ABA Section of Business Law
Business Law Today
Volume 10, Number 2 November/December 2000
Legal-ease
By Howard Darmstadter
The arithmetical lawyer
The pooling and servicing agreement for a credit card securitization provides for monthly interest payments to the class A certificates equal to the product of (i) the product of (x) the class A certificate rate and (y) a fraction the numerator of which is the actual number of days in the related interest period and the denominator of which is 360 and (ii) the class A principal balance as of the close of business on the last day of the preceding monthly period .... You've probably seen thousands of similar provisions. If you're feeling conscientious, you stop, pick up your pencil, and on a legal pad you reverse engineer the provision into something like:
We learned the arithmetical notation for equations in elementary school. Unlike the lawyer's word version, arithmetical notation is almost instantly comprehensible. It would be impossible to do any complex mathematics if we were limited to the word versions that stalk legal agreements. And, indeed, the use of verbal formulations rather than arithmetical notation is a prime contributor to the opacity of many agreements. So why didn't the drafter use arithmetical notation?
One answer I have heard is that lawyers are, as a group, a tad weak in arithmetic. Words are our delight, but numbers supposedly frighten us.
I'm suspicious of such a generalization, but we need not decide the issue here, because I'm not talking about lawyers generally. If a lawyer is not comfortable with arithmetical relations, he's going to put all the distance possible between himself and the nearest pooling and servicing agreement. He certainly will not be found drafting such a document.
A more convincing explanation is that lawyers draft that way because that's the way they're taught. We learn to draft by reading the documents that went before us, and lawyers have been describing numerical relationships in tortured prose for decades.
But that just postpones the question. There must have been a distant time when Urnie, our ur-lawyer, first had to include an equation in a document. I've got to believe that Urnie first structured the quoted provision, or its paleolithic predecessor, in arithmetical notation. Why did he then recast it in lawyer-speak?
Perhaps Urnie tried to use arithmetical notation, but failed because his secretary, Ureka, couldn't adequately produce it with the technology of her time, the typewriter. With planning and patience, Ureka might have produced something like:
Not bad, but not as instantly comprehensible as our first version. The difference is that unlike Ureka, I had available all the resources of a modern word-processing program, including an equation editor.
These days, Ureka is a lawyer, not a secretary, but she still does the typing (although we now call it word processing). And she still bangs out the equations in words. Like most lawyers, she is probably modifying an existing document. Ureka doesn't know why the document she starts with describes arithmetical relations in words rather than arithmetical notations. If she's like most lawyers - and most lawyers are - she doesn't ponder long on the technological constraints of bygone legal practice. She probably just assumes that the convoluted prose descriptions of numerical relationships represent legal, not technological requirements.
In any case, prudence dictates that Ureka not attempt to recast the entire document, but simply change a few words here and there. After all, her clients are unlikely to indulge her by paying the fees, and enduring the delays, that a full-scale rewrite would entail. Recasting a document only makes sense at an enterprise level, where the costs can be spread out over many documents and clients.
It would be nice to think that lawyers hang on to outmoded conventions simply out of solicitude for their clients. But there is a larger cause for Ureka's caution: Fear. The idea that a court would reject a contractual provision because it uses arithmetical notation familiar from grammar school, rather than word formulations only found in legal agreements, is nonsense. (Not so nonsensical, of course, that some judge somewhere might take such a position. But when you're dealing with the wackier fringes of the judiciary, all bets are off; arithmetical notation is just as likely to help as hurt you.) Nonetheless, Ureka's fear that a court might take such a position is part of legal culture. And that culture begins in law school.
One of the first things Ureka learned in law school was caution. In law school, legal eaglets are regaled with stories of lawyers who totaled the client's Ferrari because they missed some legal nicety. Be careful out there! is the constant message. No stories are told of lawyers who were right to take a chance - that is, to balance legal concerns against practical business concerns, and to find the legal concerns wanting. The law school ethos, if it were applied to doctors, would be: Don't operate, don't medicate!
Caution can lead to paralysis: In the crucible of battle ("Have that draft agreement on my desk at oh-nine-hundred!"), the raw recruits freeze up. Knowing she has to do something, yet afraid to do anything, Ureka, the associate, makes the minimal changes possible. Heinrich, the surgical intern, faces larger terrors, and probably responds no better. But Heinrich's culture is overtly interventionist, so his errors are likely to be of commission rather than omission. With luck, Ureka's errors will not be noticed, and Heinrich's will be buried.
One day, Ureka is a partner, but the culture of caution remains. For one thing, she has behind her a body of cautious work, in which she is likely to take some pride. Moreover, she now has a new source of anxiety: malpractice suits. What if something should go wrong with the new-fangled document? Better to rely on the tried, true, and as yet unsued-on, standbys.
But, hey, you and me, we're better than that. We want to lead the world to a better tomorrow. We want to shake off the fetters of convention, to seize the opportunities, to be heroes! And we'd prefer to do it without taking any chances. What safer way than using arithmetical notation?
There is of, course, a downside to using arithmetical notation. For one thing, equation editors can be extremely clunky. More important, placing a formula into arithmetical notation can lead to all sorts of manipulations, some of which can muddy the message. Consider our first formula, which could also be expressed as:
Arithmetically correct, and probably better than the original word formulation, but it doesn't explain things as well as our first arithmetical formula. On the other hand, manipulations can also clarify. We can, for example, reorganize the formula as
which explains the concept of "interest calculated on a year of 360 days and actual days elapsed" better than any word formulation. To see the power of the method, suppose that interest is being paid "over a year of twelve thirty-day months." That is, the number of days in each monthly interest period is set at 30, so our formula becomes
Of course, 30 over 360 is just 1 over 12, so the formula reduces to:
which, to my eye, is the simplest possible explanation of the drafter's intention. Unless, of course, something else was intended, in which case arithmetical notation has revealed a lurking ambiguity.
Try it, legal daredevils.Darmstadter is an assistant general counsel at Citigroup in New York City. You can e-mail him at darmstadte@citi.com.
