¹ Kim, HeeMin, Powell, Bingham and Fording, Richard, ‘Electoral Systems, Party Systems, and Ideological Representation: An Analysis of Distortion in Western Democracies’, Comparative Politics, 42 (2010), 167–185 Google Scholar

² Black, Duncan, The Theory of Committees and Elections (Cambridge: Cambridge University Press, 1958)Google Scholar

³ McDonald, Michael and Budge, Ian, Elections, Parties, Democracy: Conferring the Median Mandate (Oxford: Oxford University Press, 2005)CrossRefGoogle Scholar

⁴ McDonald and Budge, Elections, Parties, Democracy.

⁵ Powell, Bingham, Elections as Instruments of Democracy: Majoritarian and Proportional Visions (New Haven: Yale University Press, 2000)Google Scholar

Powell, Bingham, ‘Election Laws and Representative Government: Beyond Votes and Seats’, British Journal of Political Science, 36 (2006), 291–315 Google Scholar

Powell, Bingham, ‘The Ideological Congruence Controversy: The Impact of Alternative Measures, Data, and Time Periods on the Effects of Election Rules’, Comparative Political Studies, 42 (2009), 1475–1497 Google Scholar

Huber, John and Powell, Bingham, ‘Congruence between Citizens and Policy-Makers in Two Visions of Liberal Democracy’, World Politics, 46 (1994), 291–326 Google Scholar

Powell, Bingham and Vanberg, George, ‘Election Laws, Disproportionality and Median Correspondence: Implications for Two Visions of Democracy’, British Journal of Political Science, 30 (2000), 383–411 Google Scholar

⁶ Lijphart, Arend, Patterns of Democracy: Government Forms and Performance in Thirty-Six Countries (New Haven and London: Yale University Press, 1999)Google Scholar

⁷ Carey, John and Hix, Simon, ‘The Electoral Sweet Spot: Low-Magnitude Proportional Electoral Systems’, American Journal of Political Science, 55 (2011), 383–397 Google Scholar

⁸ Klingemann, Hans-Dieter, Volkens, Andrea, Bara, Judith, Budge, Ian and McDonald, Michael, Mapping Policy Preferences II. Estimates for Parties, Electors and Governments in Eastern Europe, European Union and OECD 1990-2003 (Oxford: Oxford University Press, 2006)Google Scholar

⁹ Kim, HeeMin and Fording, Richard, ‘Voter Ideology in Western Democracies, 1946-1989’, European Journal of Political Research, 33 (1998), 73–97 Google Scholar

Kim, HeeMin and Fording, Richard, ‘Voter Ideology in Western Democracies: An Update’, European Journal of Political Research, 42 (2003), 95–105 Google Scholar

Jan-Emmanuel de Neve, ‘The Median Voter Data Set: Voter Preferences Across 50 Democracies’, Electoral Studies, 30 (2011), 865–871 Google Scholar

¹⁰ Soroka, Stuart and Wlezien, Christopher, Degrees of Democracy: Politics, Public Opinion and Democracy (Cambridge and New York: Cambridge University Press, 2010)Google Scholar

¹¹ Golder, Matt and Stramski, Jacek, ‘Ideological Congruence and Electoral Institutions’, American Journal of Political Science, 54 (2010), 90–106 Google Scholar

¹² Kim and Fording, ‘Voter Ideology in Western Democracies’, p. 79Google Scholar

¹³ Stevenson, Randolph, ‘The Economy and Policy Mood: A Fundamental Dynamic of Democratic Politics?’, American Journal of Political Science, 45 (2001), 620–633 Google Scholar

¹⁴ Adams, James and Merrill, Samuel, ‘Why Small, Centrist Third Parties Motivate Policy Divergence by Major Parties’, American Political Science Review, 100 (2006), 403–417 Google Scholar

Adams, James and Somer-Topcu, Zeynep, ‘Moderate Now, Win Votes Later: The Electoral Consequences of Parties’ Policy Shifts in Twenty-Five Postwar Democracies’, The Journal of Politics, 71 (2009), 678–692 Google Scholar

Adams, James and Somer-Topcu, Zeynep, ‘Policy Adjustment by Parties in Response to Rival Parties? Policy Shifts, Spatial Theory and the Dynamics of Party Competition in Twenty-Five Post-War Democracies’, British Journal of Political Science, 39 (2009), 825–846 Google Scholar

Pontusson, Jonas and Rueda, David, ‘The Politics of Inequality: Voter Mobilization and Left Parties in Advanced Industrial States’, Comparative Political Studies, 43 (2010), 675–705 Google Scholar

¹⁵ Comparative Study of Electoral Systems, 1996-2001: Module 1 Micro-District-Macro Data [dataset], (Ann Arbor: University of Michigan, Center for Political Studies, 2003); Comparative Study of Electoral Systems, 2001-2006: Module 2 Full Release [dataset], (Ann Arbor: University of Michigan, Center for Political Studies, 2007).

