Hostname: page-component-7479d7b7d-pfhbr Total loading time: 0 Render date: 2024-07-10T11:26:06.066Z Has data issue: false hasContentIssue false
  • English
  • Français

The Bargaining Advantages of Combining with Others

Published online by Cambridge University Press:  27 January 2009

Michael Laver  and
John Underhill
Get access Rights & Permissions [Opens in a new window]

Extract

It is well-known that power relations can exhibit a ‘one plus one equals three’ effect. Two or more units can fuse into a bloc which has more power than the component units before had between them. The most obvious example of this type of synergy (whereby the whole is greater than its constituent parts) would be three people bargaining over the distribution of a fixed kitty, and needing a simple majority to impose any outcome. The three actors can, in the long run, expect one-third of the kitty (and can be thought of as having one-third of the power). If two combine into a single bloc, they will win every time. The new bloc controls all of the power (⅓ + ⅓ → 1) and its constituent members' expectations each increase to half of the kitty. Notwithstanding this, it is by no means the case that all combinations of units into blocs increase either aggregate power or individual expectations. Some combinations can result in a loss of power, although examples of this are slightly more complex, and depend upon some formal index of power for their elucidation. Thus, in the real world of coalition politics, the government coalition which actually forms controls all of the power as a bloc, despite the fact that coalition members do not control all of the power between them if they go it alone. Conversely, two parties can sometimes lose power by combining, particularly when they face a dominant opponent not far short of an overall majority.

Type
Research Article
Information
British Journal of Political Science , Volume 12 , Issue 1 , January 1982 , pp. 27 - 42
Copyright
Copyright © Cambridge University Press 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 See Brams, Stephen, Game Theory and Politics (New York: Free Press, 1975), for further discussion of this.Google Scholar

2 Using the Shapley-Shubik index discussed below, the game (49, 17, 17, 9, 8) gives the actors power indices of (·4, ·15, ·15, ·15, ·15). If the two smallest actors combine to produce (49, 17, 17, 17), the power indices are (·5, ·17, ·17, ·17). In other words, ·15 + ·15 → ·17, a loss of power.

3 See Laver, Michael, The Politics of Private Desires (Harmondsworth, Middx.: Pelican Books, 1981).Google Scholar

4 See Barry, Brian, ‘Is it Better to be Powerful or Lucky?’ Political Studies, XXVIII (1980), 183–93 and 338–52CrossRefGoogle Scholar; and Morriss, Peter, Power: A Philosophical Analysis (doctoral thesis, University of Manchester, 1978).Google Scholar

5 See Luce, R. D. and Raiffa, H., Games and Decisions (New York: Wiley, 1957), for a review of the mathematical properties of this index.Google Scholar

6 See Morriss, , Power, for an elaboration of this distinction.Google Scholar

7 See, for example, Brams, , Game Theory and Politics.Google Scholar

8 See Laver, Michael, Making Threats That People Believe (paper presented to the Political Studies Association, Hull, 1981)Google Scholar for a fuller discussion of precisely this case.

9 These, of course, correspond to two prominent categories in nearly all typologies of party systems.

10 One important non-random element that should create a greater diversity of systems than these stable states suggest concerns the interaction between any given fusion of parties and votes gained at the subsequent election. On a Downsian model, for example, two parties with two policy positions must get more votes than one combined party with a single policy position. In party competition, therefore, fusions of parties may result in a subsequent loss of weight. The process may stop short of the ideal stable states because no fusion looks attractive given the problem of electoral losses. The extent to which this will be a factor will depend on the precise distributions of electoral opinion and party policy in any given system, however. Knowing this distribution may enable us to explain any given configuration of parties, but it does not detract from the pressures exerted on party competition by the dynamics of bargaining.

11 Riker, William, ‘A Test of the Adequacy of the Power Index’, Behavioural Science, IV (1959), 276–90.Google Scholar

12 We are indebted to Peter Morriss for pointing out the analogy with the Prisoner's Dilemma.