One classic technique for coordinating distributed computations is to require each processor to get permission for certain actions from some quorum of processors, such that every processor's quorum overlaps every other processor's quorum. A dynamic quorum assignment allows the processor-to-quorum mapping to adapt during system execution, to improve performance and availability when processors fail or change load. This work considers how the run-time quorum adaptation cost is impacted by the selection of a quorum mapping function. An effective quorum mapping function exhibits not only desirable quorum size and load properties, but also a type of hysteresis that minimizes the changes made to the processor-to-quorum mapping whenever the mapping is recomputed. A new quorum mapping function called MEMRING is given that exhibits hysteresis by identifying quorums that are similar to previously chosen quorums. This behavior reduces the needed number of modifications to dynamic quorum assignment data structures, and can consequently reduce the amount of interprocessor communication needed for distributed control of quorum adaptation. The expected cost of distributed quorum adaptation using MEMRING is shown to be less than the expected cost of using other quorum mapping functions that have similar quorum size and load properties.