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Nested Games: The Cohesion of French Electoral Coalitions

Published online by Cambridge University Press:  27 January 2009

George Tsebelis
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Extract

This article introduces a theory of Nested Games which accounts for the cohesion of coalitions. The parties in a coalition are considered to be playing a game with variable payoffs. The payoffs depend on a higher-order game between the coalition and its opponents. Several political situations approximate to this conceptualization, such as Government and Opposition coalitions, factions inside parties, international coalitions, class conflict. The theory of Nested Games predicts the cohesion of coalitions as a function of the relative size of both the coalitions and the partners within each coalition.

The test case of the theory is the cohesion of French electoral coalitions in 1978. Empirical results corroborate the theory. All parties behave according to its predictions. Moreover, a difference in the way parties behave, according to whether the game is visible (by the electorate) or invisible, is discovered and explained.

Type
Research Article
Information
British Journal of Political Science , Volume 18 , Issue 2 , April 1988 , pp. 145 - 170
Copyright
Copyright © Cambridge University Press 1988

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References

1 See Riker, W., The Theory of Political Coalitions (New Haven, Conn.: Yale University Press, 1962)Google Scholar; Axelrod, R., Conflict of Interest: A Theory of Divergent Goals with Applications to Politics (Chicago: Markham, 1970)Google Scholar; Dodd, L., Coalitions in Parliamentary Government (Princeton, N.J.: Princeton University Press, 1976)Google Scholar; Luebbert, G., ‘Coalition Theory and Government Formation in Multiparty Democracies’, Comparative Politics, 15 (1983), 235–49.CrossRefGoogle Scholar

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3 Offe, C. and Wiesenthal, H., ‘Two Logics of Collective Action: Theoretical Notes on Social Class and Organizational Form’, Political Power and Social Theory, 1 (1980), 67–115Google Scholar, argue that this was the case for class conflict at the end of last century: capitalists did not need to organize at the national level. Elster, J., Making Sense of Marx (Cambridge: Cambridge University Press, 1985), p. 346Google Scholar, and Przeworski, A., ‘The Challenge of Methodological Individualism to Marxist Analysis’ in Birnbaum, P. and Leca, J., eds, Sur l' Indivualisme (Paris: Presses de la FNSP, 1985)Google Scholar, provide evidence that the Marxian conception of class struggle can be captured by this formal approach, since the force unifying each class is competition against another class. In other words, classes become classes against someone before they become classes for themselves.

4 See Chapsal, J. and Lancelot, A., La Vie Politique en France Depuis 1940 (Paris: Presses Universitaires de France, 1969).Google Scholar

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7 Several times, however, the passage of time has not been enough to heal the wounds and candidates have not endorsed their fellow-party runners, nor have activists of a defeated candidate in the primaries joined the other party (see Johnson, D. B. and Gibson, J. R., ‘The Divisive Primary Revisited: Party Activists in Iowa’, American Political Science Review, 68 (1974), 67–77.CrossRefGoogle Scholar

8 Figure 1 focuses on the internal divisions of the Left. If one wanted to examine the Right, then the dual triangular competition (between the Left, the Gaullists and the Giscardians) would be relevant. Generally, the appropriate space to represent electoral outcomes would be an n-dimensional Euclidian space (where n is the number of parties) and the corresponding n-1 dimensional simplex. The triangle of Figure 1 is in fact a two-dimensional simplex, or a barycentric system of coordinates.

9 Arguments can be made that (3) or (4) hold and that, therefore, the game is Chicken or Assurance. These modifications of the payoff matrix, however, while important by themselves, will not influence the subsequent results of this article (see Tsebelis, G., ‘An Algorithm for Generating Cooperation in a Prisoners' Dilemma Game’, Duke University Program in International Political Economy, Working Paper no. 7, 1986).Google Scholar

10 It is, however, useful to remember that all parameters are indexed by party and the value of an additional seat for Communists may be very different from that for Socialists. Consequently, all the comparative statements that follow concern the behaviour of the same party (under different expected outcomes) and not comparisons of different parties.

