Multi-Object tracking (MOT) is an important problem in a number of vision applications. For particle filter (PF) tracking, as the number of objects tracked increases, the search space for random sampling explodes in dimension. Partitioned sampling (PS) solves this problem by partitioning the search space, then searching each partition sequentially. However, sequential weighted resampling steps cause an impoverishment effect that increases with the number of objects. This effect depends on the specific order in which the partitions are explored, creating an erratic and undesirable performance. We propose a method to search the state space that fairly distributes these impoverishment effects between the objects by defining a set of mixture components and performing PS in each of these components using one of a small set of representative object orderings. Using synthetic and real data, we show that our method retains the overall performance and reduced computational cost of PS, while improving performance in scenes where the impoverishment effect is significant.