A method and apparatus for managing cache lines in a data processing system. A special purpose register is employed in which this register may be manipulated by user code and operating system code to set preferences, such as a level 2 cache management policy preference for an application thread. These preferences may be dynamically set and an arbitration mechanism is employed to best satisfy preferences of multiple threads with a single aggregate preference. Members are represented using a least recently used tree. The least recent used tree has a set of nodes forming a path to member cache lines in a hierarchical structure. A state of a selected node is selectively biased within the set of nodes in the least recently used tree. At least one node on a level below the selected node is eliminated from being selected in managing the cache lines. In this manner, members can be biased against or for selection as victims when replacing cache lines in a cache memory.