¹ Stokes, Donald, ‘Spatial Models of Party Competition’, American Political Science Review, 57 (1963), 368–377 CrossRefGoogle Scholar

Kavanaugh, Dennis, ed., Electoral Politics (Oxford: Clarendon Press, 1992)CrossRefGoogle Scholar

² Stokes, ‘Valence Politics’, p. 143.

³ Stokes, ‘Valence Politics’, p. 143.

⁴ Adams, James, ‘Policy Divergence in Multicandidate Probabilistic Spatial Voting’, Public Choice, 99 (1999), 259–274 CrossRefGoogle Scholar

Groseclose, Timothy, ‘A Model of Candidate Location when One Candidate Has a Valence Advantage’, American Journal of Political Science, 45 (2001), 862–886 CrossRefGoogle Scholar

Adams, James III, Samuel Merrill 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

Schofield, Norman and Sened, Itai, Multiparty Democracy: Elections and Legislative Politics (Cambridge: Cambridge University Press, 2006)CrossRefGoogle Scholar

Serra, Gilles, ‘Polarization of What? A Model of Elections with Endogenous Valence’, Journal of Politics, 72 (2010), 426–437 CrossRefGoogle Scholar

Bruter, Michael Erikson, Robert and Strauss, Aaron, ‘Uncertain Candidates, Voters with Valence, and the Dynamics of Candidate Position-Taking’, Public Choice, 44 (2010), 153–168 CrossRefGoogle Scholar

⁵ Adams, James and III, Samuel Merrill, ‘Policy-Seeking Parties in a Parliamentary Democracy with Proportional Representation: A Valence-Uncertainty Model’, British Journal of Political Science, 39 (2009), 539–558 CrossRefGoogle Scholar

⁶ David Fortunato and Randy Stevenson, ‘Perceptions of Partisan Ideologies: The Effect of Coalition Participation’, American Journal of Political Science (forthcoming).

⁷ Although, as we discuss immediately below, voters’ perceptions of collective responsibility hamper governing parties’ policy-seeking objectives in other ways.

⁸ We note that the coalition convergence and the coalition penalty effects are reconciled as follows. Our theoretical results imply that parties that share collective responsibility face diminished prospects of achieving their policy objectives (the coalition penalty effect). Our results also imply that parties’ best response to the strategic disadvantages associated with collective responsibility is to converge towards each other in the policy space (the coalition convergence effect). However, the computational results we report below suggest that while policy convergence between coalition partners partially mitigates the strategic disadvantages caused by collective responsibility, nevertheless in equilibrium these coalition partners’ expected policy outcomes are diminished, compared to what they would be if they did not share collective responsibility.

⁹ Strøm, Kaare, Minority Government and Majority Rule (New York: Cambridge University Press, 1990)Google Scholar

¹⁰ Adams and Merrill, ‘Policy-Seeking Parties in a Parliamentary Democracy’.

¹¹ The alternative to a parliamentary democracy is a presidential democracy, in which a president with significant constitutional powers exercises substantial influence on government policy outputs. Prominent examples of presidential democracies include the United States and many Latin American countries. By contrast, every West European country except France is best classified as a parliamentary democracy.

¹² Adams and Merrill, ‘Policy-Seeking Parties in a Parliamentary Democracy’.

¹³ Thus, if the s_k 's are ordered so that s ₁ ≤ s ₂ ≤ … ≤ s_K , then the MPP is that party k_M such that parties 1,…,k_M and parties k_M , k_M + 1,…K each include a majority of the seats in parliament.

¹⁴ We say that a function U is concave and peaks at x₀ if it is continuous, and if for all x in the domain of U for which x ≠ x ₀, $$)(--&#x003E;&#x003C;$&#x003E;\frac{{{{\partial }^2} U}}{{\partial {{x}^2} }}( x)\,\leq \,0 &#x003C;$&#x003E;&#x003C;!--$$ and U(x ₀) > U(x). Note that if U is concave and peaks at x₀ , then U is strictly increasing on the left of x₀ and strictly decreasing on the right, i.e. if x ₁ < x ₂ ≤x ₀, then U(x ₁) < U(x ₂) and if x ₀ ≤ x ₁ < x ₂, then U(x ₁) > U(x ₂).

