¹ Budge, Ian and McDonald, Michael, ‘Choices Parties Define: Policy Alternatives in Representative Elections – 17 Countries 1945–1998’, Party Politics, 12 (2006), 451–66CrossRefGoogle Scholar; see also McDonald, Michael and Budge, Ian, Elections, Parties, and Democracy: Conferring the Median Mandate (Oxford: Oxford University Press, 2005)Google Scholar.

² These factors include (but are not limited to): the electoral salience of policies relative to unmeasured sources of voters’ party evaluations, the importance of ‘valence’ dimensions of voters’ party evaluations relative to policy dimensions of evaluation, the spatial distribution of voters’ partisan affiliations, and the strategic effects of voter abstention. See, for example, Lin, Tse-Min, Enelow, James and Dorussen, Han, ‘Equilibrium in Multicandidate Probabilistic Spatial Voting’, Public Choice, 98 (1999), 59–82Google Scholar; Schofield, Norman, ‘Valence Competition in the Spatial Stochastic Model’, Journal of Theoretical Politics, 15 (2003), 371–83Google Scholar; Schofield, Norman and Sened, Itai, Multiparty Democracy: Elections and Legislative Politics (Cambridge: Cambridge University Press, 2006)CrossRefGoogle Scholar; Adams, James and Merrill, Samuel III, ‘Party Policy Equilibrium for Alternative Spatial Voting Models: An Application to the Norwegian Storting’, European Journal of Political Research, 36 (1999), 35–55Google Scholar; Hinich, Melvin and Ordeshook, Peter, ‘Plurality Maximization vs. Vote Maximization: A Spatial Analysis with Variable Participation’, American Political Science Review, 64 (1970), 772–91Google Scholar.

³ Maurice Duverger, Political Parties (New York: Wiley, 1954).

⁴ See also Rae, Douglas, The Political Consequences of Electoral Laws (New Haven, Conn.: Yale University Press, 1967)Google Scholar; Riker, William H., ‘The Two-Party System and Duverger's Law: An Essay on the History of Political Science’, American Political Science Review, 76 (1982), 753–66Google Scholar; Taagepera, Rein and Shugart, Matthew, Seats and Votes: The Effects and Determinants of Electoral Systems (New Haven, Conn.: Yale University Press, 1989)Google Scholar; Cox, Gary, Making Votes Count (Cambridge: Cambridge University Press, 1997)Google Scholar.

⁵ Hermens, F. A., Democracy or Anarchy? (Notre Dame, Ind.: Notre Dame University Press, 1941), p. 19Google Scholar.

⁶ For examples of spatial mappings on more than one dimension, see Norman Schofield, ‘A Comparison of Majoritarian and Proportional Electoral Systems Based on Spatial Modeling and “Rational” Politicians’ (paper presented at the Conference on Constitutional Issues in Modern Democracies, Messina, 1997); Dow, Jay K., ‘A Comparative Spatial Analysis of Majoritarian and Proportional Elections’, Electoral Studies, 20 (2001), 109–25CrossRefGoogle Scholar.

⁷ Budge and McDonald, ‘Choices Parties Define’, p. 453.

⁸ See, for example, Powell, G. Bingham, Elections as Instruments of Democracy: Majoritarian and Proportional Visions (New Haven, Conn.: Yale University Press, 2000)Google Scholar; Huber, John and Powell, G. Bingham, ‘Congruence between Citizens and Policymakers in Two Visions of Liberal Democracy’, World Politics, 46 (1994), 291–326Google Scholar; Powell, G. Bingham and Vanberg, Georg S., ‘Election Laws, Disproportionality, and Median Correspondence: Implications for Two Visions of Democracy’, British Journal of Political Science, 30 (2000), 383–411Google Scholar; Huber, John, ‘Values and Partisanship in Left–Right Orientations: Measuring Ideology’, European Journal of Political Research, 17 (1989), 599–621CrossRefGoogle Scholar; McDonald and Budge, Elections, Parties, and Democracy.

⁹ Dalton, Russell J., Citizen Politics, 2nd edn (Chatham, N.J.: Chatham House Publishers, 1996)Google Scholar.

¹⁰ Carter, Elisabeth, ‘Does PR Promote Political Extremism? Evidence from the West European Parties of the Extreme Right’, Representation, 40 (2004), 82–100Google Scholar.

¹¹ Alvarez, R. Michael and Nagler, Jonathan, ‘Party System Compactness: Consequences and Measures’, Political Analysis, 12 (2004), 46–62CrossRefGoogle Scholar.

¹² Cox, Gary, ‘Centripetal and Centrifugal Incentives in Electoral Systems’, American Journal of Political Science, 34 (1990), 905–35Google Scholar.

¹³ Cox, ‘Centripetal and Centrifugal Incentives in Electoral Systems’.

