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Does Collective Responsibility for Performance Alter Party Strategies? Policy-Seeking Parties in Proportional Systems

Published online by Cambridge University Press:  14 May 2012


Adams and Merrill have developed a model of policy-seeking parties in a parliamentary democracy competing in a PR electoral system, in which party elites are uncertain about voters’ evaluations of the parties’ valence attributes such as competence, integrity and charisma. This article extends that model to situations where voters hold coalitions of parties collectively responsible for their valence-related performances, such as how voters evaluate governing parties’ competence in handling issues like the economy, crime and foreign policy crises. It may also be relevant to voters’ evaluations of proto-coalitions of opposition parties. Computations suggest the central substantive conclusions reported in Adams and Merrill extend to this generalized model, and that collective responsibility enhances coalition members’ incentives to converge to similar policy positions but depresses their prospects of achieving their policy objectives.

Copyright © Cambridge University Press 2012

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Department of Political Science, University of California – Davis (email:; Department of Government, University of Essex (email:; Department of Mathematics and Computer Science, Wilkes University; and Department of Political Science, Vanderbilt University, respectively. The authors wish to thank three anonymous reviewers for valuable comments on an earlier version of this article. An online appendix with supplementary materials is available at


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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.

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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 sA * is similar to Party B's preferred position RB = 3, so that B has little incentive to moderate its strategy sB * 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 RA = 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:

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 rAB , its likelihood of being MPP would decline even more sharply.

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44 Substantively, the values VA = VB = 1, VC = VD = 0 imply that when all the parties are equidistant from the median voter's position (and rAB = 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 VA = VD = 0, VB = VC = 2 imply that when all the parties are equidistant from the median voter's position (and rAB = 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 rAB 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 rAB was high and the valences of the coalition partners A and B were highly disparate.

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

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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.

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