Inputs and Outputs vs. Rules and Standards

I don't love the name “Legal Discontinuities.” Discontinuities are perspectival. For example, in countries with progressive income taxes, as your income rises by just a dollar above some often arbitrary cutoff point, your marginal tax rate can go from, say, 20% to 30%. If we think about the relationship between income and marginal tax rate, it looks discontinuous. On the other hand, if you look at the relationship between income and total taxes owed, as you go a dollar above the threshold, you owe just a little more than you owed when you were just below the threshold.

The lesson I take is that legal input-output relationships are the central issue: how do we map things that law cares about—inputs such as reasonableness, culpability, and harm caused—onto legal outcomes that law cares about such as compensation owed, fine amounts, and years in prison? As I see it, we begin with a theory of the relationship particular inputs and outputs ought to have and compare the theoretical relationship to the one the law actually gives them. In the example above, what matters is the relationship between income and taxes owed not income and marginal tax rate. Subject to some important caveats, the input-output relationships we see in the law should match the input-output relationships our best theories recommend.

When a gradual change to an input causes a gradual change to an output, I call that a smooth relationship. By contrast, when a gradual change to an input sometimes has no effect on an output and sometimes has dramatic effects, I call that a bumpy relationship. There are, however, an infinite number of ways to map inputs and outputs, and these are just shorthand names for two common types of input-output mappings. (In his conference paper, for example, Mark Spottswood discusses a logistic relationship which is one kind of smooth relationship).

We must speak of inputs and outputs because the vocabulary of “legal discontinuities” is inadequate. People easily confuse the continuity of inputs and outputs with the relationship between them. For example, in tort law, when you just cross the threshold of being unreasonably incautious, you now owe full compensation for the harm you caused. That’s a bumpy relationship because a gradual change to your level of caution has a dramatic effect on the amount you owe. This is true even though compensation is paid in the form of money which would naturally be described as a continuous variable. “Money owed” seems scalar though it’s used here as part of a bumpy relationship. So that’s why I think it’s fine to speak of inputs and outputs as scalar or binary or continuous, but those terms don’t do justice to what we really care about, namely the underlying relationships between inputs and outputs.

The smooth-bumpy distinction is sometimes confused with the rule-standard distinction, though they are conceptually quite different. The rule-standard distinction archetypically applies to the triggering circumstances of a particular law (or regulation or the like). If the triggering circumstances are well-defined, easy to apply, require little discretion, and so on, then we deem the law to be “rule-like.” For example, a law prohibiting driving above 65 miles per hour is very rule-like because it is clearly defined, easy to apply, and requires little discretion. If, however, the triggering circumstances are difficult to define in advance, require judgment to apply, give the decisionmaker substantial discretion, and so on, then we deem the law “standard-like.” For example, a law prohibiting driving at an “unsafe” speed is very standard-like.

To see the difference between the rule-standard distinction (which applies to triggering circumstances) and the smooth-bumpy distinction (which applies to input-output relationships), consider some ways to set up a dependent child tax credit. We could make the circumstances triggering the credit standard-like: you receive the credit when you have a “big” family. Or, we could make the triggering circumstances rule-like: you receive the credit when you have “four or more dependent children.” The question of how to trigger a tax credit can easily be analyzed as a rule-standard debate.

Either way, however, there is a separate question about how inputs into our tax credit analysis relate to outputs. The result could have a somewhat smooth relationship to the input: if you’re deemed to have a “big” family, you receive a $1000 tax credit for each dependent child you have. Or the result could be more bumpy: “big” families receive a $4000 tax credit no matter how many members they have.

Now, one might insist, the rule-standard distinction could also be applied to the consequences of crossing a legal threshold. If you either get $1000 per child or $4000 total, those solutions seem rule-like because they are easy to apply and don’t require discretion. We could alternatively have standard-like consequences that provide for either a “fair” amount per child or a “fair” total credit. Those used to focusing on rules and standards might say that one triggering circumstance (that can be rule- or standard-like) is whether a tax credit applies or not and then another triggering circumstance (that can be rule- or standard-like) concerns the magnitude of the credit. Fair enough.

The key point, though, is that even though the rule-standard distinction can be applied to both triggering circumstances for applying a law and triggering circumstances for selecting a result, nothing about the rule-standard distinction captures the relationship between legal inputs and outputs. So we could have a child tax credit as follows: “big” families receive $4000 total in credit no matter the precise number of children in the family. Such an approach would be standard-like in deciding what constitutes a large enough family and rule-like in deciding the amount of the credit. More importantly, it would be an odd law from an input-output perspective. Why would we have a threshold determination as to the size of the family and not make the credit depend on family size? That question is about the relationship between an input and an output and goes beyond the focus of the rule-standard distinction. The rule-standard and smooth-bumpy distinctions simply capture different issues and considerations.

This post is adapted from my opening remarks at the Legal Discontinuities conference held at Tel Aviv University's Cegla Center for Interdisciplinary Research of the Law from Dec. 29-30, 2019. Conference contributions will appear in an open access symposium issue of Theoretical Inquiries in Law.