Norman Schofield

Activists and Partisan Realignment in the United States

In this paper, we contend that party realignments occur due to the interaction of candidates and activists. We examine independent party candidates who are motivated primarily to win elections but who use activist contributions to increase vote shares. In a two-dimensional policy space, such candidates will on occasion engage in “flanking” moves so as to enlist coalitions of disaffected voters, at the risk of alienating some of their traditional activist supporters. We argue that a result of such “flanking” moves, in the early part of the century, has been a shift in emphasis from an underlying social dimension to the economic dimension. In recent decades, electoral salience has shifted back to the social dimension. The net result is that the party cleavage line is much as it was a century ago—but the parties have switched sides.

Generic Instability of Majority Rule

Majority rule voting with smooth preferences on a smooth policy space W is examined. It is shown that there is an integer w(n), which is 2 when the size of the society n is odd and 3 when n is even such that when the dimension of W is at least w(n) then, for almost preference profiles on W, the core of the voting game is empty when the dimension of W exceeds w(n) then for almost all preference profiles on W, there exist dense preference cycles in W. Moreover in dimension w(n) + 1 the policy space can be partitioned into a finite number of path connected components, such that any two points in one of the components can be connected by a majority voting trajectory. In dimension greater than w(n) + 1 there exists only one such component.

Valence Competition in the Spatial Stochastic Model

The mean voter theorem of the stochastic spatial electoral model provides no explanation as to why multi-party systems under proportional representation display such diversity. Here, we extend the spatial model to include valence. Valence may be either a stochastic variable describing the variation in popularity for each candidate in the electorate or, alternatively, it will be generated by activist coalitions responding to the willingness of the candidate to pursue the interests of the coalition. In a general model of multiple candidates (or political agents), the first- and second-order conditions for pure strategy Nash equilibria are developed. It is shown that rational candidates will balance the gradient of electoral pull against the gradients generated by contending activist coalitions. The resulting Nash equilibria will almost never be at the mean of the voter distribution.

Multiparty electoral competition in the Netherlands and Germany: A model based on multinomial probit

A typical assumption of electoral models of party competition is that parties adopt policy positions so as to maximize expected vote share. Here we use Euro-barometer survey data and European elite-study data from 1979 for the Netherlands and Germany to construct a stochastic model of voter response, based on multinomial probit estimation. For each of these countries, we estimate a pure spatial electoral voting model and a joint spatial model. The latter model also includes individual voter and demographic characteristics. The pure spatial models for the two countries quite accurately described the electoral response as a stochastic function of party positions. We use these models to perform a thought experiment so as to estimate the expected vote maximizing party positions. We go on to propose a model of internal party decision-making based both on pre-election electoral estimation and post-election coalition bargaining. This model suggests why the various parties in the period in question did not adopt vote maximizing positions. We argue that maximizing expected vote will not, in general, be a rational party strategy in multiparty political systems which are based on proportional representation.

Bargaining Theory and Portfolio Payoffs in European Coalition Governments 1945–83

Coalition formation has been the subject of much theoretical work in the past decade or so. The theories that have been way or another, upon assumptions about the ways in accruing to a particular coalition is distributed among its less empirical work has been done on the process of payoff some of the fundamental assumptions of coalition theories, at their practical application to coalition governments, have tested. Several theories of payoff distribution have been however. It is the purpose of this article to test the application theories to the practice of coalition government in Europe. We begin by looking in more detail at the role of payoff theories formation. We then review both the theoretical and coalition payoffs, especially those payoffs denominated in posts. This sets the scene for a comparative testing of three proportional payoffs, the bargaining set and the kernel, in terms of each theory to predict portfolio payoffs in twelve post-systems. This study is conducted both on a general and a basis, since past analyses have demonstrated that differences are at least as significant as those between theories.

