Consider the following choice procedure over a finite set of n alternatives X {,...,n}. The agent evaluates each alternative using a function v(x). That is, alternative x has a "level" v(x). v can be any function. The agent has a "reference" level v*. Given any set of m alternatives A CX, denote A = {,.,im} with 9 1 i 2. Can C(A) be empty? does it satisfy WARP? 3. If the answers are "no" and "yes", then you should be able to ratio- nalize C by complete and transitive preferences. What do they look like? that is, when do we have x y? and what about a utility representation?