¹⁵ Powell, G. Bingham, Elections as Instruments of Democracy: Majoritarian and Proportional Visions (New Haven, Conn.: Yale University Press, 2000)Google Scholar

Austen-Smith, David and Banks, Jeffery, ‘Elections, Coalitions, and Legislative Outcomes’, American Political Science Review, 82 (1988), 405–422 CrossRefGoogle Scholar

¹⁶ Baron, David, ‘Comparative Dynamics of Parliamentary Governments’, American Political Science Review, 92 (1998), 593–609 CrossRefGoogle Scholar

Diermeier, Daniel and Feddersen, Timothy, ‘Cohesion in Legislatures and the Vote of Confidence Procedure’, American Political Science Review, 92 (1998), 611–621 CrossRefGoogle Scholar

¹⁷ Laver, Michael and Shepsle, Kenneth, Making and Breaking Governments (Cambridge: Cambridge University Press, 1996)CrossRefGoogle Scholar

¹⁸ Kedar, Orit, ‘When Moderate Voters Prefer Extreme Parties: Policy Balancing in Parliamentary Elections’, American Political Science Review, 99 (2005), 185–199 CrossRefGoogle Scholar

Warwick, Paul, ‘Coalition Policies in Parliamentary Democracies: Who Gets How Much and Why,’ Comparative Political Studies, 34 (2001), 1212–1236 CrossRefGoogle Scholar

III, Samuel Merrill and Adams, James, ‘The Effects of Alternative Power-Sharing Arrangements: Do “Moderating” Institutions Moderate Party Strategies and Government Policy Outputs?’ Public Choice, 131 (2007), 413–434 Google Scholar

¹⁹ McDonald, Michael and Budge, Ian, Elections, Parties, and Democracy: Conferring the Median Mandate (Oxford: Oxford University Press, 2005)CrossRefGoogle Scholar

Ian Budge, Michael McDonald, Paul Pennings and Hans Keman, Organizing Democratic Choice: The Party Mandate over Time (Oxford: Oxford University Press, forthcoming 2012)CrossRefGoogle Scholar

²⁰ See McDonald and Budge, Elections, Parties, and Democracy, chap. 8.

²¹ Cho, Seok-ju and Duggan, John, ‘Bargaining Foundations of the Median Voter Theorem’, Journal of Economic Theory, 144 (2009), 851–868 CrossRefGoogle Scholar

²² Note that the identity of the MPP is not known to the voters at the time they cast their ballots because the vote share of each party is yet to be determined. Thus, voters’ evaluations of all parties, not just the eventual MPP, is relevant to their voting decisions.

²³ Parties in parliamentary democracies publish detailed policy programmes several weeks (sometimes months) in advance of the election. These policy programmes, furthermore, usually hew closely to the policy positions that the party has staked out at its most recent annual party conference, which can take place up to a year in advance of the election.

²⁴ Adams and Merrill, ‘Policy-Seeking Parties in a Parliamentary Democracy’.

²⁵ Adams and Merrill, ‘Policy-Seeking Parties in a Parliamentary Democracy’.

²⁶ Lewis-Beck, Michael, Economics and Elections (Ann Arbor: University of Michigan Press, 1988)Google Scholar

Powell, G. Bingham and Whitten, Guy, ‘A Cross-National Analysis of Economic Voting: Taking Account of the Political Context’, American Journal of Political Science, 37 (1993), 391–414 CrossRefGoogle Scholar

Palmer, Harvey D. and Whitten, Guy D., ‘The Electoral Impacts of Unexpected Inflation and Economic Growth’, British Journal of Political Science, 29 (1999), 623–639 CrossRefGoogle Scholar

Duch, Raymond M. and Stevenson, Randy, The Economic Vote: How Political and Economic Institutions Condition Election Results (Cambridge: Cambridge University Press, 2008)CrossRefGoogle Scholar

²⁷ Clark, Michael, ‘Valence and Electoral Outcomes: A Cross-National Study of Nine West European Countries’ (doctoral dissertation, University of California at Santa Barbara, 2006)Google Scholar

²⁸ Kees van Kersbergen, ‘The Christian Democratic Phoenix and Modern Unsecular Politics’, Party Politics, 14 (2008), 259–279 CrossRefGoogle Scholar

²⁹ Helms, Ludger, ‘The Federal Election in Germany, September 2002’, Electoral Studies, 23 (2004), 143–149 CrossRefGoogle Scholar

