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Published online by Cambridge University Press: 27 January 2009
Axelrod has demonstrated the equivalence of a measure of structural propensity to conflict, based on game-theory and applicable to certain types of social interaction, and spatial conceptions of policy agreement. However his spatial model rests on assumptions of interval status not commonly met by data from which consensual interpretations have evolved and against which they have been tested. The generality and rigour of consensual explanations of democratic stability can be enhanced by integration with Axelrod's framework. At the same time consensus hypotheses focus on a question left unanswered by game-theoretic formulations: why do democratic political games continue to be played by existing rules? Following Axelrod's recommendation to integrate conflict of interest with other bodies of theory, 1 this paper assesses points of contact between Axelrod's discussion and one line of consensual reasoning, extends the equivalence between conflict of interest and policy agreement to all levels of measurement, and details the contributions which game-theoretic and consensual formulations can make to each other.
1 Axelrod, Robert, Conflict of Interest (Chicago: Markham, 1970).Google Scholar
2 A variety of other factors have been hypothesized to produce conflictful behaviour independently of conflict of interest, e.g. factual misperceptions, personality factors and social differences: Axelrod, , Conflict, p. 7.Google Scholar Thus incompatibility of goals and conflictful behaviour are not synonymous and the presumed connection is neither trivial nor semantic.
3 Axelrod, , Conflict, pp. 70–1.Google Scholar
4 Axelrod, , Conflict, pp. 158–63.Google Scholar
5 Axelrod, , Conflict, pp. 110–12.Google Scholar
6 Axelrod, , Conflict, pp. 129–35.Google Scholar
7 Axelrod, , Conflict, p. 150.Google Scholar
8 Axelrod, , Conflict, pp. 148–51 and section 1 below.Google Scholar
9 Dahl, R. A., Who Governs? (New Haven: Yale University Press, 1961) pp. 94–5Google Scholar; Budge, Ian, Agreement and the Stability of Democracy (Chicago: Markham, 1970), Chaps. 2, 4–5, 7, 9Google Scholar; Budge, Ian, Brand, J., Margolis, M., Smith, A. L. M., Political Stratification and Democracy (London: Macmillan, 1972), Chap. 5.CrossRefGoogle Scholar
10 Continuous because even if the range is not originally continuous (consisting of expenditure decisions for example) originally discrete outcomes can be made continuous by randomization, e.g. associating different outcomes with the fall of dice (Axelrod, , Conflict, p. 21Google Scholar).
11 Axelrod, , Conflict, pp. 56, 110–12.Google Scholar
12 There are of course other complications in the measurement which cannot be discussed in detail here. For example, the boundary line may be kinked not straight. But such problems can be relatively easily overcome (Axelrod, Conflict, Chaps. 1 and 2).
13 Axelrod, , Conflict, p. 149.Google Scholar Discussion here is based on Axelrod's Chap. 7.
14 Axelrod, , Conflict, p. 151.Google Scholar
15 R. A. Dahl, Who Governs? Chap. 28; Dahl, R. A., ed., Political Oppositions in Western Democracies (New Haven: Yale University Press, 1966), Chap. 12, especially p. 381Google Scholar; Dahl, R. A., Pluralist Democracy in the United States (Chicago: Rand McNally, 1967), pp. 280–1Google Scholar; Budge, Agreement, Chaps. 1, 2, 12; Budge et al.. Political Stratification.
16 Dahl, R. A., Preface to Democratic Theory (Chicago: University of Chicago Press, 1957), p. 89Google Scholar, gives the ten conditions which this definition summarizes.
