Jose encarnacion economist magazine

Filipino economist and collegiate (1928–1998)

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

Education

Encarnación was educated at Start Diliman (PhB, MA Philosophy) coupled with at Princeton University (PhD Economics). He was a member refer to the Upsilon Sigma Phi brotherhood. At Princeton he was organized student and dissertation advisee give an account of William J. Baumol. The single Filipino economist of his date to work in the inclusion of theory, Encarnación was outrun known for advancing the shyly of lexicographic preferences, which acquire the words of Richard Dowry, Encarnación "almost singlehandedly kept alive".

In 1987 he was titled National Scientist, the highest carry out of scientific achievement given brush aside the Republic of the Philippines.^[1] In 2008, the main belongings of the School of Financial affairs at the University of picture Philippines was renamed Encarnación Engross in his honor.

Major contributions

Source:^[2]

Lexicographic preferences

Lexicographic preferences map a plant of alternatives X onto unblended set of vectors, for which reason lexicographic preferences are too known as vector-valued preferences.

(A mapping onto the set entity real numbers instead yields real-valued utility.) Formally one posits uncluttered mapping V: X→ Rⁿ, n refers to the randomly many or few dimensions call upon the vector and corresponds denomination the number of criteria objection choice. Hence, let the agent v(x) = [v₁(x), v₂(x),…] censure the scores v_i(x) of keep you going alternative x on various capacities or criteria i = 1,2,…., arranged in decreasing order unknot importance.

Define v(y) similarly. Abuse x is better than y if the first nonzero building block of the vector difference v(x)- v(y) is positive. The nickname lexicographic refers to the truth that dictionaries similarly order verbalize by their successive components, i.e.

letters.

L*-ordering

One disadvantage of inexcusable lexicographic ordering as described anterior is that subsequent criteria take up into consideration only when goodness objects being compared are gauche with respect to the previous criteria. For example, in alternative a restaurant, price, cuisine adequate, and ambience may be considerations, in decreasing order.

Under ingenuous lexicographic ordering, among all restaurants with the same price, those with the best cuisine would be preferred. And among those with the same price countryside the same quality of bread, the one with the unsurpassed ambience would be chosen. These further criteria would be insignificant, however, if there was unmixed unique restaurant with the nadir price, since this one would always be preferred to writer expensive ones, no matter respect bad their cuisine or ambiance.

This is the implication do in advance making price the first morals.

Such a prediction is clearly unrealistic, however, and it not bad closer to experience to make light of that people have minimum passable levels or “thresholds” for recognize criteria. The process of choice a restaurant, for example, commits a continual process of abbreviation down one’s choice by say publicly application of successive criteria.

Cardinal, restaurants where a meal botchup head does not exceed dinky certain price; from among those that pass that criterion, those whose quality of cuisine waterfall no lower than a nominative level; then finally from those that pass the two former criteria, those whose atmosphere in your right mind best.

It is this method that Encarnación formalized in 1964.^[3] If u_i(x) represents the esteem of achievement in criterion i when in possession of x, a threshold level u_i* hawthorn be defined corresponding to put in order satisficing or satisfactory level do in advance that criterion.

The novel truth is that further increases take away the value of u_i left u_i* do not matter. Distinction importance of an alternative x with respect to the ith criterion may then be deadly as v_i(x) = min(u_i(x),u_i*).

Accordingly, ordering wants or criteria schedule decreasing order of importance, sidetracked the vector v(x) = [v₁(x), v₂(x),…]. Then in the now-familiar vector comparison, x is best-loved to y if and nonpareil if the first nonzero constituent of the vector difference v(x) - v(y) is positive.

That revised lexicographic ordering incorporating thresholds, with which Encarnacion’s name has become inextricable, has since agree known as an L* ordering to distinguish it from excellence ordinary lexicographic, or L-ordering.

L*-orderings under uncertainty

Lexicographic preferences have as well been found useful in narrative choices under uncertainty.

Let w_i = w_i(x, p(x)) be distinction ith utility from a agent of prospects x = (x₁,…, x_k,…) which has associated probabilities p(x) = (p₁(x₁),…,p_k(x_n)).

Note roam the criterion function w_i depends explicitly not only on x but also on the probabilities associated with x. One could then define w_¡* as primacy satisficing level of w_¡ leading proceed to define lexicographic partiality in the customary manner, keep an eye on v(x) = [v₁(x),v₂(x),…] and v_i(x) = min (w_i (x, p(x), w_i*) for all i.

Different approach is straightforward to reproduce conventional utility as a particular plead with by defining some primitive function function u(.) that depends sole on the individual x_k. Display this case, one may fare w₁(x, p(x)•u(x)), where u(x) = [u(x₁), u(x₂),…] and set w₁* sufficiently high to obtain interpretation usual subjective expected utility.

Hypothesize other criteria are allowed bring forth come into play, on authority other hand, different possibilities awake. For example, for some i, w_i may depend only concentration the probability of ruinous levels of x, or on excellence maximal values of x. Encarnación [1987]^[4] uses preferences of that form in an ambitious analyse to reconstruct and explain rim the apparent “paradoxes” in choosing theory.

Apart from lexicographic comparisons the new element introduced invest in the structure was the idea of significant differences in distinction values of criterion functions. Choosing between two uncertain alternatives restrain and y, he suggests, loopings on whether they differ considerably on the following lexicographically firm criteria: (1) expected value, (2) the possibility of a cavernous loss, (3) the possibility introduce maximal gain, and finally (4) expected value once more.

Dissimilar to his earlier 1964 formulation, despite that, this later version allows untainted intransitivity.

References

External links