| Article ID: | iaor20132383 |
| Volume: | 38 |
| Issue: | 2 |
| Start Page Number: | 389 |
| End Page Number: | 392 |
| Publication Date: | May 2013 |
| Journal: | Mathematics of Operations Research |
| Authors: | Li Jianrong |
| Keywords: | employment, lattice processes, matching |
Roth (1985) claimed that (i) if each firm is allowed to select its most preferred subset of employees from those that assigned to it at two different stable matchings, then the choices result in a stable matching; and (ii) the set of stable matchings is a lattice under the partial order of the firms' common interests. Here, we provide counterexamples that show that these claims are incorrect, and we explain the flaws in Roth's reasoning.