A question re: Constitutional Convention (inhabitants per seat in House of Representatives)

Thank you in advance for helping me (a Canadian) learn and understand a bit more about early US history. I am looking for an answer to the question below:

At the eleventh hour, the delegates to the Philadelphia Convention in 1787 altered a key component of their proposal for the US constitution. Specifically, they changed one of its articles so that each state would receive one representative in the House of Representatives for every 30 thousand of its inhabitants. The earlier apportionment had been one rep for every 40 thousand inhabitants.

In a book I read recently, the statement was made that this adjustment favored the more populous states (“the big states”) and, hence, that it was all the more remarkable that the Convention delegates from the small states ever agreed to it. I keep thinking that I must be missing something, and I guess I am, but I cannot see how changing the ratio of inhabitants per representative in the House favors any state, whether a big, populous one or a small one.

Regardless whether the allocation is one rep per 30 thousand or one rep for 40 thousand, all states will wind up having their percentage of the total seats in the House remain the same. Sure, with the ‘one rep per 30 thousand’ a populous state receives more seats in an absolute sense. But the ratio of that state’s reps to any other’s reps remains the same, as does any state’s percentage of the total seats in the House.

Am I missing something?


Every state has at least one rep, which skews the ratios.

Suppose State A = 20,000 people and State B = 500,000. At one rep per 40,000, A has one rep and B has 13. At one rep per 30,000, A has one rep and B has 17.

I actually thought of that problem (“rounding”) but didn’t think it applied for the state populations at the time of the Convention. Look here for some figures. I still may have miscalculated, mind you.

You’re correct when working with rational numbers. The problem is that representatives must be apportioned in whole number quantities.

Here’s an simplified example. We’ll take a country with 3 states. State A has 10,000 people, B has 80,000, and C has 150,000, for a total of 240,000.

If there is one representative for every 40,000, we need to award 6 seats. Division tells us that A gets 0.25, B gets 2, and C gets 3.75. Now, since all seats must be whole numbers and every state gets at least one, we award 1 to A, 2 to B, and 3 to C. This is true despite the fact that A is much further from actually mathematically “deserving” even one seat than C is from the 4th. Notice that the agreement of at least two states is required to accomplish anything, since A and B can team up to stop C.

Now, look at the situation where there is one representative for every 30,000. There are now 8 representatives. Division tells us that A gets 0.333, B gets 2.667, and C gets 5. Since A gets at least 1, the awards must be A: 1, B:2, C:5.

There are two important things to note here. First, two additional seats were awarded, and they both went to C. Secondly, state C can now single-handedly push through anything it likes.

I picked the numbers to be fairly simple here, but it’s essential to realize that I didn’t have to work hard to come up with this situation. The history of apportionment in the US is filled with these little mathematical quirks. In general, more seats will more often favor the larger states.

If you’re interested, there are some other paradoxes that arise through apportionment.

Other issues arise with how to deal with fractional seats. I intentionally picked my values to avoid these issues, but there have been some pretty brutal political arguments over the last 2+ centuries about how to deal with it. It’s not just academic either. A slightly bigger House or some older apportionment methods would have led to Gore winning in 2000.

Thank you - very, very helpful.

Given the brainpower at the Convention (and around here), I think it’s safe to assume that my “analysis” of the numbers was wrong :wink:

The Framers were also concerned that House districts that were too big would lead to Congressmen (and they were all men back then) being too remote and out of touch with their constituents. Now that House districts have more than half a million people each, they just might’ve been on to something.

Miracle At Philadelphia by Catherine Drinker Bowen is a good pop history of the Constitutional Convention, and is well worth a look.

After considering this at greater length, I believe you’re right and the book you were reading is wrong.

As Elendil’s Heir notes, most of the discussion of the issue revolved upon the “right size” of a House district in the abstract, not as it affected the ratio of representation between states. Because you’re right, it had very little effect on the ratio between states.

I ran the results of the first census using district size of 30,000 and 40,000, and using the simplest possible apportionment rule of rounding up or down to the nearest integer. (As it happened Congress eventually chose a baseline size of 33,000 after complicated Consitutional arguments and a George Washington veto, but that need not concern us here.)

With a 30K baseline, and considering Kentucky and Vermont as separate states (which they were by 1792), the five largest states had 74 of 120 representatives, or 61.7% of the total. The five smallest had 11 of 120, or 9.2%.

With a 40k baseline, the five largest states had 56 of 91 seats, or 61.5%. The five smallest had 9 of 91, or 9.9%. We are splitting fractions of a percentage point. The difference is trivial.

To really move the needle you have to move to a baseline size much larger than the smallest state, such as 100k or even 200k. Thirty-k versus forty-k is not a plausible big state-versus-small state issue, and it wasn’t argued as such at the time.

Just remembered that one of the two not-initially-adopted measures of the Bill of Rights dealt with apportionment: http://en.wikipedia.org/wiki/Article_the_First. Had it passed (and it still might!), we would now have a House of Representatives with more than 6,000 members.

Which is twice the size of China’s National People’s Congress; the largest legislative body in the world. It meets twice a year and delegate’s most of his work to it’s Standing Committee. It’s hard to imagine how the US House could function with that many members. Had the amendment passed it would almost certainly have been repealed long ago.

You also have to consider that the number of Congressional seats allotted to each state changes every ten years. States can gain or lose seats depending on increase or decrease of the population as determined by the decennial Census. States that started out with relatively few seats, such as California, Arizona, and Texas have since gotten much more clout simply because their populations have exploded. Conversely, states such as Pennsylvania have seen their influence drop like a rock because they lose seats due to their loss of population. (Pennsylvania is the Vestibule to the God’s Waiting Room that is Florida.)