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JAMES ADAMS [*]
The spatial maps of parties' policy programmes published by the Manifesto Research Group (MRG) for the European Consortium for Political Research reveal the following empirical patterns: that parties differentiate their policy positions from one another; that parties rarely leapfrog each other; that parties shift their positions over time but only within 'ideologically delimited' areas of the policy space. These findings are not well explained by existing spatial models of party competition, which typically predict policy convergence and which moreover do not examine temporal patterns of party policies. This article modifies the standard Downsian model to incorporate a concept originally developed by Chapman that, in addition to policies, voters are motivated by non-policy considerations arising from such factors as party leaders' images, social-psychological attachments rooted in class, religion, ethnicity and so on. For this 'biased vote' model I present illustrative arguments that vote-seeking parties are motivated to differentiate their policy positions from each other, and that over time they can be expected to vary their policy proposals but without leapfrogging -- predictions that accord well with the MRG's empirical findings. I apply the biased vote model to empirical data on the distributions of voter preferences in recent British and French elections. My results support the illustrative arguments, and also suggest that these arguments apply even when the degree of voter bias in the electorate is quite low.
The study of party policy platforms has been the focus of two very different research traditions. One approach, tracing back to Anthony Downs and before, is spatial modelling. Spatial modellers typically assume that parties compete for votes from an issue-oriented electorate, and attempt to deduce the policies that vote- or office-seeking parties will present in order to win elections. The second approach, epitomized by the work of the Manifesto Research Group of the European Consortium for Political Research, involves empirical examinations of party platforms, with the goal of estimating the parties' policy positions.  These two research traditions have evolved largely independently of each other.
From their rational choice perspective, spatial modellers typically assume that parties maximize votes, or, in multiparty systems, that they maximize their chances of obtaining membership in the governing coalition.  The general quest is for a policy equilibrium during a single election period -- i.e., a set of party platforms such that no party can improve its position by changing its policies, given the policies of its rivals.
Participants in the Manifesto Research Group (MRG), by contrast, are concerned with determining the content of parties' policy proposals, as well as how these policies evolve over time. Specifically, through comparative coding of parties' election programmes the MRG assigns positions to parties along a variety of policy dimensions. To date, this coding procedure has been applied to over 1,000 programmes, in about twenty democracies, during the post-war period.
The spatial maps of parties' policy movements published by the MRG reveal empirical patterns that spatial modellers, with their focus on party equilibrium during single election periods, rarely attempt to explain. Notably, the MRG's longitudinal analyses show that parties vary their policies in successive elections. However, these policy shifts are accompanied by two empirical regularities: first, parties typically vary their policies only within 'ideologically delimited' areas of the policy space, so that Communist, Socialist and Labour parties virtually always present left-wing positions, while Christian Democratic and Conservative parties typically locate on the right. Secondly, parties rarely leapfrog each other, and the rare instances of leapfrogging usually involve parties that are contiguous along the left-right dimension. In addition, the MRG's findings confirm the empirical observation that parties differentiate their policies from each other, so that most party systems present voters with a wide ra nge of party ideologies.
The MRG's results suggest a new puzzle for spatial modellers: rather than focusing on policy equilibria for a single election, how can we best explain the temporal patterns of parties' policies, i.e., that parties vary their policies in successive elections, yet rarely leapfrog and remain within ideologically delimited areas of the policy space? Such a model, moreover, should also explain why parties differentiate their policies from each other.
In an earlier article, Ian Budge examined several competing explanations for the MRG's results, which stressed the role of uncertainty in party decision making.  In this article I take a different approach, which combines spatial modelling with insights from behavioural research concerning the influences of non-policy factors upon the vote. Specifically, I develop a 'biased voting model' of spatial competition, which borrows from earlier game-theoretic work by Chapman, in an attempt to account for the empirical results reported by the MRG.  As in the usual Downsian model, parties have full information and can move freely about the policy space. However, I modify the standard Downsian voting model by incorporating two assumptions supported by extensive behavioural research. First, that in addition to policy concerns voters have non-policy-related motivations -- which I label biases -- which predispose them to support certain parties. These biases, which may originate in early socialization experiences, in group loyalties rooted in class, religion and party identification, or in comparisons of the competing party leaders' competence or integrity, can motivate voters to support a party even when a rival party is more attractive on policy grounds. Secondly, I posit that voters' biases correlate with their policy beliefs, so that for instance working-class voters tend to take positions on the left of the policy continuum and middle-class voters on the right. Using these assumptions I develop four arguments concerning party policy competition: three theoretical and one empirical.
First, I argue that parties have electoral incentives to differentiate their policy positions from each other. This argument, which illuminates the MRG's empirical finding that parties differ over policies, arises because a party can typically attract electoral support from rival parties' supporters only by differentiating its policies from the policies of these rivals.
Secondly, with respect to temporal aspects of party policies, I argue that although my model grants parties costless spatial mobility, they usually lose votes if they leapfrog each other. This is because leapfrogging parties are typically forced to present policies considerably more extreme than the policies of the parties they leapfrog -- due to the pressure for policy differentiation described above -- and such extreme positions are likely to prove electorally unattractive.
Thirdly, I argue that when voters are biased, then in general no multiparty policy equilibrium exists. This is because, while voter biases motivate some parties to differentiate their policies, these biases motivate other parties to blur the distinctions between their own policies and those of their rivals. This tension between rival parties' conflicting objectives typically precludes a policy equilibrium. The non-existence of equilibrium sheds light on the MRG's finding that parties vary their policies over time.
