Front Page Titles (by Subject) OPINION ON THE BILL APPORTIONING REPRESENTATION 1 - The Works, vol. 6 (Correspondence 1789-1792)
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OPINION ON THE BILL APPORTIONING REPRESENTATION 1 - Thomas Jefferson, The Works, vol. 6 (Correspondence 1789-1792) 
The Works of Thomas Jefferson, Federal Edition (New York and London, G.P. Putnam’s Sons, 1904-5). Vol. 6.
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OPINION ON THE BILL APPORTIONING REPRESENTATION1
April 4. 1792.
The Constitution has declared that representatives and direct taxes shall be apportioned among the several States according to their respective numbers. That the number of representatives shall not exceed one for every 30,000, but each State shall have at least one representative, and until such enumeration shall be made, the State of New Hampshire shall be entitled to choose 3, Massachusetts 2. &c.
The bill for apportioning representatives among the several States, without explaining any principle at all, which may show its conformity with the constitution, to guide future apportionments, says, that New Hampshire shall have 3 members, Massachusetts 16, &c. We are, therefore, to find by experiment what has been the principle of the bill; to do which, it is proper to state the federal or representable numbers of each State, and the numbers allotted to them by the bill. They are as follows:—
It happens that this representation, whether tried as between great and small States, or as between north and south, yields, in the present instance, a tolerably just result; and, consequently, could not be objected to on that ground, if it were obtained by the process prescribed in the Constitution; but if obtained by any process out of that, it becomes arbitrary and inadmissible.
The 1st member of the clause of the Constitution above cited is express, that representatives shall be apportioned among the several States according to their respective numbers. That is to say, they shall be apportioned by some common ratio—for proportion, and ratio, are equivalent words; and, in the definition of proportion among numbers, that they have a ratio common to all, or in other words, a common divisor. Now, trial will show that there is no common ratio, or divisor, which, applied to the numbers of each State, will give to them the number of representatives allotted in this bill. For trying the several ratios of 29, 30, 31, 32, 33, the allottments would be as follows:—
Then the bill reverses the constitutional precept, because, by it, representatives are not apportioned among the several States, according to their respective numbers.
It will be said that, though, for taxes, there may always be found a divisor which will apportion them among the States according to numbers exactly, without leaving any remainder, yet, for representatives, there can be no such common ratio, or divisor which, applied to the several numbers, will divide them exactly, without a remainder or fraction. I answer, then, that taxes must be divided exactly, and representatives as nearly as the nearest, ratio will admit; and the fractions must be neglected, because the Constitution calls absolutely that there be an apportionment or common ratio, and if any fractions result from the operation, it has left them unprovided for. In fact it could not but foresee that such fractions would result, and it meant to submit to them. It knew they would be in favor of one part of the Union at one time, and of another at another, so as, in the end, to balance occasional irregularities. But instead of such a single common ratio, or uniform divisor, as prescribed by the Constitution, the bill has applied two ratios, at least, to the different States, to wit, that of 30.026 to the seven following: Rhode Island, New York, Pennsylvania, Maryland, Virginia, Kentucky and Georgia; and that of 27,770 to the eight others, namely: Vermont, New Hampshire, Massachusetts, Connecticut, New Jersey, Delaware, North Carolina, and South Carolina, as follows:—
And if two ratios be applied, then fifteen may, and the distribution become arbitrary, instead of being apportioned to numbers. Another member of the clause of the Constitution which has been cited, says “the number of representatives shall not exceed one for every 30,000, but each State shall have at least one representative.” This last phrase proves that it had no contemplation that all fractions, or numbers below the common ratio were to be unrepresented; and it provides especially that in the case of a State whose whole number shall be below the common ratio, one representative shall be given to it. This is the single instance where it allows representation to any smaller number than the common ratio, and by providing especially for it in this, shews it was understood that, without special provision, the smaller number would in this case, be involved in the general principle. The first phrase of the above citations, that “the number of representatives shall not exceed one for every 30,000, is violated by this bill which has given to eight States a number exceeding one for every 30,000, to wit, one for every 27,770.
In answer to this, it is said that this phrase may mean either the 30,000 in each State, or the 30,000 in the whole Union, and that in the latter case it serves only to find the amount of the whole representation; which, in the present state of population, is 120 members. Suppose the phrase might bear both meanings, which will common sense apply to it? Which did the universal understanding of our country apply to it? Which did the Senate and Representatives apply to it during the pendency of the first bill, and even till an advanced stage of this second bill, when an ingenious gentleman found out the doctrine of fractions, a doctrine so difficult and inobvious, as to be rejected at first sight by the very persons who afterwards became its most zealous advocates?
The phrase stands in the midst of a number of others, every one of which relates to States in their separate capacity. Will not plain common sense then, understand it, like the rest of its context, to relate to States in their separate capacities?