11 Axelrod, R., The Evolution of Cooperation (New York: Basic Books, 1984) pp. 202–3Google Scholar, and Smith, J. Maynard, Evolution and the Theory of Games (Cambridge: Cambridge University Press, 1982), pp. 207–8CrossRefGoogle Scholar, prove such propositions concerning the Prisoners' Dilemma game. Tsebelis, , ‘An Algorithm for Generating Cooperation in a Prisoners' Dilemma Game’Google Scholar, proves the proposition for all three games. The proof presupposes the possibility of correlated or contingent strategies, which is the case here since the two partners can adjust their strategies to each other over time.

12 Equation 5 can be formally derived as a Taylor series first-order approximation of the likelihood of mutual co-operation (that is cohesion), if one uses the chain rule, since the signs of the required first derivatives are given in the text. This remark indicates that one could increase the precision of approximation, and use non-linear estimation routines for the empirical part. However, since this approach is a first approximation, I shall not follow this direction here.

13 See Wright, V., The Government and Politics of France (New York: Holmes and Meier, 1983), p. 190.Google Scholar

14 Overseas Departments (DOM) and Territories (TOM) are omitted.

15 This operationalization presents a problem because it ignores vote transfers that do not appear on the aggregate level. For example, if the Socialist represents the Left in the second round, one can not discriminate between the following cases: (1) all Communists transfer their votes and (2) some Communists abstain, while some abstainers in the first round vote Socialist (or vote for the Right, while some votes from the Right are transferred to the Socialist). Unfortunately, there is no way to correct for such ecological fallacies with aggregate data. However, because of the polarized electoral climate, I do not think that the ‘invisibility’ of the aggregate transfers is very significant.

16 See Denis, N., ‘Les Elections Legislatives de Mars 1978 en Metropole’, Revue Française de Sciences Politiques, 28 (1978), 977–1005.CrossRefGoogle Scholar

17 See Jaffre, J., ‘The French Electorate in March 1978’ in Penniman, H. R., ed., The French National Assembly Elections of 1978 (Washington, D.C.: American Enterprise Institute, 1980).Google Scholar

18 With the additional dummy variable for the identity of the adversary.

19 It might be argued that OLS is not appropriate in this case, since the residuals may be correlated. However, the use of OLS will not bias the estimates, but will decrease their efficiency, making hypothesis-testing more conservative. Thus, if OLS coefficients turn out to be statistically significant, this holds a fortiori for the GLS coefficients.

20 See Lavau, G. and Mossuz-Lavau, J., ‘The Union of the Left's Defeat: Suicide or Congenital Weakness?’Google Scholar in Penniman, , ed., The French National Assembly Elections of 1978, p. 138.Google Scholar

21 See Jaffre, , ‘The French Electorate in March 1978’, p. 74.Google Scholar

22 See Rochon, T. R. and Pierce, R., ‘Coalitions as Rivalries: French Socialists and Communists, 1967–1978’, Comparative Politics, 17 (1985), 437–51, p. 493.CrossRefGoogle Scholar

23 For an extended comparison between their results and the results reported in this article see Tsebelis, G., ‘When Do Allies Become Rivals?’ Comparative Politics (forthcoming).Google Scholar

24 See Sartori, G., Parties and Party Systems: A Framework for Analysis (Cambridge: Cambridge University Press, 1976).Google Scholar

25 See Jensen, M. and Meckling, W., ‘Theory of the Firm: Managerial Behaviour, Agency Costs, and Ownership Structure’, Journal of Financial Economics, 3 (1976), 305–60CrossRefGoogle Scholar and Klein, B., Crawford, R. and Alchian, A., ‘Vertical Integration, Appropriable Rents, and the Competitive Contracting Process’, Journal of Law and Economics, 21 (1978), 297–326.CrossRefGoogle Scholar