Reapportionment math is more complicated than you think

Today, we'll find out which states will gain seats in the U.S. House (and thus the Electoral College), and which will lose seats. Roughly, if you gained population at a rate significantly greater than the whole country, you gain seats. If you lost population or gained at a rate significantly below the national gain, you lose seats.

But just how they parcel out the seats involves math much more complicated than you'd expect.

To make representation actually proportional to population, you would need (a) to multiply the number of seats in Congress by a lot, or (b) to split congressional seats across state lines. Neither is happening without changing the Constitution, so we're left with some unevenness and some complex formulas.

Start by dividing the U.S. population (roughly 310 million) by the number of House seats (435). You get about 715,000 people per House seat. But not every state has a population that is a multiple of 715,000.

If you start to try to think how you would do it, you realize that there's not one simple method. There are many different ways to parcel out the seats, and over time Congress has used different methods. Every method results in nearly every state's ratio of people : congressmen differing somewhat from the mean proportion of 715,000 : 1. The current method is based on the principle of minimizing the difference between the actual proportion from the mean proportion. It's more complicated than that, and this Wikipedia article explains it as clearly as anyone:

The Huntington–Hill method of apportionment assigns seats by finding a modified divisor D such that each constituency's priority quotient (population divided by D ), using the geometric mean of the lower and upper quota for the divisor, yields the correct number of seats that minimizes the percentage differences in the size of the congressional districts[1]. When envisioned as a proportional voting system, this is effectively a highest averages method in which the divisors are given by scriptstyle D=sqrt{n(n+1)}n being the number of seats a state is currently allocated in the apportionment process (the lower quota) and n+1 is the number of seats the state would have if it is assigned to this state (the upper quota).

The loser: A state like Montana, with just under 1 million people, gets only one Rep.

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