Structural Instability of the Core

Let σ be a q-rule, where any coalition of size q, from the society of size n, is decisive. Let w(n,q)= 2q-n+1 and let W be a smooth ‘policy space’ of dimension w. Let U(W)N be the space of all smooth profiles on W, endowed with the Whitney topology. It is shown that there exists an ‘instability dimension’ w∗(σ) with 2≦w∗(σ)≦w(n,q) such that: 1. (i) if w≧w∗(σ), and W has no boundary, then the core of σ is empty for a dense set of profiles in U(W)N (i.e., almost always), 2. (ii) if w≧w∗(σ)+1, and W has a boundary, then the core of σ is empty, almost always, 3. (iii) if w≧w∗(σ)+1 then the cycle set is dense in W, almost always, 4. (iv) if w≧w∗(σ)+2 then the cycle set is also path connected, almost always. The method of proof is first of all to show that if a point belongs to the core, then certain generalized symmetry conditions in terms of ‘pivotal’ coalitions of size 2q−n must be satisfied. Secondly, it is shown that these symmetry conditions can almost never be satisfied when either W has empty boundary and is of dimension w(n,q) or when W has non-empty boundary and is of dimension w(n,q)+1.

EQUILIBRIUM IN THE SPATIAL 'VALENCE' MODEL OF POLITICS

It has been a standard result of the stochastic, or probabilistic, spatial model of voting that vote maximizing candidates, or parties, will converge to the electoral mean (the origin). This conclusion has appeared to be contradicted by empirical studies. Here, a more general stochastic model, incorporating ‘exogeneous’ valence, is constructed. Contrary to the standard result, it is shown in Theorem 1 of this paper that a potentially severe domain constraint (determined by the electoral and stochastic variance, valence as well as the dimension of the space) is necessary for the existence of equilibrium at the electoral mean. A more stringent condition, independent of the dimension of the space, is shown to be sufficient. An empirical study of Israel for 1992 shows that the necessary condition failed. This suggests that, in proportional electoral systems, a pure strategy equilibrium will almost always fail to exist at the electoral mean. Instead, in both the formal and empirical models, each party positions itself along a major electoral axis in a way which is determined by the valence terms. A second empirical analysis for Britain for the elections of 1992 and 1997 shows that, in fact, the necessary and sufficient condition for the validity of the ‘mean voter theorem’ was satisfied, under the assumption of unidimensionality of the policy space. Indeed the low valence party, the Liberal Democrat Party, did appear to locate at the electoral center. However, the high valence parties, Labour and the Conservatives, did not. This suggests that, in polities based on plurality rule, valence is a function of activist support rather than a purely exogenous factor. Theorem 2 shows, as in Britain, that exogeneous and activist valence produce opposite effects.

Political Economy: Institutions, Competition and Representation

The contents of this volume are drawn from the seventh International Symposium in Economic Theory and Econometrics, and represent recent advances in the development of concepts and methods in political economy. Contributors include leading practitioners working on formal, applied, and historical approaches to the subject. The collection will interest scholars in the fields of political science and political sociology no less than economics. Part I outlines relevant concepts in political economy, including implementation, community, ideology, and institutions. Part II covers theory and applications of the spatial model of voting. Part III considers the different characteristics that govern the behaviour of institutions, while Part IV analyses competition between political representatives. Part V is concerned with the way in which government acquires information held by voters or advisors, and Part VI addresses government choice on monetary policy and taxation.

Social equilibrium and cycles on compact sets

One proof of existence of general equilibrium assumes convexity and continuity of a preference correspondence on a compact convex feasible set W. Here the existence of a local equilibrium for a preference field which satisfies, not convexity, but the weaker local acyclicity is shown. The theorem is then applied to a voting game, σ, without veto players. It is shown that if the dimension of the policy space is no greater than ν(σ) − 2, where ν(σ) is the Nakamura number of the game, then no local cycles may occur and a local equilibrium must exist. With convex preferences, then, there will exist a choice of the game from W.

The Transformation of the Republican and Democratic Party Coalitions in the U.S.

Because the space of policies is two-dimensional, parties in the United States are coalitions of opposed interests. The Republican Party contains both socially conservative and socially liberal groups, though both tend to be pro-business. The increasing dominance of the social conservatives has angered some prominent Republicans, even causing a number of them to change party allegiance. Over time, the decreasing significance of the economic axis may cause the Republican Party to adopt policies that are analogous to those proposed by William Jennings Bryan in 1896: populist and anti-business. In parallel, the Democratic Party will increasingly appeal to pro-business, social liberals, so the party takes on the mantel of Lincoln.