# Random assignment: Redefining the serial rule

Article

Journal of Economic Theory

Issue number:

Volume 158, Part A, July 2015

Publisher:

Elsevier

Year:

2015

Journal pages:

308-318

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.