Encarnación was educated at UP Diliman (PhB, MA Philosophy) and at Princeton University (PhD Economics).

[1] In 2008, the main building of the School of Economics at the University of the Philippines was renamed Encarnación Hall in his honor.

Formally one posits a mapping V: X→ Rn, where n refers to the arbitrarily many or few dimensions of the vector and corresponds to the number of criteria of choice.

Hence, let the vector v(x) = [v1(x), v2(x),…] represent the scores vi(x) of an alternative x on various characteristics or criteria i = 1,2,…., arranged in decreasing order of importance.

The term lexicographic refers to the fact that dictionaries similarly order words by their successive components, i.e. letters.

These further criteria would be irrelevant, however, if there was a unique restaurant with the lowest price, since this one would always be preferred to more expensive ones, no matter how bad their cuisine or ambience.

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][4] 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.