Repre mpleteness since u is a real va alued function

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Unformatted text preview: e repre c esented by a utility fun nction. As i turns out, the answe it er is no But I'll lea that inv o. ave vestigation to your furt ther studies s... 338 B PPROACH THE CHOICE BASED AP OICE RULE ES CHO In the second approach to the theory of decision making, c e n choice beha avior itself is s taken to be the primitive ob n bject of the theoretical construct. Formally, choice l beha avior is repr resented by means of a choice st y tructure. A choice stru ucture (B, C()) consists of two bits: f 1. B is a family (a set) of n y nonempty s subsets of X that is, every eleme of B is a X; ent set B X. This simp means th the elem ply hat ments B B are budget sets. The T budget sets in B ca be thoug of as a complete listing of all the choice an ght experiments that the re s estricted (institutionally physically socially, o y, y, or s n bly t otherwise) situation can conceivab present to the decision maker. A warning, tho w ough, it nee not includ all of the elements of X (the se of all ed de e et possible alte ernatives). C() oice rule tha assigns a nonempty set of cho at y osen elemen C(B) nts 2. C is a cho B for every budget set B B. When C(B) co b ontains a sin ngle elemen that nt, element is th individua choice from among the altern he al's natives in B The set B. C(B) may, however, co C ontain more than one e e element. W When it does the s, elements in B are the a alternatives in B that th decision maker mig choose. he ght Hunh?!? H These are his/her acce T eptable alternatives fro B. In this case, the set C(B) om e can be thoug of as co ght ontaining th hose alterna atives that w would a we actually see e chosen if the decision m e maker were to repeate e edly face th problem of choosing he g an alternativ from set B. ve EXAMPLE: pose that X = {x, y, z} and B = {{x y}, {x, y, z One po x, z}}. ossible choi structur ice re Supp is (B, C1 ()), wh here the cho oice rule C1() is: C1({x y}) = {x} a C1({x, y z}) = {x}. x, and y, In thi case, we see that x is chosen no matter w is e what budge the decisi maker...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.

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