A processor allocation mechanism for a logically partitionable computer system allows an administrator to specify processing capability allocable to each partition as an equivalent number of processors, where the processing capability may be specified as a non-integer value. This processing capability value is unaffected by changes to the processing capability values of other partitions. The administrator may designate multiple sets of processors, assigning each physical processor of the system to a respective processor set. Each logical partition is constrained to execute in an assigned processor set, which may be shared by more than one partition. Preferably, the administrator may designate a logical partition as either capped, meaning that a partition can not use excess idle capacity of the processors, or uncapped, meaning that it can.