Commentaries on Representation

The Blog for Thirty-Thousand.org

Commentaries on Representation

The Blog for Thirty-Thousand.org

Reconstructing Article the First: David Kyvig’s Graduated Reading and Why It Cannot Hold

A distinguished historian gallantly tried to rescue Article the First from absurdity by imputing to it an imagined formula. However, the amendment’s own words — and its progenitors passed in each chamber — will not allow it. Pressed for consistency, the formula is forced to revert to the very text that had been inexplicably replaced.

A clause in need of rescue

The first of the twelve amendments Congress proposed in 1789 — Article the first — laid out a three-tiered formulation for sizing the House of Representatives as our nation’s population grew. However, the version of this proposal that was sent to the states for ratification contained a defect in its formulation. Not only did that defect effectively doom the proposal, but it has created a remarkable amount of confusion.

As proposed to the states, the first Article’s operative final clause provides that once the House reaches two hundred members (at a population of eight million), “there shall not be less than two hundred Representatives, nor more than one Representative for every fifty thousand persons.” If so ratified, that last phrase would cap the House at the national population divided by fifty thousand — roughly 6,600 today — while simultaneously setting a corresponding minimum size of 200 Representatives. Yet that proposal has rarely been understood for what it is: Most readers mistakenly interpret the clause as a command to establish a minimum House size at that same ratio (one for every fifty thousand). This textual illusion has fooled scholars for over two centuries.

The subject of this essay is one historian’s attempt to make sense of this broken clause. David E. Kyvig interpreted it in two incompatible ways, across successive editions of his Bancroft Prize–winning history of the amending process. And both interpretations were wrong, adding him to the list of scholars who have misinterpreted the defective version. The point here is not that a careful historian stumbled over arithmetic, but how persistently misleading the defective proposal is.

From five thousand to sixteen hundred

In his original treatment,¹ Kyvig misread the clause as fixing a maximum district size² of fifty thousand, which would require at least one Representative for every fifty thousand people. Though he probably didn’t realize it, he was interpreting the defective proposal as if it were the coherent version the House had passed earlier, with a floor that guarantees a minimum level of representation, rather than a ceiling that caps it. But the defective enrolled text actually states the reverse: It sets a minimum district size — no district smaller than fifty thousand — which would therefore set the maximum number of Representatives instead of the minimum. That a ceiling can be subconsciously perceived as a floor is the inexplicable inversion at the heart of Article the first, and Kyvig, like most readers, was caught in the textual illusion’s trap.

Presumably aware of his mistake, Kyvig later changed his mind. The revised edition of his book, published twenty years later,³ advances an alternative reading:

Historians (myself included) and political scientists, following the lead of Clinton Rossiter’s 1966 study of the American founding, have misunderstood and overlooked Madison’s unratified first amendment, some assuming incorrectly that it would have fixed congressional districts at 50,000 inhabitants. Such a mandate would have required an unwieldy body of 5,200 representatives by the last decade of the twentieth century. In reality, Madison’s formula was far more modest. After the 1990 U.S. census, district size would have been set at 170,000 rather than 572,467 residents, and the House of Representatives would have had 1,465 members. Twenty years later, in response to the 2010 census, the formula would have raised the size of districts to 190,000, instead of the average size of 710,767, and the House would have had 1,625 members, in place of the current 435-seat limit.

What Kyvig calls “Madison’s formula” is, in fact, his own imaginative extrapolation of the defective version sent to the states. From its three pivot ratios — one Representative per thirty thousand, then per forty thousand, then per fifty thousand — Kyvig infers the opening steps of a graduated pattern meant to continue.

As a result, Kyvig went from imagining a House of five thousand members in his first book to one of sixteen hundred in his second. That such a careful historian could read a single short clause two incompatible ways — both of them wrong — is itself a measure of how deceptively this version of Article the first is worded.

