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) 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)). 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. © 2015 Elsevier Inc. All rights reserved.
There has been a surge of interest in stochastic assignment mechanisms that have proven to be theoretically compelling thanks to their prominent welfare properties. Contrary to stochastic mechanisms, however, lottery mechanisms are commonly used in real life for indivisible goods allocation. To help facilitate the design of practical lottery mechanisms, we provide new tools for obtaining stochastic improvements in lotteries. As applications, we propose lottery mechanisms that improve upon the widely used random serial dictatorship mechanism and a lottery representation of its competitor, the probabilistic serial mechanism. The tools we provide here can be useful in developing welfare-enhanced new lottery mechanisms for practical applications such as school choice.