¹⁶ McDonald and Budge, Elections, Parties, Democracy, pp. 113–114Google Scholar

¹⁷ This article also assumes that the analyst who is calculating the KF median shares the voters’ knowledge of party locations. If this is not the case, the result may be inaccurate even if all the other assumptions are met.

¹⁸ Clark, Michael, ‘Valence and Electoral Outcomes in Western Europe, 1976–1998’, Electoral Studies, 28 (2009), 111–122 Google Scholar

¹⁹ Clark, ‘Valence and Electoral Outcomes’.

²⁰ Rabinowitz, George and Macdonald, Elaine, ‘A Directional Theory of Issue Voting’, American Political Science Review, 83 (1989), 93–121 Google Scholar

Grofman, Bernard, ‘The Neglected Role of the Status Quo in Models of Issue Voting’, The Journal of Politics, 45 (1985), 230–237 Google Scholar

Kedar, Orit, ‘When Moderate Voters Prefer Extreme Parties: Policy Balancing in Parliamentary Elections’, American Political Science Review, 99 (2005), 185–199 Google Scholar

Duch, Raymond, May, Jeff and Armstrong, David, ‘Coalition-Directed Voting in Multiparty Democracies’, American Political Science Review, 104 (2010), 698–719 Google Scholar

²¹ The sole limitation imposed on party positions is that they cannot all be located on one side of the median voter's position.

²² Some of the interactions used in our analyses are dominated by one of their components, which undermines the interaction's capacity to play its intended role and creates excessive collinearity in the models. To deal with this problem, we standardized each variable before forming products.

²³ Interestingly, even at very high levels of dimensional correlation (r is never exactly 1 in these simulations but becomes very close), the lines never converge.

²⁴ The exception is Chile 2005, where 62 per cent of respondents placed themselves, improbably, at ‘1’ on the scale.

²⁵ Warwick, Paul V., ‘Bilateralism or the Median Mandate? An Examination of Rival Perspectives on Democratic Governance’, European Journal of Political Research, 49 (2010), 1–24 Google Scholar

²⁶ Warwick, ‘Bilateralism or the Median Mandate?’, pp. 11–12Google Scholar

Curini, Luigi, ‘Experts’ Political Preferences and Their Impact on Ideological Bias’, Party Politics, 16 (2010), 299–321 Google Scholar

²⁷ If voters collectively misperceive party locations and act accordingly, the inaccuracy in the KF measure will tend to resemble that produced by random error. If positions derived from other sources are used, which do not agree with the voters’ collective estimates, an additional source of possible inaccuracy is introduced.

²⁸ McDonald and Budge, Elections, Parties, Democracy, pp. 114–115Google Scholar

²⁹ Lyman Ott and Michael Longnecker, An Introduction to Statistical Methods and Data Analysis, 6^th edition (Belmont, CA: Brooks/Cole Cengage Learning, 2010), p. 80Google Scholar

³⁰ The simulated data bear this out. In the data set in which vote choice is determined solely by left-right proximity, allocating each voter to the nearest 0.1 on the 0-1 scale (which is roughly equivalent) and applying this method produces an absolute mean error of 0.0008 (SD = 0.0006) across 10,000 simulated elections. This is one-third less than the KF error (mean = 0.0012, SD = 0.0018). Both levels of error are, of course, very small. The difference is that the KF median will become more deviant as valence and other facfactors come to play a role, whereas this median will not.

³¹ Markussen, Simen, ‘How the Left Prospers from Prosperity’, European Journal of Political Economy, 24 (2008), 329–342 Google Scholar

³² For example, Pontusson and David Rueda, ‘The Politics of Inequality’; Adams and Somer-Topcu, ‘Moderate Now, Win Votes Later’ and Adams and Somer-Topcu, ‘Policy Adjustment by Parties in Response to Rival Parties?’.

³³ Following standard practice, the government positions are estimated from the seat-weighted mean positions of their member parties.

³⁴ Warwick, ‘Bilateralism or the Median Mandate?’, p. 15Google Scholar

³⁵ Warwick, ‘Bilateralism or the Median Mandate’, p. 15Google Scholar

Warwick, Paul V., ‘Government Intentions and Citizen Preferences in Dynamic Perspective”, British Journal of Political Science, 41 (2011), 599–619Google Scholar

³⁶ Kang, Shin-Goo and Powell, Bingham, ‘Representation and Policy Responsiveness: The Median Voter, Election Rules, and Redistributive Welfare Spending’, The Journal of Politics, 72 (2010), 1014–1028 Google Scholar

³⁷ Kang and Powell, ‘Representation and Policy Responsiveness’, p. 1016Google Scholar

³⁸ Kang and Powell, ‘Representation and Policy Responsiveness’, p. 1016Google Scholar