just enough seats for a majority, and the remaining third were surplus, with parties included in the coalition unnecessary for the majority. In the absence of a core, the spatial theory suggests that bargaining between the parties will focus on a domain in the policy space known as the “heart.” In the simplest case where it is assumed that parties have “Euclidean” preferences determined by policy distance, the “hear...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• 1 Introduction
• 2 Social Choice
• 3 Voting Rules
• 4 The Core
• 5 The Heart
• 6 A Spatial Model of Coalition
• 7 A Spatial Model of Elections
• 8 Activist Coalitions
• 9 Coalitions in the United States
• 10 Final Remarks