Fractional Top Trading Cycle on the Full Preference Domain

Abstract: Efficiency and fairness are two desiderata in market design. Fairness requires randomization in many environments. Observing the inadequacy of Top Trading Cycle (TTC) to incorporate randomization, Yu and Zhang (2020) propose the class of Fractional TTC mechanisms to solve random allocation problems efficiently and fairly. The assumption of strict preferences in the paper restricts the application scope. This paper extends Fractional TTC to the full preference domain in which agents can be indifferent between objects. Efficiency and fairness of Fractional TTC are preserved. As a corollary, we obtain an extension of the probabilistic serial mechanism in the house allocation model to the full preference domain. Our extension does not require any knowledge beyond elementary computation.