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  • Print publication year: 2015
  • Online publication date: February 2015

6 - Two Dimensions: Elusive Equilibrium*


The nature of man is intricate; the objects of society are of the greatest possible complexity; and, therefore, no simple disposition or direction of power can be suitable either to man’s nature or to the quality of his affairs. When I hear the simplicity of contrivance aimed at and boasted of in any new political constitutions, I am at no loss to decide that the artificers are grossly ignorant of their trade or totally negligent of their duty…

The rights of men are in a sort of middle, incapable of definition, but not impossible to be discerned… Political reason is a computing principle; adding, subtracting, multiplying, and dividing, morally and not metaphysically, or mathematically, true moral denominations.

Edmund Burke, Reflections on the Revolution in France, 1790, Part IV

Equilibrium and the Middle

The previous chapter introduced the idea of “spatial” utility functions for choices along a single dimension, and laid out the solution of equilibrium at the median position. Now, we ask whether this notion of the “middle” also is a plausible result in more complex political spaces, with two or more dimensions. Burke’s claim is intriguing: Is the “middle” in complex political choices really “incapable of definition, but not impossible to be discerned”? Is the middle a general concept, or is it restricted to policy choices of one dimension?

To introduce the logic of the multidimensional spatial model, it is useful first to consider an example of a legislative committee. We will call this the “Appropriations Committee;” it is responsible for choosing a budget with two line items. That is, the budget will be sum of the spending on Policy 1 and spending on Policy 2. The choosers may have preferences on each policy, prefer one policy to another, or have a complex preference regarding how the two policies go together.

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Choosing in Groups
  • Online ISBN: 9781107707153
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