Preference modeling requires some specialized notation:

• The symbol ~ denotes the indifference relation: if X_1i~X_2i, then worker i is indifferent between X₁ and X₂;

• The symbol > denotes the strict preference relation: if X_1i>X_2i, then worker i prefers X₁ to X₂; and

• The symbol ≥ introduces indifference into the preference relation: if X_1i ≥ X_2i, 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, X_1i ≥ X_2i or X_2i ≥ X_1i) and transitive (for all X_{1 ,} X₂ , X₃ in the choice set, if X₁ ≥ X₂ and X₂ ≥ X₃, then X₁ ≥ X₃).