The allocation of water through private markets has frequently been challenged because property rights to water are deemed to be ill defined. Historically wayer rights to both surface and ground water in most of the arid regions of thr western United States have developed under the appropriative doctrine. Although most of the recent literature on water transfer and allocation concurs with Millman that the approriative system is more flexible as regards transfers and that it provides greater security than the riparian doctrine, cirticism nonetheless has abounded. For instance, externaliities resulting from ill-defined property rights are viewed as arising because water can be used and reused along a river basin. Transfer by one individual can affect the return flow available to others. To prevent damage to third parties, earlier writers on this subject such as Meyers and Posner called for establishing property rights in return flows.