¹⁴ Dow, ‘A Comparative Spatial Analysis of Majoritarian and Proportional Elections’.

¹⁵ There is both a theoretical and empirically-based literature suggesting that parties in multiparty elections (i.e. elections involving at least three parties) maximize votes by presenting centrist positions. Theoretically, when voting is probabilistic and voters do not attach too much salience to policy distance compared with unmeasured, non-policy motivations, then a unique vote-maximizing equilibrium exists in which all parties in a multiparty election locate at the mean voter position (Lin, Enelow and Dorussen, ‘Equilibrium in Multicandidate Probabilistic Spatial Voting’; but see Schofield, ‘Valence Competition in the Spatial Stochastic Model’). Empirically, scholars report computations on survey data from real world elections which suggest that the non-centrist parties that contested these elections could have increased their support in elections held in Britain, France, The Netherlands, Germany and Canada (see Alvarez, R. Michael, Nagler, Jonathan and Willette, Jennifer, ‘Measuring the Relative Impact of Issues and the Economy in Democratic Elections’, Electoral Studies, 19 (2000), 237–53Google Scholar; Alvarez, R. Michael, Nagler, Jonathan and Bowler, Shaun, ‘Issues, Economics, and the Dynamics of Multiparty Elections: The 1997 British General Election’, American Political Science Review, 42 (2000), 55–96CrossRefGoogle Scholar; Adams, James and Merrill, Samuel III, ‘Spatial Models of Candidate Competition and the 1988 French Presidential Election: Are Presidential Candidates Vote-Maximizers?’ Journal of Politics, 62 (2000), 729–56CrossRefGoogle Scholar; Adams, James, Merrill, Samuel III and Grofman, Bernard, A Unified Theory of Party Competition: A Cross-National Analysis Integrating Spatial and Behavioral Factors (Cambridge: Cambridge University Press, 2005)CrossRefGoogle Scholar. For static analyses, see also Ezrow, Lawrence, ‘Are Moderate Parties Rewarded in Multiparty Systems? A Pooled Analysis of Western European Elections, 1984–98’, European Journal of Political Research, 44 (2005), 881–98.Google Scholar

¹⁶ In addition, votes are less directly tied to office in proportional systems – i.e., parties with smaller vote shares can still participate in governing coalitions in PR systems. By contrast disproportional, plurality-based voting systems frequently manufacture single-party parliamentary majorities, as is the case in Britain, as well as in New Zealand prior to its switch to proportional representation for the 1996 election (for a review of evidence on this issue, see McDonald, Michael, Mendes, Sylvie and Budge, Ian, ‘What are Elections For? Conferring the Median Mandate’, British Journal of Political Science, 34 (2004), 1–26CrossRefGoogle Scholar). In these cases, ‘losing’ parties have no chance of becoming part of the government. Alternatively, proportional systems give small parties the opportunity to coalesce with larger parties and take part in the governing coalition (e.g., the Free Democratic Party (FDP) throughout most of the post-war period in Germany).

¹⁷ Cox, ‘Centripetal and Centrifugal Incentives in Electoral Systems’.

¹⁸ See also Eaton, Curtis B. and Lipsey, Richard G., ‘The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition’, Review of Economic Studies, 42 (1975), 27–49.Google Scholar

¹⁹ Merrill, Samuel III and Adams, James, ‘Centrifugal Incentives in Multi-Candidate Elections’, Journal of Theoretica l Politics, 14 (2002), 275–300Google Scholar.

²⁰ Duverger, Political Parties.

²¹ Related to this is Duverger's Hypothesis, that proportional voting systems are associated with multipartism (Duverger, Political Parties).

²² See Lijphart, Arend, Patterns of Democracy: Government Forms and Performance in Thirty-Six Countries (New Haven, Conn.: Yale University Press, 1999)Google Scholar; Taagepera and Shugart, Seats and Votes; Cox, Making Votes Count.

²³ Lijphart, Patterns of Democracy.

²⁴ Gallagher, Michael, ‘Proportionality, Disproportionality and Electoral systems’, Electoral Studies, 10 (1991), 33–51Google Scholar. The equation for the Gallagher Index of Disproportionality is

, where v_i and s_i are the vote shares and subsequent seat shares for party i.

²⁵ The criteria used to select these fifteen countries are discussed below.

²⁶ See Table 12.1 in Taagepera and Shugart, Seats and Votes.

²⁷ Lijphart, Arend, Electoral Systems and Party Systems: A Study of Twenty-Seven Democracies, 1945–1999 (Oxford: Oxford University Press, 1994), p. 27Google Scholar.

²⁸ These additional analyses, using an alternative measure of proportionality, also directly address endogeneity concerns for the specifications identified in Equations 3 and 4, i.e. the concern that vote share is a component of the Gallagher Index as well as the weighted version of average party policy extremism (the dependent variable).

