websimka

продолжение на сайте:

статья предоставлена студией веб-дизайна Simka

Часть I

FOR the purpose of formulating a theory of value, the econo¬mist assumes that an individual can at any moment be regarded as confronted with a number of alternatives between which he must choose and that his choice is determinate, i.e. if we knew all the relevant circumstances we could deduce which alternative is chosen. But the economist assumes that it is unnecessary for him to enquire into this full determination. All that he requires to know is a certain partial determination of his choice. If he relies on the evidences of introspection, he finds that an individual sometimes prefers one alternative to another and sometimes is indifferent as between alternatives. If he is indifferent to a number of alternatives but prefers these to all other alternatives simultaneously presented the economist assumes, of course, that the actual choice made is determinate, but he also ,assumes that, so far as the determination of value is concerned, it matters not which of the alternatives, between which he is indifferent, is chosen. In other words, he can ignore those factors on which the choice of a particular member of this indifference¬-class depends. From the point of view of economics, choice within the indifference-class can be regarded as indeterminate. Even the economist who refuses to consider such revelations of introspection appears to adopt the same standpoint and to assume that it is unnecessary for him to investigate the full determinateness of choice, and that it would be an error of method to do so, since values can be explained on the basis of the deter¬mination of classes equivalent to the indifference-classes observed by the introspectionist.
Let us call such a class of alternatives an indifference-class, whether or not we assume that the introspective test is a satis¬factory one; then the economist's assumption with regard to choice may be expressed as the assumption that for any given individual at a given moment there is a function, which we will call the utility-function of the alternatives, any of which could conceivably be presented to the individual, and this function determines an indifference-class of alternatives, one of which will be chosen as a consequence of factors which the economist can ignore since they are irrelevant to the determination of value. It is assumed that the precise delimitation of this class is signifi¬cant for the determination of value; in other words, the rejection of all the alternatives outside the indifference-class is significant.
On this point all economists are agreed, and in the above sense of the term utility all economists make use of the concept of utility and assume a utility function giving the required partial determinateness of choice. But with regard to the nature of utility, the form of the utility function, and the way the indifference-class (between the members of which choice can be regarded as indeterminate so far as value-theory is concerned) is determined by the utility function, there are grave differences of opinion. In anticipation of the argument to be developed it may be noticed that the following views have at one time or another been held: (1) An estimate of the relative pleasurableness or painfulness of the alternatives is made, and the alternative estimated to be most pleasurable is chosen. If a number of alternatives are indistinguishable in this respect, then choice between these alternatives is indeterminate (i.e., those circumstances which determine the choice of one of these alternatives are irrelevant to the determination of value and can be neglected by the economist). (2) The alternatives are wanted with varying intensities and the alternative wanted most is chosen. If a number of alternatives are wanted equally, then choice between these alternatives is indeterminate in the above sense. (3) The alternatives fall into relations of preference or indifference and 'the alternative pre¬ferred to all others is chosen. If no single alternative is preferred to all others, then it is assumed that the individual is indifferent to a number of alternatives and that no alternative is preferred to these. Choice between the alternatives between which there is such indifference is assumed to be indeterminate in the above sense. All the above views agree in postulating what it has been agreed to call a utility function. It is assumed that for a given person at a given moment there exists a function of the alter¬natives that could conceivably be presented, and that this function partially determines choice when any selection of these alternatives is presented, and that this partial determination is sufficient for the explanation of value. If Ca represents the class of all conceivable alternatives, then it is assumed that each alternative can be regarded as having a certain variable quality, which we agree to call utility, given by the utility function. Let Cp be that selection of these alternatives actually presented to the individual, so that the individual can be regarded as potentially able to choose anyone of the alternatives Cp. The utility func¬tion of Ca settles the utility of each member of Cp and partially (in some cases wholly) determines the choice of one of these alternatives. In other words, the utility function determines the division of Cp into two classes, Cc and Cr which we will call the chosen class and rejected class respectively, a division having the characteristic that while Cr may have no members, Cc must have at least one member. The peculiarity of Cc is the indeterminate¬ness of choice as between its members when there is more than one member, while the peculiarity of Cr is the determinateness of the rejection of all its members. If Cc has only one member choice is completely determined by the utility function, but in all other cases choice is only partially determined by the utility function. If we use the term" rejection" for the selection of the class Cr then in all, cases of choice we can say that rejection (including the case of rejection of no alternatives) is completely determined by the utility function.
The controversies amongst economists as to the foundations of value-theory arise over the differences of view as to the nature of utility and the utility function and the way in which the utility function settles the division of Cp into Cc and Cr.
Let us first see what measure of agreement on these points exists. It is clear, in the first place, that utility is assumed to have simple orderliness, i.e., it is assumed that there is a certain asymmetrical transitive relation holding between any two different utilities. If we call this relation p. then if U1. U2 . . . are a set of utilities, i.e., particular values of the utility function, then these utilities fall into a simple order, e.g., U1. U2 . . . , such that any earlier member is P to any later member of the series. It is also clear, in the second place, that it is assumed that the utility of any member of the class Cc is P to the utility of any member of the class Cr.
We have reached the conclusion that all economists are agreed that if U1 and U 2 are the utilities of two alternatives, then there is an asymmetrical relation P such that either U1 is P to U2, or U2 is P to U 1, or U1 is identical with U 2 and this relation is transi¬tive, so that if we have three alternatives with utilities U 1, U2, U3 such that U1PU2 (i.e., U1 is P to U2) and U2PU3 then U1PU3. It follows, therefore, that if we consider the utilities of the class of all possible alternatives, Ca, these utilities may be arranged in an ordered series of classes of identical utilities, and therefore any selection Cp (the class of presented alternatives) from this class may also be so arranged. and therefore there will be a class Cb the utilities of which are identical with one another and in the relation P to all other members of Cp. If now we assume that this class Cb is the chosen class Cc, we have a theory of determina¬tion of choice by utility without making any assumption about the nature of utility other than its simple orderliness. This is the Lausanne theory ,in its most general form, and it has the great merit of utilizing the minimum assumption as to the nature of utility and the utility function, on which there is agreement amongst all economists. The assumption disputed explicitly or by implication by other schools of thought. is the assumption that the chosen class is a class of alternatives of identical utility.
We propose to show that this latter assumption leads to insu¬perable difficulties, and that it is the necessity of giving some other explanation of the division of Cp into the classes Cc and Cr which forces the economist to assume that utility is measurable' and not merely orderly.



Cambridge
W. E. ARMSTRONG
 

Статья предоставлена студией веб-дизайна Simka