THE INDEXING PROBLEM PART THREE

Let me turn, finally, to a third example drawn from a very different sphere, namely Gerald Cohen’s attempt in his important book, KARL MARX'S THEORY OF HISTORY, to define an objective measure of the increase in productivity of an economy. Cohen undertakes to defend a quite orthodox, uncomplicated version of Marx’s theory of historical materialism, one that many would call economistic, technological, and determinist. After distinguishing, by some careful conceptual analysis and textual exegesis, between the productive forces of an economy and the social relations of production, Cohen summarizes his version of Marx in two theses, which he labels the Development Thesis and the Primacy Thesis.

            The development thesis states that ‘the productive forces tend to develop throughout history.’ The primacy thesis offers a functional explanation of the social relations of production in terms of their suitability for furthering the development of the productive forces. The thesis states: ‘The nature of the production relations of a society is explained by the level of development of its productive forces.’ [Cohen, p.134] Cohen then goes on to give an original and controversial defense of functional explanation in terms of what he calls consequence laws.

            Most of the comment on Cohen’s book, not surprisingly, has concentrated on the notion of consequence laws, but there is, it seems to me, a prior problem concerning the development thesis, a problem which, oddly enough, involves the same issue of indexing that we have been examining in connection with Rawls' work and the problem of wage determination and comparable worth.

            At the risk of appearing to have wondered away from Professor Buchanan’s work into a critique of Cohen, let me elaborate a bit the structure of Cohen’s argument, so that we can see precisely where and how an indexing problem arises.

            At this point, since the precise statement of Cohen’s thesis will become rather involved, I will ask you to refer to the handouts distributed at the beginning of my remarks.

            According to Cohen, consequence laws have the following doubly hypothetical form: {see handout, number 1}

IF   it is the case that if  an event of type E were to occur at t1, then it would bring about an event        of type F at t2

THEN  an event of type E occurs at t3.

            To put the matter less technically and more provocatively, what explains the occurrence of event E is the fact that if it were to occur, it would bring about event F. Or, even more succinctly, E is explained by the fact that it is functional for F.

            Using this formal structure we can now state Cohen’s primacy thesis in proper consequence law form, namely:

IF        it is the case that if the production relations conductive to the use and development of the productive forces available in a society at that time come into being, then the productive forces available at that time will be used and developed,

THEN the production relations conductive to the use and development of the productive forces available in that society at that time come into being.

            To defend his primacy thesis, Cohen must do four things. First, he must explain what he means by ‘productive forces available in a society’ and ‘production relations of a society’ with sufficient precision and clarity that we can tell them apart, and also ascertain, for a given society, what productive forces are available and what the production relations are in the society. Second, he must explain what he means by the 'development’ of productive forces, and specify some way of telling as between two states of affairs in society, which constitutes a higher development of the productive forces. Third, he must defend explanation by consequence laws in general. And finally, he must offer some evidence or argument in support of the particular consequence laws that express the primacy thesis. It is in his attempt to meet the second of these needs that Cohen runs of afoul of the indexing problem, in my judgment.

            Cohen defines an increase in productivity as an increase in the quantity of product or output that can be produced with a given amount of direct labor. For example, in a simple one-commodity economy that uses corn and labor to produce corn, an increase in productivity is an increase in the net output of corn per unit input of labor.

            This measure of productivity becomes problematical, as Cohen recognizes, as soon as there are two or more commodities being produced, for a new technique might permit us to produce more of the first commodity but less of the second, with a given quantity of labor. Would this be an increase, a decrease, or no change in productivity? Some technological innovations, of course, might enable us to produce more of every commodity with the same labor, or at least more of some and no less of others. In those cases we could appeal to a Pareto principle to establish a rank ordering of relative productivity. But in the general case, some way must be found to make what Cohen calls ‘global productivity’ comparisons. Here is Cohen’s solution:

            Of course, if everything producible at stage s1 is producible at stage s2, and each thing at s2 in less time than s1, then we need no common measure of the magnitude of products to claim that productivity is higher at s2. But suppose forces at s2 outclasses those at s1 with respect to some products, and are less powerful with respect to others. How can we then make a global productivity comparison between s1 and s2?

            In certain instances of the type just identified comparison will still be possible without a common measure of product size. Thus supposed that at both s1 and s2 twelve hours per day is the length of time each producer is able to labor productively: marginal product is negative beyond that point. Imagine that there are just three products, p, q, and r. At s1 it thakes 3 hours to produce a unit of p, 4 hours to produce a unit of q, and 5 hours to produce a unit of r.  At s2 it takes 2 hours to produce a unit of p, 3 hours to produce a unit of q, and 6 hours to produce a unit of r.  Then s2 is more productive with respect to p and q, and less productive with respect to r.   Note, however, that only 11 of the 12 hours available at s2 are used up when it produces one unit each of p, q, and r.  Suppose the remaining hour were allocated to producing r: then as long as some r were produced in that hour, we should be able to say that s2 is globally more productive than s1, even though we have stated no ratios between units of one product and units of any other. [Cohen, p.57]

            But Cohen’s argument is quit incorrect. To see why, let us suppose that the technologies of s1 and s2 are just as Cohen specifies, but that final demand for commodities p, q, and r is different from that assumed by Cohen. In other words, let us suppose that these societies, using these technologies, do not wish to produce one unit of each p, q, and r.

            Instead, let final demand be .75 units of p, .5 units of q, and 1.5 units of r.  In that case, s1 is globally more productive that s2, for the desired final demand requires 12 units of labor in s2 and only 11.75 units of labor in s1.

            Now assume final demand to be one unit of p, 4/9 units of q, and 13/9 units of r.   In that case, s2 and s1 are equally globally productive, for the desired final demand requires just 12 units of labor in each system.

            But ‘global productivity’ is supposed to be an objective measure of the level of development of productive forces, independent of consumer taste and final demand. Thus Cohen’s measure is unsatisfactory.

            It should be obvious that this result is perfectly general. For any two technologies, one of which is more productive with respect to commodity i and the other of which is more productive with respect with commodity j, there will always be some final demand that makes the first technology globally more productive, and yet a third final demand that makes them equally globally productive.

            In fact, of course, we are presented here with exactly the same need for a normative or evaluative principle as the basis for our indexing rule. Either we must assume that the final demand manifested in the market by consumer behavior has a moral sanction, so that consumer tastes will ultimately determine the relative productivity of two stages of capitalist development – an assumption which undermines any attempt to mount a critique of the formation of consumer tastes- or else we must simply stipulate that some commodities are worthier that others, and hence will count for more in the index by which we measure productivity. For example, suppose that the advent of industrialization and the decline of craft skills made it less costly in labor hours to produce food, but more costly to produce hand-carved furniture. Is that technological change an advance in productivity or not? It depends on our moral evaluation of the relative importance of food and beautiful furniture.

            Lest we imagine that this is a purely theoretical quibble, let us reflect that current debates about the effects of the economy on the environment are, from a certain point of view, really arguments about the proper weights to use in an index designed to measure increases in productivity.

            I hope it is clear from these three examples – Rawls, comparable worth, and Cohen – both that the indexing problem arises repeatedly in theoretical and practical contexts, and that it is always impossible to solve it in a value-neutral manner. Here, as in so many other cases, supposedly objective formal methods of analysis carry with them covert evaluation presuppositions which, if not acknowledged, serve the ideological function of rationalizing particular political or economic positions. I take this as one important example of the general truth that politics cannot be reduced to rational administration, or class conflict to impartial calculation.