Fourthly, on the empirical side, I use survey data on voters' biases and policy preferences in recent British and French elections to investigate the impact of bias on parties' policy strategies. I show that even quite modest degrees of bias dramatically affect party positioning. Most importantly, for realistic model parameters I find that the patterns of policy competition that vote-seeking parties pursue under the biased voting model strongly resemble the empirical patterns identified by the MRG, and, furthermore, that alternative models of party competition which ignore voter bias cannot similarly account for the MRG's findings.
My approach differs from most spatial models in that I do not rely on formal proofs, but instead develop illustrative arguments concerning party strategies. This is because, as I show below, one can construct counterexamples to these arguments, and hence it is not possible to develop general theorems to support my results. This is an important limitation. However, I give reasons why my illustrative arguments are likely to hold given the actual configurations of voter policy preferences (and biases) observed in real-world electorates, a claim that I support with empirical applications to Britain and France. These show that my illustrative arguments apply to the voter distributions that were actually observed in each country and also to virtually all alternative voter distributions that appeared plausible, given the distributions that were actually observed.
I begin by reviewing the MRG's empirical findings on party policies. A biased voting model is then presented that combines policy voting with the non-policy motivations that behavioural researchers find important. Next I explore parties' policy strategies for this model, and present illustrative arguments that parties should differentiate their policies and avoid leapfrogging, but that parties are motivated to change their policies overtime. The next section presents empirical applications to British politics, which demonstrate a surprising degree of fit between the model's theoretical predictions and the MRG's empirical findings, and this approach is extended to France. Finally, the wider implications of the biased voting model are discussed.
PATTERNS OF POLICY COMPETITION IN POST-WAR DEMOCRACIES
The analysis of parties' election programmes carried out by the MRG represents the most ambitious attempt to date to measure parties' policies in post-war democracies. Through an analysis of these programmes, which have been collected from all significant parties in some twenty democracies, the MRG has traced the policy evolution of over eighty parties during the post-war period.
The coding procedures used to map the parties' policies from their election programmes are described in several of the MRG's publications, and I review them only briefly here.  The logic underlying the coding rules is that parties take positions by emphasizing the importance of certain policy areas compared to others. The coding procedure used to assess a party's policy positions therefore involves sorting the sentences -- actually quasi-sentences, since they include the phrases between colons and semi-colons -- in the party's election programme into varying categories (e.g., welfare, defence, law and order, etc.), and then taking the percentages in each category as a measure of the party's priorities. By comparing the relative policy emphases in different parties' programmes, one can compare the priorities of different parties; by comparing the emphases in the same party's programmes during different election periods, one can chart changes in this party's policy priorities. Hence the MRG's empirical anal yses can be used to analyse parties' policy priorities both temporally and comparatively.
Budge has undertaken such an analysis of parties' left--right positioning in twenty post-war democracies. Figure 1 shows how this procedure works when applied to British parties during the post-war period. The parties' positions, as estimated from the MRG's coding procedures, accord well with historical impressions: these policies converge during the 'Social Democratic Consensus' of the 1950s and 1960s, but diverge during the 1970s and 1980s, when the Conservatives shifted sharply to the right. The MRG's methodology also registers Labour's shift towards the centre between 1992 and 1997.
In addition to according with historical scholarship, Figure 1 reveals three comparative and temporal patterns which are the particular focus of this article:
(1) The parties differentiate their policy priorities from each other. This is clearly the case during the period 1945-50 and again after 1959. Only during the period of the 'Social Democratic Consensus' is there a move towards policy convergence, and even during this period the Liberals are coded as providing distinct alternatives to the two major parties.
(2) The parties rarely leapfrog each other, and when leapfrogging does occur it typically involves contiguous parties. During the entire post-war period there are only five occasions (1950, 1951, 1955, 1964 and 1997) in which the parties leapfrog each other. Each of these occasions involves the Liberals, whose centrally-located position is contiguous with both Labour and the Conservatives
(3) The parties' policies are not static but instead evolve over time. However, the parties' positions typically vary only within ideologically delimited areas of the policy space. Thus the Labour party's priorities changed substantially between 1964 and 1969 and again between 1983 and 1987, yet only its 1997 election programme was coded as being (barely) to the right of centre. Likewise, the Conservatives converged towards the centre during the 1950s and veered right during Thatcher's leadership, yet with the exception of the three election programmes 1954-59-64 they are coded as taking right-of-centre positions.
Budge finds that each of these patterns of British party competition also generalize to other post-war democracies.  The question therefore arises as to how these empirical findings can best be explained. Below I present a biased voting model of spatial competition, which I argue can illuminate the MRG's results. First, however, note that the standard Downsian model -- in which parties maximize votes while voters support the most proximate party in the policy space -- cannot explain the MRG' s findings, at least in the case of three-party British politics. This is because under this model the Labour and Conservative parties are motivated to converge towards the centre, thereby 'squeezing' the Liberal Democrats. This would in turn give the Liberal Democrats an incentive to leapfrog their competitors. Thus the standard Downsian model implies that the British parties should present convergent policies, and that they will continually leapfrog each other -- precisely the opposite of the patterns identified by the MRG. 
A BIASED VOTER MODEL OF PARTY COMPETITION
The above analysis raises the question, why does the Downsian model fail to account for the MRG's empirical findings? While numerous variations on the basic Downsian model have been proposed,  here I explore the implications of a 'biased voting' model which incorporates insights from behavioural research.
A Downsian Model with Biased Voters
In contrast to spatial modellers, behavioural researchers see more than policy issues …