³⁰ Glasgow, Garrett Golder, Matt and Golder, Sona N., ‘Who Wins? Determining the Party of the Prime Minister’, American Journal of Political Science, 55 (2011), 936–953 CrossRefGoogle Scholar

Martin, Lanny and Stevenson, Randolph T., ‘Incumbency, Context, and Government Formation in Multiparty Parliamentary Democracies’, American Political Science Review, 104 (2010), 503–518 CrossRefGoogle Scholar

³¹ We note that coalition partners’ long-term valence images also plausibly reflect their joint responsibility for valence-related effects that occur prior to the dates when they select their policy strategies for the upcoming election. However because we assume that parties’ long-term valence images are known at the time they choose their policy strategies, parties’ collective responsibility for past events that contribute to their long-term valence images – which party elites can assess at the time they select their policy strategies – does not complicate our analyses in the same way as joint responsibility for the short-term valence-related events that elites cannot anticipate at the time they select their strategies.

³² McFadden, Daniel, ‘Conditional Logit Analysis of Qualitative Choice Behavior’, pp. 105–142Google Scholar

Zarembka, Paul, ed., Frontiers in Econometrics (New York: Academic Press, 1974)Google Scholar

³³ Adams and Merrill, ‘Policy-Seeking Parties in a Parliamentary Democracy’.

³⁴ A Nash equilibrium is a configuration of strategies such that no player (here a party) can increase its expected utility by unilaterally changing its position.

³⁵ The equilibrium result and the CVE result for the basic model are given by Theorems 1–2 in Adams and Merrill, ‘Policy-Seeking Parties in a Parliamentary Democracy’. A result for two-party elections, that reaches the same conclusion as the CVE theorem, can be found on pp. 430–1 of Serra, ‘Polarization of What?’

³⁶ Note that this CVE result appears contrary to the extremist underdog result that Groseclose presents in ‘A Model of Candidate Location when One Candidate Has a Valence Advantage’, which states that valence-disadvantaged candidates have policy-seeking incentives to present more radical positions than their valence-advantaged competitors. As discussed in Adams and Merrill, ‘Policy-seeking Parties in a Parliamentary Democracy’, the contrast between the Adams–Merrill CVE result and Groseclose's extremist underdog result reflects the fact that in Groseclose's model electoral uncertainty centers on the median voter's position, whereas in the Adams–Merrill model uncertainty is over the parties’ short-term valence images.

³⁷ Note that quadratic loss is a concave function, as specified in the model. As discussed in Adams and Merrill, ‘Policy-Seeking Parties in a Parliamentary Democracy’, the policy salience parameter a = 0.25 is suggested by empirical studies on voting (see, e.g., Tables 4.1, 6.3 and 9.3A in Adams, Merrill and Grofman, A Unified Theory of Party Competition). We note that realistic variations in the specified value of a did not substantially affect the parties’ equilibrium positions (decreasing a resulted in somewhat more dispersed equilibrium positions and increasing a somewhat depressed party dispersion). With respect to variations in the other model parameters used for our examples, we found that: (1) Results for linear loss utility for parties were similar to those for quadratic losses, but somewhat more dispersed; (2) Results for larger party systems (i.e. more than four parties) were somewhat more dispersed. Results for alternative sets of assumptions about the parties’ valence images are reported below.

³⁸ Nash equilibrium strategies are determined by modifying a focal party's strategy in steps of 0.001 on the full scale from 1 to 7, while the strategies of the other parties are held fixed, and repeating this process for each party as the focal party in a cyclic fashion until no further change in strategies are observed. A systematic investigation strongly supporting the existence and uniqueness of Nash equilibria is reported in the section on simulation analysis below.

³⁹ Note that this grouping into opposing blocs occurs despite the fact that in our illustrative examples, the parties’ sincere policy preferences are evenly spaced along the Left–Right dimension.

