## Infinite regress in law (a theoretical critique of the Hand formula)

Adjudication is the process of making decisions in law, but decision-making is a costly activity. For simplicity, we can model the process of adjudication (and decision-making generally) as a function consisting of two costly inputs: (i) RESEARCH or information-gathering and (ii) DELIBERATION or information-processing.

Consider, for example, the so-called Hand formula or “calculus of negligence” in tort law. In summary, the Hand calculus is a simple economic decision rule for finding the optimal level of care x*, or B = P*L in the standard formulation of the Hand test. But this simple decision rule imposes non-trivial research and deliberation costs on judges and jurors (assuming, of course, that jurors actually use this formula). That is, finding the optimal level of care under the Hand formula is a first-order decision problem with costly inputs: in order to find the optimal level of care x*, the decision-maker must not only be aware of the Hand formula, he must also go out and collect sufficient data in order to find the actual or approximate values for B, P, and L (the main variables in the Hand formula) and he must then “crunch the numbers” and solve for x*. But how much data should the decision-maker collect? And how much time should he or she spend crunching the numbers? These simple questions pose a second-order decision problem, a new problem with non-trivial information and deliberation costs, just like the original, first-order decision problem (i.e. finding the level of optimal care). This second-order problem, in turn, produces a new, third-order problem, and so on …

Furthermore, because information and deliberation are costly inputs, notice that the regress problem does not just apply to the Hand formula in tort law. It applies to any decision rule requiring the collection of information and deliberation! In the words of Holly Smith in her essay “Deciding how to decide“: It begins to appear that the use of decision guides in decision-making is threatened with some form of infinite regress. To decide how to act, one must first decide how to decide to act. But to decide this, we must first decide how to decide how to decide how to act. But to decide this, we must first decide … ad infinitum. So, does this regress problem have a solution, or is it merely an academic or purely theoretical problem? (Quick acknowledgement: I owe this critique of the Hand formula to Prof. Oren Perez.)

This is what an infinite regress looks like …