1. A computer program product operable on a computer for automatically reallocating memory among a plurality of logical partitions, the program product comprising: a computer readable memory; first instructions to define a plurality of donor candidates, wherein each donor candidate is a system designated by a user as eligible to donate memory to another system; second instructions to define a plurality of recipient candidates, wherein each recipient candidate is a system designated by the user as eligible to receive memory from another system; third instructions to select a performance parameter, wherein the performance parameter is a measure of memory paging activity; fourth instructions to define a memory grain; fifth instructions to define a capture interval, wherein the capture interval is a first interval of time; sixth instructions to define a sampling interval, wherein the sampling interval is a second interval of time at least as long as the first interval of time; seventh instructions to capture, for each donor candidate and for each recipient candidate, a value of the performance parameter for each capture interval within the sampling interval; eighth instructions to calculate, for each donor candidate and for each recipient candidate, a composite performance parameter equal to an average of the performance parameters captured for said each donor candidate and for said each recipient candidate during the sampling interval; ninth instructions to define a donor load threshold, wherein the donor load threshold is a first value of the composite performance parameter; tenth instructions to define a recipient load threshold, wherein the recipient load threshold is a second value of the composite performance parameter; eleventh instructions to identify a donor system, wherein the donor system is a donor candidate with a composite performance parameter below the donor load threshold; twelfth instructions to identify a recipient system, wherein the recipient system is a recipient candidate with a composite performance parameter greater than the recipient load threshold; thirteenth instructions to calculate a recipient workload ratio of the recipient system, wherein the recipient workload ratio is equal to the composite performance parameter of the recipient system divided by the recipient load threshold; fourteenth instructions to define a memory multiplier, wherein the memory multiplier associates the recipient workload ratio of the recipient system with a number of memory grains; and fifteenth instructions to reallocate the number of memory grains from the donor system to the recipient system; wherein memory paging activity is a number of pages read into a memory over the capture interval; wherein the memory grain is a finest granularity of memory which may be reallocated from a donor candidate to a recipient candidate; wherein the memory multiplier is a table associating recipient workload ratios with numbers of memory grains to reallocate, and wherein the number of memory grains to reallocate increases as the recipient workload ratio increases; and wherein the first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth eleventh, twelfth, thirteenth, fourteenth, and fifteenth instructions are stored on the computer readable memory.