¹ For theoretical spatial modelling results, see William Riker and Peter Ordeshook, ‘A Theory of the Calculus of Voting’, American Political Science Review, 62 (1968), 25–42; James Enelow and Melvin Hinich, The Spatial Theory of Voting (Cambridge: Cambridge University Press, 1984); and Jon Roemer, Political Competition: Theory and Applications (Cambridge, Mass.: Harvard University Press, 2001). For empirical applications of spatial modelling, see Ian Budge, ‘A New Theory of Party Competition: Uncertainty, Ideology, and Policy Equilibria Viewed Comparatively and Temporally’, British Journal of Political Science, 24 (1994), 443–67; James Adams, Samuel Merrill III and Bernard Grofman, A Unified Theory of Party Competition: A Cross-National Analysis Integrating Spatial and Behavioral Factors (Cambridge: Cambridge University Press, 2005); Michael McDonald and Ian Budge, Elections, Parties, Democracy: Conferring the Median Mandate (Oxford: Oxford University Press, 2005); Norman Schofield and Itai Sened, Multiparty Democracy: Parties, Elections, and Legislative Politics (Cambridge: Cambridge University Press, 2006).

² We note that this hypothesis is also implied by spatial models of policy-seeking parties, i.e. parties that seek office in order to implement their preferred policies. Policy-seeking parties’ strategic imperative to win office – which is necessary in order to implement their pre-election policy promises – motivates them to calibrate their strategies against the position of the median voter (although policy-seeking parties do not typically converge to the median, provided there is uncertainty about the election outcome), so that they can be expected to update their policy strategies when the median voter’s position shifts. On these points, see Donald Wittman, ‘Spatial Strategies When Candidates Have Policy Preferences,’ in James Enelow and Melvin Hinich, eds, Advances in the Spatial Theory of Voting (Cambridge: Cambridge University Press, 1990), pp. 66–98.

³ On American politics, see Robert Erikson, Michael MacKuen and James Stimson, The Macro Polity (Cambridge: Cambridge University Press, 2002). On European politics, see James Adams, Michael Clark, Lawrence Ezrow and Garrett Glasgow, ‘Understanding Change and Stability in Party Ideologies: Do Parties Respond to Public Opinion or to Past Election Results?’ British Journal of Political Science, 34 (2004), 589–610; also Lawrence Ezrow, ‘The Variance Matters: How Party Systems Represent the Preferences of Voters’, Journal of Politics, 69 (2007), 182–92.

⁴ See, e.g., Jay K. Dow, ‘A Comparative Spatial Analysis of Majoritarian and Proportional Elections’, Electoral Studies, 20 (2001), 109–25; Bonnie Meguid, ‘Competition between Unequals: The Role of Mainstream Party Strategy and Niche Party Success’, American Political Science Review, 99 (2005), 347–60; Adams, Merrill and Grofman, A Unified Theory of Party Competition; Schofield and Sened, Multiparty Democracy; Kenneth Greene, Defeating Dominance: Party Politics and Mexico’s Democratization in Comparative Perspective (Cambridge: Cambridge University Press, 2007).

⁵ Budge, ‘A New Theory of Party Competition’.

⁶ If the parties’ positions diverge in a two-party, unidimensional spatial model with deterministic policy voting and full voter turnout, then either party can enhance its support by unilaterally shifting its position in the direction of the rival party.

⁷ James Adams, Party Competition and Responsible Party Government: A Theory of Spatial Competition Based Upon Insights from Behavioral Voting Research (Ann Arbor: University of Michigan Press, 2001). On pp. 55–61 of this book Adams, using a spatial model where voters are motivated by a combination of policy distance and party identification, presents illustrative arguments that when moderate parties shift to the left, for instance, then this depresses left-wing parties’ prospects of competing successfully for support from centre-left voters, and that these leftist parties therefore have electoral incentives to shift their own positions farther to the left, in the direction of their core partisan constituencies. Adams also presents arguments that this scenario provides right-wing parties with electoral incentives to shift in a leftward direction.

⁸ James Adams and Samuel Merrill III, ‘Why Small, Centrist Third Parties Motivate Policy Divergence by Major Parties’, American Political Science Review, 100 (2006), 403–17; James Adams and Samuel Merrill III, ‘Policy-Seeking Parties in a Parliamentary Democracy with Proportional Representation: A Valence-Uncertainty Model’, British Journal of Political Science, 39 (2009), forthcoming.

