Preference modeling requires some specialized notation:
- The symbol ~ denotes the indifference relation: if X1i~X2i, then worker i is indifferent between X1 and X2;
- The symbol > denotes the strict preference relation: if X1i>X2i, then worker i prefers X1 to X2; and
- The symbol ≥ introduces indifference into the preference relation: if X1i ≥ X2i, then X1 is at least as good as X2 for worker i.
The worker’s preferences are rational if they are complete (for all X1 and X2 in his or her choice set, X1i ≥ X2i or X2i ≥ X1i) and transitive (for all X1 , X2 , X3 in the choice set, if X1 ≥ X2 and X2 ≥ X3, then X1 ≥ X3).