  The Central Educational Institutions (Reservation in Teachers' Cadre) Act,
2019 provides for reserving teaching vacancies in India's central educational
institutions for beneficiaries of its affirmative action policy. Reservation of
teaching vacancies had been a contentious issue, and the act was introduced to
resolve it after the Supreme Court's solution was met with protests from the
Teachers' Union. Our paper demonstrates an impossibility result in the Supreme
Court's solution and the act, which are flawed in reserving seats
simultaneously at both the university and within its departments. To overcome
this impossibility, we propose an alternative solution based on approximate
implementation of fractional assignments, offering a promising middle-ground
between the two disputed solutions practiced in India. This novel application
demonstrates the practical relevance of the approximate implementation approach
(Akbarpourand Nikzad(2020)) beyond the constraint structures examined in the
literature.
