# Specialized Notation

Preference modeling requires some specialized notation:

- The symbol ~ denotes the indifference relation: if
*X*_{1i}~*X*_{2i}, then worker*i*is indifferent between*X*_{1 }and*X*_{2};

- The symbol
denotes the strict preference relation: if*>**X*_{1i}*>**X*_{2i}, then worker*i*prefers*X*_{1 }to*X*_{2}; and

- The symbol
introduces indifference into the preference relation: if*≥**X*_{1i}*≥**X*_{2i}, then*X*_{1 }is at least as good as*X*_{2}for worker*i*.

The worker’s preferences are rational if they are complete (for all *X*_{1 }and *X*_{2} in his or her choice set, *X*_{1i} *≥**X*_{2i }or *X*_{2i} *≥**X*_{1i}) and transitive (for all *X*_{1 ,} *X*_{2} , *X*_{3} in the choice set, if *X*_{1} *≥ **X*_{2} and *X*_{2} * ≥ **X*_{3}, then *X*_{1 }*≥ **X*_{3}).