Conclusions
The link derived in Theorem 1 between centrality (relative to the yolk) and power (defined in Shapley-Owen terms) has important political implications. For example, if the policy is composed of interest groups, then any interest group whose ideal point falls far from the political “center” (defined as the center of the yolk) can have very little power in Shapley-Owen terms. Power is not only a function of the number of votes an interest group has, but it is also a function of its position. Centrally located interest groups have more power than peripheral ones.
In terms of policy positions, Shapley-Owen power refers to the power to move an outcome from one median line to another-shifts that are not likely to make much difference to the actor who is pivotal. However, if an actor can exact rents for being the pivotal actor, then these differences are important, and centrally located actors may be in the best position to derive non-policy benefits from having this ability to shift outcomes by a shift of their vote.
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Feld, S.L., Grofman, B. A theorem connecting Shapley-Owen power scores and the radius of the yolk in two dimensions. Soc Choice Welfare 7, 71–74 (1990). https://doi.org/10.1007/BF01832922
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DOI: https://doi.org/10.1007/BF01832922