⁴⁰ Readers may wonder why the strategic imperatives relating to collective responsibility delineated in this paragraph do not motivate Party B to significant moderate its policies, in order to improve its electoral standing vis-à-vis its coalition partner, Party A. The answer is that, first, Party A's optimal strategy s_A * is similar to Party B's preferred position R_B = 3, so that B has little incentive to moderate its strategy s_B * in order to improve its electoral standing vis-à-vis Party A (by contrast, B's optimal strategy is spatially distant from A's preferred position R_A = 1, so that A has stronger incentives to improve its electoral standing vis-à-vis Party B). Secondly, in the examples we investigate here the governing Party B is already in a strong electoral position vis-à-vis Party A due to its greater proximity to the median voter position, and so experiences less strategic pressure to further moderate its position.

⁴¹ See supplementary materials available at: http://journals.cambridge.org/action/displayJournal?jid=JPS.

⁴² Note that the reduction in the governing parties’ prospects of being MPP, as collective responsibility increases, occurs despite the fact that Party A significantly moderates its equilibrium policies when collective responsibility is high. If A did not moderate its position in response to increases in r_AB , its likelihood of being MPP would decline even more sharply.

⁴³ Kenneth Train, Qualitative Choice Analysis, Cambridge, Mass: MIT Press, 1986)Google Scholar

⁴⁴ Substantively, the values V_A = V_B = 1, V_C = V_D = 0 imply that when all the parties are equidistant from the median voter's position (and r_AB = 0), then the probability that one of the governing parties (A or B) will be MPP is about 0.73.

⁴⁵ Adams and Merrill, ‘Policy-Seeking Parties in a Parliamentary Democracy’.

⁴⁶ The values V_A = V_D = 0, V_B = V_C = 2 imply that when all the parties are equidistant from the median voter's position (and r_AB = 0), then the probability that either B or C will be MPP is about 0.88.

⁴⁷ Adams and Merrill, ‘Policy-Seeking Parties in a Parliamentary Democracy’.

⁴⁸ All three aberrant scenarios occurred when the collective responsibility coefficient r_AB was high (above 0.8) and the valence of one coalition partner was very low relative to that of the other coalition partner, resulting in an extremely flat utility function for the low valence party and an unstable calculated optimal strategy for that party.

⁴⁹ In all five of the scenarios in which different starting values led to distinct computed strategies for a party, the parties’ computed equilibrium positions for different starting points differed by less than 0.07 units along the 1–7 scale. In each of these five cases the value of r_AB was high and the valences of the coalition partners A and B were highly disparate.

⁵⁰ Adams and Merrill, ‘Policy-Seeking Parties in a Parliamentary Democracy’.

⁵¹ See, e.g., Strøm, Minority Government and Majority Rule.

⁵² Adams, James, Clark, Michael Ezrow, Lawrence and Glasgow, Garrett, ‘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), 513–529 CrossRefGoogle Scholar

Spoon, Jae-Jae, Political Survival of Small Parties in Europe (Ann Arbor: University of Michigan Press, 2011)CrossRefGoogle Scholar

⁵³ Fortunato and Stevenson, ‘Perceptions of Partisan Ideologies’.

⁵⁴ We thank an anonymous reviewer for drawing our attention to this point.

⁵⁵ We thank Hugh Ward for drawing our attention to this issue.

⁵⁶ Norpoth, Helmut, Lewis-Beck, Michael and Lafay, Jean-Dominique, eds, Economics and Politics: The Calculus of Support (Ann Arbor: University of Michigan Press, 1991)Google Scholar

⁵⁷ Allen, Nicholas and Bartle, John, eds, Britain at the Polls 2010 (London: Sage, 2011)CrossRefGoogle Scholar

⁵⁸ Adams, James, ‘Policy Divergence in Multicandidate Probabilistic Spatial Voting’, Public Choice, 99 (1999), 259–274 CrossRefGoogle Scholar

⁵⁹ The central intuition underlying Adams's result is that when two governing parties, say parties A and B for instance, share collective responsibility for valence-related events, then, if they converge to similar policy positions, they will tend to split the votes of the same group of supporters – i.e. most voters who prefer Party A to the rival parties C and D will also prefer Party B to parties C and D. Thus, in this example the collectively responsible parties A and B have electoral incentives to diverge in the policy space, so as to draw support from different voting constituencies. However, when A and B are policy-seeking this strategic incentive no longer applies, because policy-seeking parties cannot rationally announce policies that diverge too sharply from their sincere policy beliefs, at least in situations where they are obligated to fulfil their pre-election promises in the event they gain power, as we assume in our model.

⁶⁰ Train, Qualitative Choice Analysis.