17 Neubauer, D. E., ‘Some Conditions of Democracy’, American Political Science Review, LXI (1967), 1002–9.CrossRefGoogle Scholar
18 Dahl, R. A., Who Governs? p. 311Google Scholar; Budge, Agreement, Introduction.
19 E.g. Axelrod, , Conflict, pp. 20–1.Google Scholar
20 This line of research was initiated by Stouffer, S., Communism, Conformity, and Civil Liberties (New York: Doubleday, 1955).Google Scholar The findings reported here are drawn chiefly from J. Prothro and C. M. Grigg, ‘Fundamental Principles of Democracy’, and Mcclosky, H., ‘Consensus and Ideology in American Polities’, in Cnudde, C. and Neubauer, D. E., eds., Empirical Democratic Theory (Chicago: Markham, 1969), pp. 236–52 and 268–302.Google Scholar
21 Budge, Agreement, Chaps. 8 and 9.
22 Critics and criticism are cited in Budge, , Agreement, pp. 16–18, 26–9.Google Scholar
23 Budge, , Agreement, p. 18.Google Scholar
24 Cnudde has commented that American survey evidence of less than 50 per cent support for specific democratic procedures does not invalidate the idea that popular opinion support of democratic procedures is necessary for democraticstability: Cnudde, C., ‘Elite-Mass Relationships and the Democratic Rules of the Game’, American Behavioral Scientist, XIII (1969).Google Scholar Accepting this point it still remains true that opinion support is not distributed randomly but correlates highly with characteristics like political activity. Recognition of the necessary supportive role of those moderately active thus meets Cnudde's point. The opinion support given by low level activists in Britain is investigated in Budge, Agreement, Chap. II.
25 Propounded in R. A. Dahl, Who Governs? Chap. 28 and Key, V. O., Public Opinion and American Democracy (New York: Knopf, 1963), pp. 546–56Google Scholar, on the basis of Prothro and Grigg's work.
26 Because of the greater predisposition of activists to act in any political sphere and the relationship between activism and opinion support, the connection is not symmetrical: i.e. opinion support is more likely to prompt pro-democratic action, in a stable democracy, than opinion opposition is to prompt anti-democratic action.
27 Mcclosky, , in Cnudde, and Neubauer, , eds., Empirical Democratic Theory, p. 284.Google Scholar
28 It is made by Dahl, in Political Oppositions in Western Democracies, p. 381Google Scholar, and Pluralist Democracy in the United States (Chicago: Rand McNally, 1967), pp. 280–1.Google Scholar The point is expanded in Budge, , Agreement, pp. 28–30, 40 –1.Google Scholar
29 Axelrod, , Conflict, pp. 65,70,104,119–20.Google Scholar
30 Axelrod, , Conflict, p. 150.Google Scholar The assumption is necessary in the game-theoretical context to ensure that every participant has some interest in bargaining with others. As applied to a societal distribution of preferences it takes the form noted below, of assuming that revolutionary or antisystem behaviour is absent, or at least unimportant. This is not of course to assume that revolutionary behaviour is unimportant either for Axelrod or consensus theorists: simply that both are assuming a context – a bargaining situation in stable democracies – in which such behaviour is, by definition, currently unimportant. While conflict of interest reasoning could relate to revolutionary behaviour in another context, this part of its theory does not deal with it.
31 Axelrod uses the Connecticut Supreme Court's threat to redistrict the state itself if the party politicians could not come to an acceptable compromise as a similar no-agreement point in a real political situation: Axelrod, , Conflict, pp. 4, 7–8.Google Scholar
32 The amazing survival of Belgium is a case in point. Immobilisme in many functioning democracies (Italy, the Fourth Republic in France) may be used as an objection to this argument. However both these polities display much anti-system behaviour, so the consensual explanation does not purport to cover these cases. On the other hand it does cover the stable multi-party systems so far as it goes. Another objection is that politicians’ ability to reach agreed outcomes is used as an explanation of their support for democratic procedures, while their support is concurrently used to explain their ability to reach agreed outcomes. The connection is not tautologous, however, for such a mutually reinforcing effect is quite likely empirically and proposition 2 allows for a twoway flow of influence.
33 Budge et al., Political Stratification, Chap. I.
34 Irreconcilable disagreement being defined in this context as relatively equal numbers endorsing policy alternatives which cannot be pursued simultaneously, so that one side or the other must lose completely. This has obvious affiliations with maximum conflict of interest in Axelrod's argument, which we shall consider below.
