16.5 It has sometimes been suggested that lexicographic preference is a form of rational behavior that is not captured by utility theory. Lexicographic preferences rank attributes in some order X i , ..., Xn, and treat each attribute as infinitely more important than attributes later in the order. In choosing between two prizes, the value of attribute X, only matters if the prizes have the same values for X\, ..., X,_ i. In a lottery, an infinitesimal probability of a tiny improvement in a more important attribute is considered better than a dead certainty of a huge improvement in a less important attribute. For example, in the airport-siting problem, it might be proposed that preserving human life is of paramount importance, and therefore if one site is more dangerous than another, it should be ruled out immediately, without considering the other attributes. Only if two sites are equally safe should they be compared on other attributes such as cost.

a. Give a precise definition of lexicographic preference between deterministic outcomes.

b. Give a precise definition of lexicographic preference between lotteries.

c. Does lexicographic preference violate any of the axioms of utility theory? If so, give an example. (Hint: consider pair-wise preference comparisons of three different possibilities.)

d. Suggest a set of attributes for which you might exhibit lexicographic preferences.