The Bargaining Advantages of Combining with Others

Michael Laver and John Underhill

British Journal of Political Science, 1982, vol. 12, issue 1, 27-42

Abstract: 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.

Date: 1982
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