²⁹ Laakso, Markku and Taagepera, Rein, ‘ “Effective” Number of Parties: A Measure with Application to West Europe’, Comparative Political Studies, 12 (1979), 3–27CrossRefGoogle Scholar; Lijphart, Patterns of Democracy.

³⁰ The Effective Number of Parliamentary Parties (ENPP) is calculated using the following equation developed by Laakso and Taagepera: , where s_i is the proportion of seats of the ith party (Laakso and Taagepera, ‘ “Effective” Number of Parties’). The authors’ alternative measure, the Effective Number of Elective Parties (ENEP) is based on votes (i.e., , where v_i is the proportion of votes of the ith party). The measure based on seats (ENPP) is employed in the empirical analyses reported below. However, I also ran these analyses using the Laakso–Taagepera measure based on vote share weightings (ENEP), as well as a third measure which is based on the number of parties receiving over a minimum threshold of votes (5 per cent) in the election. In all cases the substantive conclusions were unchanged.

³¹ Huber, John and Inglehart, Ronald, ‘Expert Interpretations of Party Space and Party Locations in 42 Societies’, Party Politics, 1 (1995), 73–111CrossRefGoogle Scholar; Castles, Francis and Mair, Peter, ‘Left–Right Political Scales: Some Expert Judgments’, European Journal of Political Research, 12 (1984), 73–88.CrossRefGoogle Scholar

³² Alvarez, Nagler and Bowler, ‘Issues, Economics, and the Dynamics of Multiparty Elections’; Adams and Merrill, ‘Party Policy Equilibrium for Alternative Spatial Voting Models’; Adams and Merrill, ‘Spatial Models of Candidate Competition and the 1988 French Presidential Election?’

³³ Budge, Ian, Klingemann, Hans-Dieter, Volkens, Andrea, Judith Bara and Tanenbaum, Eric, Mapping Policy Preferences: Estimates for Parties, Electors, and Governments 1945–1998 (Oxford: Oxford University Press, 2001)Google Scholar. In addition, scholars have employed the technique of multidimensional scaling, which involves estimating the parties’ positions relative to voters’ positions via analyses of voters’ policy preferences in combination with their party evaluations (see Dow, ‘A Comparative Spatial Analysis of Majoritarian and Proportional Elections’; Schofield and Sened, Multiparty Democracy).

³⁴ Alvarez and Nagler, ‘Party System Compactness’; Dow, ‘A Comparative Spatial Analysis of Majoritarian and Proportional Elections’; Kollman, Ken, Miller, John H., and Page, Scott E., ‘Political Parties and Electoral Landscapes’, British Journal of Political Science, 28 (1998), 139–58CrossRefGoogle Scholar. The argument for weighting average party policy extremism by party size is that such weighting accounts for the fact that the small parties in some countries (e.g., the American Green party, the British Socialist party, and so on) have virtually no political influence, so that their policy proposals do not enlarge the menu of policy choices available to voters in any meaningful sense. The arguments for relying on an unweighted measure of party policy extremism are, first, that any weighting system is unavoidably arbitrary given that parties’ policy influence does not necessarily correlate with vote (or seat) share, and, secondly, that small parties provide a vehicle through which voters can express their policy preferences, regardless of whether or not such parties significantly influence government policy outputs.

³⁵ Aspecial issue of Electoral Studies presents several articles which analyse the tradeoffs that accompany each approach used to estimate parties’ policy positions (Marks, Gary, ed., ‘Special Symposium: Comparing Measures of Party Positioning: Expert Manifesto, and Survey Data’, Electoral Studies, 26 (2007), 1–141CrossRefGoogle Scholar).

³⁶ I rely on the Eurobarometer surveys from 1980 (13), 1981 (15), 1982 (17), 1983 (19) for the analyses based on experts and manifestos, and the Eurobarometer surveys from 1987 (27), 1988 (29), 1989 (31A), and 1990 (33) for the analyses that are based on the citizen placements of parties’ left–right policy positions. The questions in the Eurobarometer are phrased: ‘In political matters, people talk of “the left” and “the right”. How would you place your views on this scale? [The following question is included only in the Eurobarometer 31A (1989)] And, where would you place the political parties (of your country)?’

For analyses of political systems outside of the European Community, I rely on Table 7.1 in Powell (Elections as Instruments of Democracy, p. 168) for left–right self-placements of voters. The benefit of using the information from this table is that it allows for the addition of Australia, Canada, Finland, Norway, Sweden and the United States to the analysis of West European countries in the early 1980s. Also, note that the Castles–Mair survey does not ask experts to place parties in Greece, Luxembourg and Portugal.