⁹ For instance, in a unidimensional spatial model with deterministic policy voting, each party’s supporters are located in the segment of the continuum that is bounded by two ‘cut-points’, that represent the midpoints between the party’s position and the position of the adjacent party on its left and the adjacent party on its right (if the focal party is the right-most or left-most party in the system, then there is a single cut-point). In such unidimensional models, a party’s vote share changes in response to marginal shifts by the adjacent parties along the continuum, but its vote share will not change in response to marginal shifts by other parties. See, e.g., Curtis B. Eaton and Richard G. Lipsey, ‘The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition’, Review of Economic Studies, 42 (1975), 27–49; and Gary Cox, ‘Centripetal and Centrifugal Incentives in Electoral Systems’, American Journal of Political Science, 34 (1990), 905–35.

¹⁰ Budge, ‘A New Theory of Party Competition’; Michael Laver, ‘Policy and the Dynamics of Political Competition’, American Political Science Review, 99 (2005), 263–81.

¹¹ For a more thorough description of the coding process, see Appendix 2 in Ian Budge, Hans-Dieter Klingemann, Andrea Volkens, Eric Tannenbaum and Judith Bara, Mapping Policy Preferences: Estimates for Parties, Electors, and Governments 1945–1998 (Oxford: Oxford University Press, 2001).

¹² See Derek Hearl, ‘Checking the Party Policy Estimates: Reliability’, in Budge et al., eds, Mapping Policy Preferences, pp. 111–25; Michael McDonald and Sylvia Mendes, ‘Checking the Party Policy Estimates: Convergent Validity’, in Budge et al., eds, Mapping Policy Preferences, pp. 127–41; Michael Laver, Kenneth Benoit and John Garry, ‘Extracting Policy Positions from Political Texts Using Words as Data’, American Political Science Review, 97 (2003), 311–31.

¹³ See James Adams, Michael Clark, Lawrence Ezrow and Garrett Glasgow, ‘Are Niche Parties Fundamentally Different from Mainstream Parties? The Causes and the Electoral Consequences of Western European Parties’ Policy Shifts, 1976–1998’, American Journal of Political Science, 50 (2006), 513–29; Erikson, Mackuen, and Stimson, The Macro Polity.

¹⁴ Hee Min Kim and Richard Fording, ‘Voter Ideology in Western Democracies 1946–1989’, European Journal of Political Research, 33 (1998), 73–97; Hee Min Kim and Richard Fording, ‘Extending Party Estimates to Governments and Electors’, in Budge et al., eds, Mapping Policy Preferences, pp. 157–77. See the latter citation for a detailed description of the Kim-Fording procedure for inferring the median voter position. The Kim–Fording estimates of the median voter position are included on the CD-ROM that accompanies Budge et al., eds, Mapping Policy Preferences.

¹⁵ McDonald and Budge, Elections, Parties, Democracy.

¹⁶ There exist several cross-national, survey-based, public opinion instruments – such as the World Values Study surveys and the Eurobarometer surveys – but these measures do not extend back before the mid 1970s, nor do they encompass the full set of twenty-five democracies included in our study. However, below we report sensitivity analyses on sub-sets of the cases in our dataset, for which survey-based public opinion measures are available.

¹⁷ See pp. 199–202 in McDonald and Budge, Elections, Parties, Democracy.

¹⁸ Specifically, in order to estimate the coefficients of the model depicted in Figure 1, we would need to specify certain exogenous variables as ‘instrumental variables’, i.e. as measured variables that influenced one party’s policy positions but not the other party’s positions. Our substantive conclusions would then depend entirely on these strong assumptions. Furthermore, from a practical standpoint, even to the extent that we are prepared to employ the instrumental variables approach, there are no plausible instrumental variables that we can measure continuously over the large set of political parties (193 in all) and the long time period (1945–1998) of our study.

¹⁹ See Stimson, Erikson and Mackuen, The Macro Polity, p. 383.

²⁰ We thank an anonymous referee for suggesting this argument on why parties may be expected to lag in their responses to outside conditions and events. In addition, we note that there are some spatially-based perspectives that admit the possibility of lagged party responses. The most obvious example is Budge’s approach to modelling party competition under conditions of radical uncertainty (Budge, ‘A New Theory of Party Competition’). However, it strikes us that the agent-based modelling approach of Laver (‘Policy and the Dynamics of Political Competition’) also incorporates the possibility of lags in parties’ responses to rival parties’ strategies. In Laver’s specification voters respond to the parties’ current policy positions but the parties themselves respond to their competitors’ policy strategies from the previous time period (see also Kenneth Kollman, John Miller and Scott Page, ‘Adaptive Parties in Spatial Elections’, American Political Science Review, 86 (1992), 929–37). This approach appears compatible with the perspective we present here.

²¹ Below we report sensitivity analyses which suggest that our substantive conclusions on how parties respond to the competitors’ previous policy shifts extend to alternative specifications, which control for factors related to rival parties’ current shifts.

