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Tuesday, November 04, 2014

What the Binary-Scalar Distinction Misses

In a recent iteration of the Legal Theory Lexicon, Larry Solum cogently describes the binary-scalar distinction. Some legal variables take on binary values (e.g., guilty/not guilty; consensual/non-consensual), while others take on scalar values (e.g., amounts of money owed; durations of prison sentences). But the distinction  is not always helpful. If you lose your negligence cause of action, you receive no money at all. If you win, you are generally owed full compensation. Though amounts of money seem scalar because they take on a range of values, they seem binary at trial: plaintiffs either receive full compensation or no compensation at all.

What matters more, though, than trying to categorize a legal variable as binary or scalar is trying to understand how legal inputs should affect legal outputs. In a recently-published essay, Smooth and Bumpy Laws, I argue that one must have a theory about which inputs and outputs are pertinent and how they ought to relate to each other. When a gradual change to an input variable causes a gradual change to an output variable, I call that a "smooth" relationship. (Think of a dimmer switch that gradually increases room lighting.) By contrast, when a gradual change to an input sometimes causes no change to an output and sometimes causes a dramatic change, I call that a "bumpy" relationship. (Think of a traditional light switch. As you gradually move the switch, it has no effect on room lighting until you cross a particular threshold. Then, the lighting changes suddenly and dramatically.)

What matters most about the relationship between level of caution and amount of damages is that it's bumpy: reductions in level of caution have no effect on damages owed, until you cross the threshold of negligence. At that point, a small reduction in level of caution dramatically increases compensation owed. (The relationship arguably becomes smooth for a certain range of values when punitive damages kick in. Put that aside for now as punitive damages are not available in run-of-the-mill cases.)

One important feature of bumpy relationships is that they lose information. No matter how incautious you were, you still owe the same compensation. Perhaps this is the right approach. But if you think level of caution contains morally-relevant information, then you should at least question the grounds for the bumpiness. And a good theory of just compensation should either explain why the law of negligence is so bumpy or reveal what the relationship ought to be instead. There are issues of consistency, too. The doctrine of pure comparative negligence creates a rather smooth relationship between one's responsibility for an injury and the amount of compensation received or owed.

Some of the questions I address in the paper (and in subsequent draft papers) include: When should legal relationships be smooth as opposed to bumpy? Should factual uncertainty in tort or criminal cases lead to smoother outputs than they do now? To what extent does sentencing smooth the criminal law? I'll blog about several such issues in the coming days.

Posted by Adam Kolber on November 4, 2014 at 02:12 AM | Permalink


Thanks, Litigator! In a post I just put up, http://prawfsblawg.blogs.com/prawfsblawg/2014/11/advantages-of-bumpy-laws.html, I do discuss some of the advantages of bumpy laws. When I give the fourth advantage, I think I leave room for some of the things you mention.

But I confess that I'll need more evidence to be convinced. You mentioned an oddball judge. An oddball judge faced with some smooth issue might make say, a 10% error, that leads to a 10% error as to the outcome. But an oddball judge faced with some bumpy issue might make a similar 10% error that switches to one side or the other of a threshold. Now the outcome could range enormously (a murderer is erroneously deemed innocent or an innocent person erroneously deemed a murderer). It's true that the 10% error may not be noticed in run-of-the-mill bumpy cases, but when it does come into play, it makes a huge difference (perhaps the way analog tape may degrade over time but still be watchable, but throw off some key bits in your digital recording and now you can't get your software to play the thing at all). In short, you may be right, but a lot may depend on the details (good software won't fall victim to a few bad bits). But even if you're right in terms of what information theory dictates, it would still be interesting to see how well the theory holds up in real-world legal contexts.

Finally, you may also be right about a kind of virtual smoothing when lots of smaller bumpy decisions pile up. There, too, it would be helpful to give more information. In the paper, I emphasize that "smooth" and "bumpy" are really just proxies for what matters more deeply: namely, deviation from our underlying theories. So, if you or someone else can show how multiple bumpy determinations actually better match our underlying theories, that would satisfy me, at least in that particular context.

Posted by: Adam Kolber | Nov 7, 2014 10:13:16 AM

You seem to give bumpy relationships short shrift -- they have a number of advantages, at least according to information theory and signal processing. Think about digital signals, which gained currency due to the limitations of analog. Analog signals were difficult to transmit precisely in noisy conditions. Moreover, analog signals degrade over time as they are re-transmitted.

Those insights seem applicable here. The meaning of a smooth legal decision can be obscured by noise and re-transmission. One example of noise could be an oddball judge or procedural irregularity which may distort the weight participants ought to give a ruling. And there are problems of re-transmission when judges subsequently recharacterize a smooth decision in an inaccurate way, either by overemphasizing or underemphasizing salient facts. A bumpy rule is largely immune from these forms of informational corruption.

Finally, it's not clear to me that bumpy rules necessarily lack nuance. After all, a digital signal is limited in range, but when combined in combinatio with other signals, they are capable of expressing a nearly infinite range of concepts. Taking that cue, maybe the solution is to design a set of bumpy rules that, when viewed in a bigger context, are capable of shedding light on complex issues.

Posted by: Litigator | Nov 6, 2014 9:32:29 PM

Thanks, WG! Sure, I'll be happy to address the inevitability question in the coming days. (The short answer, though, is that they're definitely not inevitable. The easiest example of that is comparative negligence. For a long time, most states used principles of contributory negligence which are very bumpy. Over the course of several decades, most states switched to some form of comparative negligence which is considerably smoother (and in its pure form is quite smooth).) Katz does speak as though the law has to be all-or-nothing, but there are many counterexamples in which the law could be made less all-or-nothing.

Posted by: Adam Kolber | Nov 5, 2014 3:36:36 PM

I'm looking forward to your posts. In additions to the questions you list, could you address whether bumpy laws are in some way inevitable (I'm thinking of Leo Katz's work, for example)?

Posted by: WG | Nov 5, 2014 8:12:05 AM

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