Where the reading comes from

Kyvig’s graduated construction is an inference, and it is worth being precise about what it infers from — and who has made the inference explicit. The revised edition’s text supplies only endpoints: Districts of 170,000 and a House of 1,465 after 1990; districts of 190,000 and a House of 1,625 after 2010. It never states the rule that produces those numbers. The rule behind those figures was later spelled out by Greg Blonder, a physicist and inventor writing as an interested non-specialist, whose account historians and encyclopedias have since followed.⁴ He put it plainly: Fifty thousand is not a cap but “merely the appropriate divisor until Congress has 300 members, at which point district sizes rise to 60,000.” On that reading the divisor climbs by ten thousand with each additional hundred seats — fifty thousand to three hundred members, then sixty thousand to four hundred, seventy thousand to five hundred, and upward without end.

That this is a faithful definition of Kyvig’s rule is not in doubt: It reproduces his published figures exactly. A divisor of 170,000 applied to the 1990 population yields his 1,465 members; a divisor of 190,000 applied to the 2010 population yields his 1,625. Kyvig’s endpoints and Blonder’s rule are the same object seen from two ends.

But Kyvig’s rule cannot be logically derived from the amendment; it can only be creatively imputed into it. The text supplies three divisors and then stops, at the third tier, where it imposes only outer constraints: Not fewer than two hundred, nor more than one per fifty thousand. What drives the extrapolation past that terminus is not anything in the proposed amendment, but an assumption about what the founders intended. Initially interpreted as a flat fifty-thousand maximum on district size, the clause would yield a House of several thousand — unworkably large from Kyvig’s perspective — so he sought something that would produce a slower increase in House size, and an ascending schedule supplies it. He appears to reason backward from the preferred destination — a modestly sized chamber — to a formula that would reach it. The impulse is understandable. It is not, however, an interpretation. It is a repair.

The schedule breaks down

Even if Kyvig’s interpretation seems plausible in principle, it would fail spectacularly in execution — a breakdown more readily apparent to a mathematician than to a historian. At each step, the larger divisor yields fewer seats for the same population than the tier it is leaving; so at the very moment the House would “graduate” to a higher divisor, the rule calls for it to lose seats before it can grow again. And this is not a one-off at some unlucky figure: the break repeats at every step the schedule takes beyond the amendment’s own text.

In each of those dead zones — the shaded bands in the chart — the rule specifies no House size at all. The first such gap falls exactly where the proposed amendment’s text runs out, as the House passes three hundred members, and each gap is wider than the last as the schedule climbs: Roughly a million people of no-man’s-land at the first step, then two million, three, four, five.

What the void leaves is not silence but nearly unbounded discretion; the only limits still standing are the floor the amendment keeps — not fewer than two hundred — and the Constitution’s ceiling (of one Representative for every thirty thousand).⁵ Between the two, in each gap, any size at all would satisfy the rule — at a population of sixteen million, anywhere from two hundred to better than five hundred seats; at twenty-six million, from two hundred to past eight hundred. And because those gaps keep widening, that band of bare discretion grows as the nation does: a provision written to fix the size of the House, in the very gaps it opens, hands the question back — and hands back more of it with every census. That so few plain words can read as a binding rule and yet settle nothing is the quiet trap at the heart of this interpretation of Article the first.

The proposed amendment’s tiers do not have this problem, because a transitional floor is defined between each of its tiers: “Not less than one hundred Representatives,” the text says at the first threshold, and “not less than two hundred” at the second. A floor of that kind holds the House at its current size across the gap until population catches up, smoothing the steps into a nearly continuous progression. The text supplies such a floor at one hundred and at two hundred — and then it stops. Kyvig’s extension to three hundred, four hundred, and beyond supplies none. Perhaps to bridge exactly these gaps, Blonder offered a repair to Kyvig’s repair in the form of a square root rule.⁶

So Kyvig’s graduated reading produces a dilemma with no solution. Leave the gaps unbridged, and the schedule is no schedule at all: It directs the House to shrink at the very moment it grows. Bridge them, and one must insert at each new step instructions similar to those used between the initial transitions — not less than the number already reached. But “not less than” is a floor, and a floor is exactly what the defective version does not contain in its final tier. Its defining act was to replace the third tier’s intended “nor less than” with “nor more than.” To make the graduated reading run, in other words, one must restore the intended wording to remove the defect.