²² Note that because the focal party’s position is excluded from this computation, the variable [average shift − other parties (t − 1)] can take on different values with respect to different parties competing in the same election. Suppose, for instance, that an election at time t involves three parties A, B and C, and that these parties’ observed left–right shifts between election t − 2 and election t − 1 were −2 for Party A, 0 for Party B, and +4 for Party C. Then the value of the [average shift − other parties (t − 1)] variable with respect to Party A is the average of the previous shifts of parties B and C, which equals (0 + 4)/2 = + 2; the value of this variable with respect to Party B is the average of the previous shifts of parties A and C, which equals (−2 + 4)/2 = +1; and the value of this variable with respect to Party C is the average of the previous shifts of parties A and B, which equals (−2 + 0)/2 = −1.

²³ Stimson, Erikson and Mackuen, The Macro Polity; Adams et al., ‘Understanding Change and Stability in Party Ideologies’; McDonald and Budge, Voters, Parties, Elections.

²⁴ Budge (‘A New Theory of Party Competition’), who argues that party elites may pursue this strategy of ‘policy alternation’ because they recognize the need to satisfy both the moderate and the radical wings of their parties, finds empirical support for the alternation hypothesis in his analysis of CMP data from twenty post-war democracies. Adams, in Party Competition and Responsible Party Government, develops a spatial model in which voters are moved by a combination of policy distance and non-policy considerations, and concludes that voters’ nonpolicy-related attachments (such as party identification) can give political parties electoral incentives to shift their policies back and forth over time, thereby creating a pattern that resembles Budge’s alternation model.

²⁵ Party family designations are taken from Appendix 1 in Budge et al., Mapping Policy Preferences, where the third digit of the party identification code denotes the party’s family. We note that we also controlled for party membership in the family of centrist parties, which we defined as those parties that the CMP classified as belonging to the Liberal family. However, because very few of the party systems in our study featured multiple members of the Liberal family, we did not include this variable in our empirical specification.

²⁶ For parties that do not have ideological family members in their party system, the variance of the marginal effect of changes in other parties’ previous policy shifts is simply the variance of b ₂. For parties that do have ideological family members in their party system, the variance is [VAR(b ₂) + VAR(b ₅) + 2 × COV(b ₂ + b ₅)].

²⁷ We required at least three consecutive party programme codings in order to construct the [party shift (t)] variable and the [party shift (t − 1)] variable that we include in our empirical specifications.

²⁸ See Cheng Hsiao, Analysis of Panel Data, 2nd edn (Cambridge: Cambridge University Press, 2003); and Donald P. Green, Soo Yeon Kim, and David H. Yoon, ‘Dirty Pool’, International Organization, 55 (2001), 441–68.

²⁹ Budge, ‘A New Theory of Party Competition’; Adams, Party Competition and Responsible Party Government.

³⁰ On this point, see Nathaniel Beck and Jonathan N. Katz, ‘What to Do (and Not to Do) with Time-Series Cross-Section Data’, American Political Science Review, 89 (1995), 634–47.

³¹ See William H. Rogers, ‘Regression Standard Errors in Clustered Samples’, Stata Technical Bulletin, 13 (1993), 19–23; Rick L. Williams, ‘A Note on Robust Variance Estimation for Cluster-Correlated Data’, Biometrics, 56 (2000), 645–6.

³² Budge, ‘A New Theory of Party Competition’; Adams et al., ‘Understanding Change and Stability in Party Ideologies’.

³³ We thank three anonymous referees and the Editor for suggesting many of the sensitivity analyses that we report in this section. The results of all of these sensitivity analyses are available from the authors upon request.

³⁴ Riccardo Pelizzo, ‘Party Position or Party Direction? An Analysis of Party Manifesto Data’, West European Politics, 26 (2003), 67–89. See also Herbert Kitschelt, The Transformation of European Social Democracy (New York: Cambridge University Press, 1994).

³⁵ For all twenty-five sets of parameter estimates on the Fully Specified Model, the estimated coefficient on the [average shift − other parties (t − 1)] variable was positive and statistically significant at the 0.05 level. For twenty of the twenty-five estimates, the estimated coefficient on the [average shift − family members (t − 1)] variable was positive and statistically significant at the 0.05 level, and in four of the remaining five cases this estimate was positive and statistically significant at the 0.10 level.

