A tax whose amount is not affected by the taxpayer's actions. If the lump-sum tax is the same for all taxpayers, it is called a poll tax. Lump-sum taxes can be varied across consumers, and may even be negative for some consumers. A negative lump-sum tax is called a lump-sum subsidy. The differentiation of lump-sum taxes across taxpayers results in redistribution. Lump-sum taxes have a central role in the theory of taxation due to their efficiency in raising revenue and achieving distributional objectives. As taxpayers cannot affect the level of a lump-sum tax by changing their behaviour, there is no distortion in choice. The imposition of lump-sum taxes therefore causes no deadweight loss. This allows revenue to be raised, and redistribution to be achieved, with no efficiency cost and, hence, permits decentralization of a first-best allocation. Unfortunately, the differentiation of lump-sum taxes across taxpayers requires the taxes to be levied on the basis of some unalterable characteristic. There are few characteristics that are both publicly verifiable and relevant for redistribution, which makes this differentiation difficult to implement in practice. See also optimal taxation.