Random assignment: Redefining the serial rule

We provide a new, welfarist, interpretation of the well-known Serial rule in the random assignment problem, strikingly different from previous attempts to define or axiomatically characterize this rule. For each agent i we define ti(k)ti(k) to be the total share of objects from her first k indifference classes this agent i gets. Serial assignment is shown to be the unique one which leximin maximizes the vector of all such shares (ti(k))(ti(k)). This result is very general; it applies to non-strict preferences, and/or non-integer quantities of objects, as well. In addition, we characterize Serial rule as the unique one sd-efficient, sd-envy-free, and strategy-proof on the lexicographic preferences extension to lotteries.