The Taking Clause of the Fifth Amendment to the US Constitution provides, "not shall private property be taken for public use, without just compensation." The text makes clear that compensation is required for takings of conversion of private property to public property, but not vice versa. It's worth considering why the Taking Clause operates in only one direction, despite the fact that privatization of public property clearly imposes costs on the public.
Just last week, for instance, the US Supreme Court heard oral arguments in the case of Golan v. Holder, concerning a federal statute that confers copyright protection on works already in the public domain (Congress passed the law to comply with the Uruguay Round Agreements of the WTO). Putting to one side the merits of the statute, it is clear that the act of privatizing works already in the public domain imposes costs on consumers of music and literature by limiting access and use. Why shouldn't those consumers be compensated for the costs they suffer as a consequence of the appropriation of their property? (This is not a novel question but in similar contexts throughout history. See, for example, E.P. Thompson's Whigs and Hunters, which chronicles the history of the enclosure movement in early eighteenth-century England.
Offhand, a few plausible answers (or parts of a single answer) come to mind:
(1) The framers of the Fifth Amendment were myopic because, when it was written and enacted, the costs (to the public) of privatization were relatively low because resources were, generally speaking, abundant relative to demand.
(2) Majoritarianism was then (but no longer) thought likely to preserve socially-valued common-pool resources. By contrast, Madison was explicitly concerned that majoritarianism might lead to widespread deprivation of private property.
(3) The costs of privatization are diffuse and thinly spread among the population. The transaction costs of providing compensation may exceed the value of the compensation received by each member of the affected public.
Modern scholars understand acts of privatizing the public domain as "givings," the obverse of takings. It remains unclear to me, however, why they should not be thought of simply as a taking in the opposite direction, especially when the resource's prior status as public property is well-defined and legally recognized.