The Most Ordinally-Efficient of Random Voting Rules

Aziz and Stursberg [1] propose an “Egalitarian Simultaneous Reservation” rule (ESR), a generalization of Serial rule, one of the most discussed mechanisms in random assignment problem, to the more general random social choice domain. We provide an alternative definition, or characterization, of ESR as the unique most ordinally-egalitarian one. Specifically, given a lottery "p" over alternatives, for each agent "i" we define "t p/ii (k)" to be the total share in "p" of objects from her first "k" indifference classes. ESR is shown to be the unique one which leximin maximizes the vector of all such shares ("t p/i (k))_i;k." Serial rule is known to be characterized by the same property (see [2]). Thus, we provide an alternative way to show that ESR, indeed, coincides with Serial rule on the assignment domain. Moreover, since both rules are defined as the unique most ordinally-egalitarian ones, out result shows that ESR is "the right way" to think about generalizing Serial rule