A characterization of the extended serial correspondence

We study the problem of assigning objects to a group of agents. We focus on probabilistic methods that take agents' ordinal preferences over the objects. Importantly, we allow for indifferences among objects. Katta and Sethuraman (2006) propose the extended serial correspondence to solve this problem. Our main result is a characterization of the extended serial correspondence in welfare terms by means of stochastic dominance efficiency, stochastic dominance no-envy and "limited invariance," a requirement we adapt from Heo (2014a). We also prove that an assignment matrix is selected by the extended serial correspondence if and only if it satisfies "non-wastefulness" and "ordinal fairness," which we adapt from Kesten et al. (2011).