¹ Barry, Brian, British Journal of Political Science, VII (1977), 99–113, 217–53CrossRefGoogle Scholar. All further references to these articles will be accompanied by the appropriate page number in the text.

² Taylor, Michael, ‘The Theory of Collective Choice’, in Greenstein, Fred I. and Polsby, Nelson W., eds., Handbook of Political Science (Reading, Mass.: Addison-Wesley, 1975), p. 469.Google Scholar

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⁴ Lipset, S. M., ‘Some Social Requisites of Democracy’, American Political Science Review, LIII (1959), 69–105.CrossRefGoogle Scholar

⁵ Almond, Gabriel A., Flanagan, Scott C. and Mundt, Robert J., eds., Crisis, Choice, and Change: Historical Studies of Political Development (Boston: Little, Brown, 1973), pp. 12, 28, 49, 59, 65 and 627.Google Scholar

⁶ Adrian, Charles and Press, Charles, ‘Decision Costs in Coalition Formation’, American Political Science Review, LXII (1968), 556–63.CrossRefGoogle Scholar

⁷ Flanagan, Scott C., ‘Theory and Method in the Study of Coalition Formation’, Journal of Comparative Administration, V (1973), 267–314.CrossRefGoogle Scholar

⁸ For instance in the Indian case, endemic environmental crises (war, famine, communal conflict) do not engender a systemic crisis; discontent is quarantined, and the polarization among elite actors remains low. Thus issues do not cumulate, but are isolated with different coalition configurations resolving each. The principal contenders are factional alignments within the ruling party, whose compositions differ from issue to issue to the point of noncomparability. Winning affects policy but not the composition of government. Obviously, then, this case deviated in many fundamental ways from the kind of coalition game that our model was designed to analyze.

⁹ Flanagan, , ‘Models and Methods of Analysis’, in Crisis, Choice, and Change, p. 57.Google Scholar

¹⁰ Flanagan, in ‘Theory and Method’, pp. 273–7.Google Scholar

¹¹ Flanagan, in ‘Theory and Method’, p. 297.Google Scholar

¹² Flanagan, in ‘Theory and Method’, pp. 298–308.Google Scholar

¹³ In addition to the seven case studies that appeared in Crisis, Choice, and Change, an eighth case study was conducted which constituted a more extensive treatment of the project's analytic approach, taking a series of crucial choice points in the political development of Japan from 1912 to 1941, with special attention to the fall of party government in the early 1930s. Flanagan, Scott C., ‘Crises in the Political Development of Modern Japan: 1880–1945’ (Ph.D. dissertation, Stanford University, 1971).Google Scholar

¹⁴ Our two central measures were designed to evaluate the utility each member feels he would derive from membership in a given coalition and the capacity to rule or ruling potential of the coalition. A member's utility score is a function of his share of the total resources held by the coalition (his weight within the coalition) and his perception of the extent to which the other coalition members agree or disagree with his policy preferences. A coalition's ruling potential is a function of (1) its resource strength, (2) its internal agreement on the issues, and (3) the size and intensity of the opposition. Barry, however, was clearly confused by all the transformations and terms employed in Appendix C of Crisis, Choice, and Change. Many of the transformations were employed either to simplify the computation procedures required of the contributors or simply to produce aesthetically more pleasing ranges and intervals. A number of terms such as CDS (coalition desirability scores), PP (performance potential), OD (opposition distance) and NVP (nonincumbent veto potential) were manufactured to keep the separate steps in the calculation procedures straight in the user's mind. These labels represent only intermediary steps in our calculation procedures and have no intrinsic meaning by themselves. For some reason, however, Barry has chosen to consider them as fully independent additional coalition measures. Thus, for instance, he attacks the ability of the PP term to discriminate levels of coalition effectiveness. Naturally the PPterm cannot accomplish this without being combined with the other terms in the ruling potential formula. So while he does provide an example of a situation where the PP term would be equivalent for coalitions with one-half and one-fifth of the resources, the ruling potentials of the two would clearly not be equivalent, and he could devise no example in which his coalition with only one-fifth of the resources would emerge with the highest or even with a credible ruling potential score. (Barry, , p. 223.)Google Scholar

¹⁵ For instance, most game theoretic models assume that a coalition and its complement cannot both be potential coalitions. That is, in a four-player game coalitions AB and CD cannot both be counted as possible winning coalitions. But in the context of crisis, where fixed parliamentary decision rules do not obtain, this constraint no longer holds. In fact, in highly polarized situations the principal contest may be between a coalition and its complement (AB versus CD). We were thus faced with the need to modify the notion of dominance to avoid situations in which both coalitions would mutually dominate and thereby eliminate each other. Thus in our formulation a coalition is dominated by a second only if all contenders who are members of both coalitions prefer the second to the first. Barry's attack on our failure here to conform to standard procedures simply misses the point, as do his other criticisms of our procedures for isolating the preferred set. (See Barry, , pp. 232–5.)Google Scholar

¹⁶ For instance, Barry suggests that it would be more theoretically coherent if we dispensed with ruling potential as an independent measure of the strength and effectiveness of a coalition and rather allowed ‘the strength of a coalition to affect its utility to its members’. Certainly this could be done, but we fail to see how jacking up utility scores for stronger coalitions is an improvement over eliminating weaker coalitions on the grounds of ineffectiveness. The results would be much the same and it seems to us better to keep the criteria of coalition attractiveness and coalition effectiveness separate, since it is often precisely this kind of strategic trade-off that the contenders have to grapple with. (Barry, , p. 225.)Google Scholar

¹⁷ While Barry is apparently unaware of the fact, models that base the players' weights on their pivotal position (their ability to make non-winning coalitions winning) were elegantly elaborated by Lloyd Shapley and Martin Shubik many years ago. See, for example, Shapley, and Shubik, , ‘A Method for Evaluating the Distribution of Power in a Committee System’, American Political Science Review, XLVIII (1954), 787–92.CrossRefGoogle Scholar

¹⁸ Having been convinced by his own logic, Barry wonders aloud why it is that the Free Democrats in Germany do not have an equal number of cabinet posts in relation to the Social Democrats, since they hold the balance of power. This example illustrates the absurdity of claiming that all members who by withdrawing can make a winning coalition nonwinning possess an equally credible threat and have an equal claim on the winnings. Clearly the criterion of replaceability needs to be added here, and it is quite obvious that small members are much more easily replaced than large members. It is also apparent that large members bring more to the coalition in the way of leadership, power, legitimacy, etc., and hence naturally draw more of the payoffs. See Shapley's ‘value added’ concept as a means of determining a player's weight in Shapley, L., ‘A Value of N-Person Games’, in Kuhn, H. W. and Tucker, A. W., eds., Contributions to the Theory of Games, Vol. II (Princeton, N.J.: Princeton University Press, 1953)Google Scholar. Barry also incorrectly assumes that all cabinet positions are equal in ‘value’.