35 Budge, Ian and O'leary, C., ‘Cross-cutting Cleavages, Agreement and Compromise’, Midwest Political Science Review, XV (1971), 1–30;Google Scholar Budge, Agreement, Chap. 6; Budge et al., Political Stratification, Chaps. 2, 5, 7; Mcclosky, et al. , ‘Issue Conflict and Consensus among Party Leaders and Followers’ American Political Science Review, LIV (1960), 406–27CrossRefGoogle Scholar, finds greater division on socioeconomic and welfare issues among delegates to the party conventions than in a sample of the American population. However activist divergence was not great compared to what one might expect to find in less stable systems. Also issues were defined as those in conflict between the parties, which means that activists would tend to be more disagreed than on other issues.
36 Budge, Agreement, Chaps. 6, 7, 9; Budge et al., Political Stratification, Chap. 5.
37 Budge et al., Political Stratification, Chap. 6.
38 Previous studies are summarized and new results reported in Taylor, M. J., ‘Towards a Mathematical Theory of Influence and Attitude Change’, Human Relations, XXI (1968), 121–39.CrossRefGoogle Scholar
39 The fact that conflict of interest can be measured for Nash's bargaining game and for the Prisoner's Dilemma encourages attempts at comparison although Axelrod does not commit himself to this position. The possibility of losing more than one's starting utility in the Prisoner's Dilemma together with absence of communication, clearly shows it is a different game, referring to different political situations. However we commonly attempt to apply the same measures (agreement, cross-cutting, inequality) to different situations on the assumption that differences in resulting values are not due to the non-comparability of the situations but are instead substantive differences which account for the differing situations. For example, when we claim that cross-cutting in stable polities is higher than cross-cutting in unstable polities we implicitly assume that the measure of cross-cutting can be applied impartially to both. If we made the more modest assumption that measures were affected by different situations, and thus non-comparable across them, we should be abandoning much of empirical political science. With this general consideration in mind it does seem possible to view the normalization of the two games proposed by Axelrod as creating a comparable space. In both games the (0,0) point is the starting utilities of the players, and (1,1) is the best they can respectively do from the game. The fact that a player can fall below (0,0) on the final outcome of the Prisoner's Dilemma, and cannot do this in Nash's bargaining game, does not affect the normalization itself, and hence the comparability of conflict of interest across the two games. Only, conflict of interest will always be higher in Prisoner's Dilemma than in Nash's game – as, given the nature of the situation, it should be. Conversely, when used in data analysis, a higher conflict of interest in one situation compared with a lower value in another should alert us to the possibility of modelling the first situation by Prisoner's Dilemma and the second by Nash's game. On conflict of interest in the two types of game cf. Axelrod, , Conflict, pp. 46, 64.Google Scholar Axelrod also notes (p. 56), ‘An expansion of feasible agreements will lower conflict of interest provided that the maximum each player can hope to achieve is not raised.’ This is what happens in the transition from Prisoner's Dilemma to Nash's game, since the latter permits randomization and hence expansion of feasible agreements without raising the maximum.
40 An extensive comparison of communication among these groups has been made in Budge et al., Political Stratification, Chap. 4.
41 Apart from the different type of game played by activists, constant communication is likely, other things being equal, to modify their conflict of interest in various areas over time independently of their policy disputes. M. J. Taylor, ‘Towards a Mathematical Theory’; Axelrod, , Conflict, p. 196Google Scholar, notes the importance of these processes.
42 Budge, Agreement, Chaps. 6, 9.
43 On the importance of these points for establishing the applicability of his model see Axelrod, , Conflict, pp. 102–3.Google Scholar
44 This strategy is suggested by Stokes, D. E., ‘Spatial Models of Party Competition’, American Political Science Review, LVII (1963), 368–77.CrossRefGoogle Scholar Axelrod likewise suggests treating extent of information as a variable (pp. 89–90). Information seems similarly to vary with activism: Budge, , Agreement, pp. 81–2, 88Google Scholar; Budge et al., Political Stratification, Chaps. 3, 4.
