Value Pluralism and Rational Choice

Abstract

Theorists skeptical of rational choice theories often base their doubts on the claim that values are plural and incommensurable. According to the value-pluralists, including Finnis, Pildes and Anderson, and Kronman, incommensurability implies that no common measure exists that would permit direct comparison of different value-packages, and hence rational choice among them. I call this the "Incommensurability-Undecidability Thesis" (IUT): Because values are incommensurable, rational choice among packages of values is often impossible. Value pluralists also maintain the "Incommensurability-Intransitivity Thesis" (IIT), which states that if values are incommensurable, transitive decision among packages of values is often impossible, because along one dimension of value package 1 may be preferable to package 2, and package 2 preferable to package 3, without package 1 being preferable to package 3, because 3 is preferable to 1 along an orthogonal value-dimension.

I deny both the IUT and the IIT, and argue that because these theses fail, the issue of value incommensurability is largely beside the point in debates over the usefulness of rational choice techniques. Provided that each of the incommensurable values may be quantitatively measured (although of course the measures cannot be compared between values), a small set of plausible assumptions permits rational choice among value packages, and also induces a transitive ordering of value packages. These assumptions are Nash's axioms for bargaining theory.

Consider the following thought experiment: Suppose that each of the incommensurable values is represented by a fanatic fiduciary ? a rational bargainer whose sole aim is to maximize the value he or she is assigned to represent. Then the choice situation among value packages may be described as an arbitration game among the fanatic fiduciaries, and Nash's bargaining theorem implies that a unique solution exists, namely that point in the choice set where the product of the fiduciaries' marginal gains over the status quo (the "Nash product") attains a maximum. The Nash solution is rationally preferable to all other value packages without being superior to the alternatives in any evaluative sense except the trivial one: it is superior to them in respect of rational preferability. In particular, it is rationally preferable despite the absence of a common measure. The IUT fails.

Let the status quo point in the k-dimensional choice space be the origin. I argue that there is a plausible sense in which all points with the same Nash products - these points all lie on a hyperbolic surface - are rationally indifferent to each other, because there is no arbitration game whose Pareto frontier contains one point on the surface such that any other point on the surface is its Nash solution. Thus, hyperbolic surfaces consisting of points with the same Nash products are indifference curves. This argument justifies constructing a "Nash preference relation" in which point x is preferable to point y if the product of x's coordinates is greater than the product of y's. This is a transitive ordering of the positive part of the choice space, and the IIT fails. The failure of the IIT and the IUT does not by itself justify rational choice techniques. The argument against these two theses assumes that all values may be quantitatively measured, and in many contexts that assumption has little to recommend it. However, the argument shows one important fact: the real limitation on rational choice is not the incommensurability of values, but rather their immensurability.