³⁶ Studies on the effect of global economic variables on parties’ policy positions include Andrea Haupt, ‘Globalization’s Effects on Parties’ Economic Policy Positions’, Party Politics, forthcoming; James Adams, Andrea Haupt and Heather Stoll, ‘What Moves Parties? The Role of Public Opinion and Global Economic Conditions in Western Europe’, Comparative Political Studies, forthcoming; and Steven Nelson and Christopher Way, ‘Party Crashers: The Determinants of Left Party Ideological Shifts in Wealthy Democracies’, presented at the annual meeting of the Midwest Political Science Association, Chicago, 2007. For analyses of the effects of the voting system on party positioning, see Gary Cox, Making Votes Count (Cambridge: Cambridge University Press, 1997); Lawrence Ezrow, ‘Parties’ Policy Programmes and the Dog that Didn’t Bark: No Evidence that Proportional Systems Promote Extreme Party Positioning’, British Journal of Political Science, 38 (2008), 470–98; and Dow, ‘A Comparative Analysis of Majoritarian and Proportional Systems’.

³⁷ Specifically, we re-estimated our specifications while excluding parties that the CMP classified as belonging to the Ecology, Nationalist, Agrarian, Ethnic/Regional and ‘Special Interest’ party families, i.e. parties that emphasize issues that do not necessarily map onto the left–right economic dimension. We also conducted additional analyses where we further restricted our focus to the sub-set of party systems in our dataset that previous studies, conducted by Laver and Benoit and by Huber and Inglehart, identify as revolving primarily around issues that map onto the left–right dimension. These analyses again supported our substantive conclusions. See John Huber and Ronald Inglehart, ‘Expert Interpretations of Party Space and Party Locations in 42 Societies’, Party Politics, 1 (1995), 73–111; and Kenneth Benoit and Michael Laver, Party Policy in Modern Democracies (London: Routledge, 2006).

³⁸ Budge, ‘A New Theory of Party Competition’. See also Jack Nagel, ‘Center-Party Strength and Major-Party Polarization in Britain’, presented at the Annual Meeting of the American Political Science Association, San Francisco, 2001.

³⁹ Adams et al., ‘Are Niche Parties Fundamentally Different from Mainstream Parties?’

⁴⁰ Specifically, the estimated coefficient on the [public opinion shift (t)] variable in column 4, 0.511, implies that, ceterus paribus, mainstream parties shift their policies by 0.511 units in response to a one-unit shift in public opinion. The estimated coefficient on the [public opinion shift (t) × niche party] variable, −0.208, is statistically significant (p < 0.01, two-tailed test) and implies that niche parties shift their policies by only (0.511 − 0.208) = 0.303 units in response to a one-unit public opinion shift.

⁴¹ Budge, ‘A New Theory of Party Competition’, p. 454.

⁴² Laver, ‘Policy and the Dynamics of Political Competition’; Kollman et al., ‘Adaptive Parties in Spatial Elections’; James Fowler and Michael Laver, ‘A Tournament of Party Strategies’, Journal of Conflict Resolution, 52 (2008), 68–92.

⁴³ The policy preferences of a party’s electoral constituency can change either due to changes in the constituency’s composition – i.e. due to exit/entry by some members of the party constituency – or as a result of shifts in the policy preferences in the existing constituency, i.e. the composition of the party’s electoral constituency is constant but some members of this constituency shift their opinions. Laver’s analyses focus on the consequences of compositional changes in parties’ electoral constituencies. We note that McGann’s equilibrium analysis of aggregating parties in multiparty elections suggests similar substantive conclusions (see Anthony McGann, ‘The Advantages of Ideological Cohesion: A Model of Constituency Representation and Electoral Competition in Multiparty Democracies’, Journal of Theoretical Politics, 14 (2002), 37–70).

⁴⁴ Ezrow, ‘The Variance Matters’; Ronni Abney, Andrea Morrison and Gary Stradiotto, ‘On the Stability of Representation: A Cross-National Study of the Dispersion of Parties’ Policy Positions in Plurality and Proportional Representation Systems’, Representation, 43 (2007), 151–65. We note that these empirical studies focus primarily on parties’ positions on the overarching left–right dimension, so that they do not necessarily address the diversity of parties’ policy positions along emerging, cross-cutting, cleavages such as European integration or globalization. For multidimensional analyses that address these points, see Josephine Andrews and Jeannette Money, ‘The Spatial Structure of Party Competition: Party Dispersion within a Finite Policy Space’, unpublished, University of California – Davis.

⁴⁵ On these points, see Margit Tavits, ‘Principle versus Pragmatism: Policy Shifts and Political Competition’, American Journal of Political Science, 51 (2007), 151–65; and Andrews and Money, ‘The Spatial Structure of Party Competition’.

⁴⁶ See Meguid, ‘Competition between Unequals’; and Margit Tavits, ‘Party System Change: Testing a Model of New Party Entry’, Party Politics, 12 (2006), 99–119.

⁴⁷ On this point see Money and Andrews, ‘Parties’ Electoral Strategies’.