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This Essay examines two alternative designs for hierarchical institutions: “bounded” and “unbounded.” In a bounded structure, a principal decides on a bounded aggregate numerical allocation, and then an agent makes the allocation to an underlying subject population while complying with the bound. In an unbounded structure, the principal provides no aggregate numerical cap, but instead provides some other form of guidance to the agent regarding allocation. An example of a bounded institution is grading to a pre-arranged curve (“X students receive As”), while an example of an unbounded institution is granting a particular grade to each student who meets a particular threshold (“each student who displays mastery of the material receives an A”). Bounded and unbounded institutions are common in many legal contexts and differ in their strengths and weaknesses. From the principal’s perspective, bounded institutions are increasingly desirable to the extent that (a) there is a homogeneous and large subject population, (b) the agent is likely to be biased or to make systematic errors, and (c) it is difficult to devise other rules to guide the agent’s decision. If agents are biased but otherwise share preferences with the principal—and the principal knows the underlying subject population’s traits—then bounded institutions can produce the precise outcome that the principal wants even though neither the principal nor the agent is fully informed or free of error. The Essay applies these insights to government appropriations, environmental law, and administrative law (among other areas). Consider, for example, funding scientific research through the National Science Foundation (NSF). Congress should give the NSF a fixed (bounded) budget if it thinks the NSF is biased in favor of funding scientific research and the distribution of quality of scientific research proposals is relatively predictable from year to year. If the NSF always wants to fund the same projects that Congress would, by contrast, then Congress should tell the NSF to fund all research projects the NSF deems worthy, thereby giving the NSF an unbounded source of funding.
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