³⁷ The Manifesto Research Group provides vote shares in a CD-ROM in its 2001 publication.

³⁸ Alvarez and Nagler, ‘Party System Compactness’; Kollman, Miller and Page, ‘Political Parties and Electoral Landscapes’.

³⁹ Alvarez and Nagler, ‘Party System Compactness’.

⁴⁰ The Alvarez and Nagler formula is: , which is identical to the one above with the noted exceptions that the party system centre is identified as the mean voter's ideological position, and that the numerator and dominator have been switched. However, empirical analyses have been conducted that substitute the weighted mean party position, , as the measure for the party system centre. Furthermore, the parameters have been estimated for each of the specifications featured in Equations 3–5, employing a version of the dependent variable that squares the party policy deviations from the party system centre (i.e. based on variances), and the results for each of these analyses support the substantive conclusions reported in this study.

⁴¹ Specifically, WPE is calculated (0.289×|3.07-5.87|+0.144×|5.14-5.87|+0.122×|5.50-5.87|+0.444×|8.02-5.87|)/2=0.96, where the parties’ deviations from the centre of the voter distribution are weighted by their relative shares of the vote, and the denominator (which equals 2) represents the standard deviation of the British respondents’ left–right self-placements on the 1983 Eurobarometer survey. Alternatively, UPE is calculated (0.25×|3.07-5.87|+0.25×|5.14-5.87|+0.25×|5.50-5.87|+0.25×|8.02-5.87|)/2=0.76, where each of the four parties’ deviations from the mean party placement on a left–right scale is counted equally, so that consequently each is weighted at 0.25.

⁴² Based on the countries included in the analyses, the correlation coefficient between proportionality and the effective number of parties is 0.58, which is statistically significant at the 0.05 level.

⁴³ The parameters for each of these specifications were also estimated using the left–right estimates of party positions presented in Huber and Inglehart (Huber and Inglehart, ‘Expert Interpretations of Party Space and Party Locations in 42 Societies’) for the early 1990s. The substantive conclusions based on these results are identical to the ones reported below.

⁴⁴ See Stokes, Donald, ‘Spatial Models of Party Competition’, American Political Science Review, 57 (1963), 368–77CrossRefGoogle Scholar.

⁴⁵ See Schofield, Norman and Sened, Itai, ‘Modeling the Interaction of Parties, Activists and Voters: Why Is the Political Centre so Empty?’ European Journal of Political Research, 44 (2005), 355–90Google Scholar; Schofield, ‘Valence Competition in the Spatial Stochastic Model’; Adams, James, ‘Policy Divergence in Multiparty Probabilistic Spatial Voting’, Public Choice, 100 (1999), 103–22Google Scholar. See also Macdonald, Stuart Elaine and Rabinowitz, George, ‘Solving the Paradox of Nonconvergence: Valence, Position, and Direction in Democratic Politics’, Electoral Studies, 17 (1998), 281–300CrossRefGoogle Scholar.

⁴⁶ Adams and Merrill present an alternative argument that voters’ partisan loyalties can motivate vote-seeking parties to diverge from the centre, in the direction of the policies favoured by the members of their partisan constituencies (Adams and Merrill, ‘Party Policy Equilibrium for Alternative Spatial Voting Models’; Adams and Merrill, ‘Spatial Models of Candidate Competition and the 1988 French Presidential Election?’; see also Adams, Merrill and Grofman, A Unified Theory of Party Competition).

⁴⁷ Miller, Gary and Schofield, Norman, ‘Activists and Partisan Realignment in the United States’, American Political Science Review, 97 (2003), 245–60Google Scholar; Aldrich, John, ‘A Downsian Spatial Model with Party Activists’, American Political Science Review, 77 (1983), 974–90CrossRefGoogle Scholar; Aldrich, John, ‘A Spatial Model with Party Activists: Implications for Electoral Dynamics’, Public Choice, 41 (1983), 63–100CrossRefGoogle Scholar; Aldrich, John, Why Parties? (Chicago: University of Chicago Press, 1995)CrossRefGoogle Scholar.

⁴⁸ Schofield, Norman, Martin, Andrew, Quinn, Kevin and Nixon, David, ‘Multiparty Electoral Competition in the Netherlands and Germany: A Model Based on Multinomial Probit’, Public Choice, 97 (1999), 257–93Google Scholar.

⁴⁹ See Axelrod, Robert, Conflict of Interest (Chicago: Markham, 1970)Google Scholar; Laver, Michael and Shepsle, Kenneth, Making and Breaking Governments (Cambridge: Cambridge University Press, 1996)Google Scholar; Powell, Elections as Instruments of Democracy; Huber and Powell, ‘Congruence between Citizens and Policymakers in Two Visions of Liberal Democracy’.

⁵⁰ Schofield and Sened, Multiparty Democrcacy.