45 Axelrod, , Conflict, p. 7.Google Scholar
46 Budge et al., Political Stratification, Chap. 2, gives findings on this point for Glasgow which have been replicated in Belfast.
47 Rae and Taylor point out that high cross-cutting depends on at least a moderate degree of diversity, rather than agreement, on preferences on the two cleavages which cross-cut each other. Taylor, M. and Rae, D., ‘Analysing Crosscutting between Cleavages’, Comparative Politics, I (1969), Sect. 3 (IV) and Sect. 5.Google Scholar
48 Axelrod, , Conflict, p. 161, words in brackets inserted.Google Scholar The weights are suggested as being proportional to the importance of each group to that individual.
49 However in the case of opinion agreement on nominal policy alternatives, considered below, membership of groups with different preferences could not result in the averaging of these preferences. Individuals in this case are likely either to withdraw or decide to follow the lead of the group most important to them. In this case cross-cutting would not affect opinion agreement.
50 Axelrod, , Conflict, p. 150.Google Scholar
51 Leik, R. K., ‘A Measure of Ordinal Consensus’, Pacific Sociological Review, IX (1966), 85–90.CrossRefGoogle Scholar
52 Leik, , ‘A Measure of Ordinal Consensus’, pp. 85, 87.Google Scholar
53 Leik, , ‘A Measure of Ordinal Consensus’, pp. 86–7.Google Scholar
54 Axelrod, , Conflict, p. 147.Google Scholar
55 However when D is normalized, Leik demonstrates its equivalence to an analogous measure of interval dispersion based on variance. For the case of maximal dispersion (0·5 of the group at opposite ends of the policy continuum) Max where m is the number of ordinal points on the continuum. Thus the normalized. An analogous normalized measure of interval agreement is. For m categories, assuming I unit intervals, Leik shows max equal to. This normalized interval. The close resemblance between these measures of ordinal and interval dispersion is reinforced by an empirical comparison which shows them to be broadly monotonic, although in the middle ranges the variance-based measure varies around the ordinal by up to half its value. Since Axelrod demonstrated the equivalence between conflict of interest and variance, these correspondences between the variance-based and ordinal measure strengthen the case for regarding the latter as a good estimate of conflict of interest at its own level of measurement.
56 It is of course true that may carry a different meaning for different ordinal policy-dimensions, even when it assumes the same numeric value. For different dimensions may vary in the distances separating the ordinal ranks – the reason that such dimensions are ordinal rather than interval is that the precise distances are unknown. However, comparisons of agreement on the same policy dimension can be made between different groups. And where there is evidence that the distances between ranks, though unknown, are approximately equal, Leik's measure can be used to compare agreement or conflict of interest between different policy dimensions.
57 Rae, D. and Taylor, M. J., The Analysis of Political Cleavages (New Haven: Yale University Press, 1970).Google Scholar
58 Analysts of consensus have usually used the percentage endorsing one alternative as a measure of agreement; cf. Prothro and Grigg, and McClosky, in Cnudde and Neubauer, eds., Empirical Democratic Theory. The percentage difference between endorsements has also been used: Budge, Agreement, Chap. 3. All these percentage-based measures try to gauge the extent of clustering on one alternative as opposed to others which is caught more exactly by F, and can be given the same interpretation as assessments of potential utility loss.
59 For an assessment of the advantages of allowing respondents to answer unrestrictedly see Budge, Agreement, Chaps. 3, 6 and Appendix A.
60 Averaging F over all possible preferences does not give the important information as to whether the mixed pairs on each dichotomy in the distribution consist of the same or different individuals which otherwise less flexible percentage differences do: Budge, Agreement, Chap. 3. Tendencies for the set of individuals to fall into two mutually exclusive groups over the whole range could, however, be captured in the measure of cross-cutting based on F, described in D. Rae and M. J. Taylor, The Analysis of Political Cleavages, Chap. 3.