But if the phrase of one for 30,000 is only meant to give the aggregate of representatives, and not at all to influence their apportionment among the States, then the 120 being once found, in order to apportion them, we must recur to the former rule which does it according to the numbers of the respective States; and we must take the nearest common divisor, as the ratio of distribution, that is to say, that divisor which, applied to every State, gives to them such numbers as, added together, come nearest to 120. This nearest common ratio will be found to be 28,058, and will distribute 119 of the 120 members, leaving only a single residuary one. It will be found too to place 96,648 fractional numbers in the eight northernmost States, and 105,582 in the seven southernmost. The following table shows it:
Whatever may have been the intention, the effect of neglecting the nearest divisor, (which leaves but one residuary member,) and adopting a distant one (which leaves eight), is merely to take a member from New York and Pennsylvania, each, and give them to Vermont and New Hampshire. But it will be said, this is giving more than one for 30,000. True, but has it not been just said that the one for 30,000 is prescribed only to fix the aggregate number, and that we are not to mind it when we come to apportion them among the States? That for this we must recur to the former rule which distributes them according to the numbers in each State? Besides does not the bill itself apportion among seven of the States by the ratio of 27,770? which is much more than one for 30,000.
Where a phrase is susceptible of two meanings, we ought certainly to adopt that which will bring upon us the fewest inconveniences. Let us weigh those resulting from both constructions.
From that giving to each State a member for every 30,000 in that State results the single inconvenience that there may be large portions unrepresented, but it being a mere hazard on which State this will fall, hazard will equalize it in the long run. From the others result exactly the same inconvenience. A thousand cases may be imagined to prove it. Take one. Suppose eight of the States had 45,000 inhabitants each, and the other seven 44,999 each, that is to say each one less than each of the others. The aggregate would be 674,993, and the number of representatives at one for 30,000 of the aggregate, would be 22. Then, after giving one member to each State, distribute the seven residuary members among the seven highest fractions, and though the difference of population be only an unit, the representation would be the double.
Here a single inhabitant the more would count as 30,000. Nor is the case imaginable, only it will resemble the real one whenever the fractions happen to be pretty equal through the whole States. The numbers of our census happen by accident to give the fractions all very small, or very great, so as to produce the strongest case of inequality that could possibly have occurred, and which may never occur again. The probability is that the fractions will generally descend gradually from 29,999 to 1. The inconvenience then of large unrepresented fractions attends both constructions; and while the most obvious construction is liable to no other, that of the bill incurs many and grievous ones.
1. If you permit the large fraction in one State to choose a representative for one of the small fractions in another State, you take from the latter its election, which constitutes real representation, and substitute a virtual representation of the disfranchised fractions, and the tendency of the doctrine of virtual representation has been too well discussed and appreciated by reasoning and resistance on a former great occasion to need development now.
2. The bill does not say that it has given the residuary representatives to the greatest fraction; though in fact it has done so. It seems to have avoided establishing that into a rule, lest it might not suit on another occasion. Perhaps it may be found the next time more convenient to distribute them among the smaller States; at another time among the larger States; at other times according to any other crotchet which ingenuity may invent, and the combinations of the day give strength to carry; or they may do it arbitrarily by open bargains and cabal. In short this construction introduces into Congress a scramble, or a vendue for the surplus members. It generates waste of time, hot blood, and may at some time, when the passions are high, extend a disagreement between the two Houses, to the perpetual loss of the thing, as happens now in the Pennsylvania assembly; whereas the other construction reduces the apportionment always to an arithmetical operation, about which no two men can ever possibly differ.
3. It leaves in full force the violation of the precept which declares that representatives shall be apportioned among the States according to their numbers, i. e., by some common ratio.
Viewing this bill either as a violation of the constitution, or as giving an inconvenient exposition of its words, is it a case wherein the President ought to interpose his negative? I think it is.
1. The non-user of his negative begins already to excite a belief that no President will ever venture to use it; and has, consequently, begotten a desire to raise up barriers in the State legislatures against Congress, throwing off the control of the constitution.
2. It can never be used more pleasingly to the public, than in the protection of the constitution.
3. No invasions of the constitution are fundamentally so dangerous as the tricks played on their own numbers, apportionment, and other circumstances respecting themselves, and affecting their legal qualifications to legislate for the union.
4. The majorities by which this bill has been passed (to wit: of one in the Senate and two in the Representatives) show how divided the opinions were there.
5. The whole of both houses admit the constitution will bear the other exposition, whereas the minorities in both deny it will bear that of the bill.
6. The application of any one ratio is intelligible to the people, and will, therefore be approved, whereas the complex operations of this bill may never be comprehended by them, and though they may acquiesce, they cannot approve what they do not understand.
[1 ]Hamilton’s and Randolph’s Opinions are printed in Hamilton’s Writings of Hamilton, IV., 207; as also a summary of the three by Jefferson.