Incoherent Equality

I’ve pointed to James Buchanan’s attempt to apply an incoherent notion of generality to constitutional law. This principle of generality is really what people mean by “equality before the law”. In a review of Politics by Principle, Not Interest by Buchanan and Roger Congleton, Anthony de Jasay gently, but thoroughly, shreds the principle.

Consider taxation: The principle of generality, or equality before the law, posits that all individuals should be taxed equally. That sounds pleasing to many. Unfortunately the principle can give us no guidance on what such generality or equality needs to look like. Does a poll tax where every citizen pays an equal sum satisfy equality before the law? How about a flat tax on income where every citizen pays an equal percentage? But then again, why a tax on income instead of total wealth? Or why not a tax where every citizen is left with an equal income after taxes?

Which of these proposed polices satisfies the principle of equality before the law? Sober reflection reveals that the principle provides no standard by which one may choose between these polices – any ranking of the policies depends on an entirely subjective understanding of equality which has nothing to do with equality before the law.


Although the “treat like cases alike” meaning of generality is no more than a tautology for “apply the rule,” the “non-discrimination” meaning clearly does not bear pushing anywhere near its logical limit – a telling sign that it has some defect that comes to light when the meaning comes to be stretched a little. In fact, Buchanan and Congleton are far too intelligent not to sense this problem. They are fairly diffident about providing a working definition that would tell us, in every case, what rule would pass for general.

In one basic case, though, they are perfectly confident about what rule would be the truly general one. This case is the two-person (or two-coalition), two-strategy game of benefit- or burden-sharing, as exemplified by Hume’s farmers digging a drainage ditch. A two-by-two matrix describes four alternative allocations of the workload. Along what the authors call the diagonal, both farmers dig for two days or neither digs. Along the off-diagonal, either one digs for three days and the other for one, or the other way round. Which of the two off-diagonal, asymmetrical alternatives is the actual solution depends on which “farmer” is enabled by the political choice mechanism to coerce the other. A rule applied to this type of case is general if it outlaws the off diagonal solution, so that only the symmetrical, equal-sharing solutions remain available.

Both farmers work the same length of time. Obviously, the Pareto-optimal solution among all the symmetrical ones is that they should both work as long as it takes to complete the ditch; but this is not the point. The point is that generality has been found to reside in symmetry. From here, a promising avenue seems to lead toward a more developed form of generality. The simple version of the rule would say that the farmers, when placed in the circumstances described, should dig the same number of days, preserving one kind of equality, albeit a rather rudimentary one.

However, there is no compelling reason why equality of days worked should be regarded as the best, let alone the sole valid criterion of symmetry. If one farmer is frail, old, or arthritic, or if one has a higher opportunity cost because when he digs he cannot attend to the calving or lambing, or if his end of the ditch has a nasty, sticky, clayey patch, then a rule laying down equality of labor time might well be held to produce asymmetrical shares of pain or cost. Likewise, it might also be argued that symmetry calls for labor time to vary inversely with productivity or directly with the benefit each farmer will derive from the drained meadow. Symmetry in the relevant variable must prevail, but why is labor time the relevant variable rather than pain, productivity, opportunity cost, benefit, or something else?

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