In fact, confronting the clause’s confounding arithmetic, Blonder did exactly that; he reprinted its final phrase with a single word restored — “nor more (LESS) than” — noting that he had added “less” to show how the inconsistency could be resolved. He does not appear to have recognized that he was restoring the defective first Article to its intended version: It reconstitutes, word for word, the version the House had actually passed. Reaching only for the word that makes the clause cohere, he arrived back at the text the drafters meant to send. The graduated reading, pressed for consistency, reverts to the proposal it was meant to replace.

And its progenitors will not bear it

There is a further obstacle, one Kyvig appears not to have weighed — likely because his attention was fixed on the final version sent to the states rather than on the amendment’s lineage. The enrolled text had two authentic predecessors. The version passed by the House set the final tier as a floor: Not less than one Representative per fifty thousand — a guaranteed minimum number of Representatives, perpetually rising with population. The Senate’s counterpart pegged the continuing ratio at one per sixty thousand (both a minimum and a maximum). Whatever their differences, both of these coherent versions point toward more representation as the nation grows, secured by a fixed or minimum ratio.

Kyvig’s ascending divisor points the opposite way. A schedule in which the divisor climbs — fifty, sixty, seventy thousand and upward — is a schedule of steadily thinning representation, each citizen sharing a Representative with ever more people. Because none of the defective first Article’s predecessor versions behaves this way, it could not have been intended. The House floors the ratio at 1:50,000; the Senate fixes it at 1:60,000; neither lets the proportional minimum escalate. Though he may not have realized it, the floor Blonder reached for to rescue the formulation is, precisely, the floor specified in the intended version.

A formula that yields no single answer

The defective first Article is akin to a Rorschach test: It reveals more about the reader’s expectations than about the inkblot itself. In this case, a single clause has been read to describe wildly different Houses, depending only on how the reader misinterprets it.

Interpreted literally, the defective version adds a ceiling: “No more than one Representative for every fifty thousand persons” caps the House at the national population divided by fifty thousand — today, about 6,600.⁷ Read instead as nearly everyone misperceives it, with “less” subconsciously replacing “more,” the very same clause becomes a floor: It would require about 6,600, and more as the nation grows. Same forty words, the same division, the same number at the end of it — yet one reading fixes the most seats the House may have and the other the fewest. That is the whole of the matter: a single inverted word is all that stands between a ceiling and a floor — between a House that may be held, as it has been, at 435, and a House compelled to grow without limit.

Kyvig’s graduated reading escapes that fork only by supplying a rule of continuation the text never states — and, having supplied it, can settle on no single answer of its own. Continue the schedule one way and the House is 1,465; another way, 1,625; another way still, something else again. Set those beside the flat reading’s several thousand, and the same forty words have been taken to mean a House of about 1,500, or 5,000, or 6,600 — the figure set by the reader, not by the text. A genuine formula does not return a range of answers according to who consults it; the dispersion is itself the evidence that each reader supplies the rule the text leaves out.

A repair presupposes a defect

The graduated reading is creative, and its motive is honorable: it tries to construct a workable interpretation of Article the first. But every version of that effort begins by conceding that the enrolled text, read as written, does not work — which is precisely the point. One does not search for an implied formula unless the explicit one has failed. And the search ends where it must: the only adjustment that makes the clause cohere is the restoration of the word the conference committee replaced. Kyvig’s construction is therefore not a rival to the conclusion that the defective version is broken; it is a response to it. A repair presupposes a defect.

Read against its own words, and against the two versions the founders actually wrote, the defective version of Article the first is not a mandate to enlarge the House. It is only a ceiling; and because the sole floor it sets is two hundred, it would permit a House as small as two hundred Representatives — smaller even than today’s 435.