José Encarnación Jr.

Encarnación was educated at UP Diliman (PhB, MA Philosophy) and at Princeton University (PhD Economics). He was a member of the Upsilon Sigma Phi fraternity. At Princeton he was a student and dissertation advisee of William J. Baumol. The only Filipino economist of his generation to work in the field of theory, Encarnación was best known for advancing the theory of lexicographic preferences, which in the words of Richard Day, Encarnación "almost singlehandedly kept alive". In 1987 he was named National Scientist, the highest recognition of scientific achievement given by the Republic of the Philippines. In 2008, the main building of the School of Economics at the University of the Philippines was renamed Encarnación Hall in his honor.

Lexicographic preferences have also been found useful in describing choices under uncertainty. Let wi = wi(x, p(x)) be the ith utility from a vector of prospects x = (x1,…, xk,…) which has associated probabilities p(x) = (p1(x1),…,pk(xn)). Note that the criterion function wi depends explicitly not only on x but also on the probabilities associated with x. One may then define w¡* as the satisficing level of w¡ and proceed to define lexicographic preference in the customary manner, with v(x) = [v1(x),v2(x),…] and vi(x) = min (wi (x, p(x), wi*) for all i. It is straightforward to reproduce expected utility as a particular case by defining some primitive utility function u(.) that depends only on the individual xk. In this case, one may write w1(x, p(x)•u(x)), where u(x) = [u(x1), u(x2),…] and set w1* sufficiently high to obtain the usual subjective expected utility. If other criteria are allowed to come into play, on the other hand, different possibilities arise. For example, for some i, wi may depend only on the probability of ruinous levels of x, or on the maximal values of x. Encarnación [1987] uses preferences of this form in an ambitious attempt to reconstruct and explain all the apparent “paradoxes” in choice theory. Apart from lexicographic comparisons the new element introduced into the structure was the notion of significant differences in the values of criterion functions. Choice between two uncertain alternatives x and y, he suggests, turns on whether they differ significantly on the following lexicographically arranged criteria: (1) expected value, (2) the possibility of a large loss, (3) the possibility of maximal gain, and finally (4) expected value once more. Unlike his earlier 1964 formulation, however, this later version allows for intransitivity.

It is this process that Encarnación formalized in 1964. If ui(x) represents the degree of achievement in criterion i when in possession of x, a threshold level ui* may be defined corresponding to a satisficing or satisfactory level of that criterion. The novel idea is that further increases in the value of ui beyond ui* do not matter. The importance of an alternative x with respect to the ith criterion may then be written as vi(x) = min(ui(x),ui*). Hence, ordering wants or criteria in decreasing order of importance, define the vector v(x) = [v1(x), v2(x),…]. Then in the now-familiar vector comparison, x is preferred to y if and only if the first nonzero component of the vector difference v(x) - v(y) is positive. This revised lexicographic ordering incorporating thresholds, with which Encarnacion’s name has become inextricable, has since become known as an L* ordering to distinguish it from the ordinary lexicographic, or L-ordering.

José Encarnación Jr. (November 17, 1928 – July 5, 1998) was a Filipino professor of economics at the University of the Philippines Diliman, where he served as dean of the School of Economics from 1974 until his retirement in 1994.