A House committee will soon consider a measure to admit the District as the 51st state. Skeptics have their doubts. (J. Scott Applewhite/AP)

A House committee will soon consider a measure to admit Washington as the 51st state. Don’t hold your breath: D.C. residents are overwhelmingly Democrats, so the Republican-led Senate and President Trump are unlikely to go along.

But imagine that a future Democratic Congress and White House pave the way for statehood for the District and possibly Puerto Rico. Expanding the number of states — but not increasing the size of the House — would raise a host of practical and politically prickly challenges for both parties.

Here are five things you need to know about the math and politics of adding new states.

1. It’s a fight as old as the country

The Great Compromise between the “large” and “small” states that made the U.S. Constitution possible required resolving the dilemma of congressional apportionment. More-populous states wanted to base each state’s number of seats on how many people lived there; smaller states demanded equal representation. The Great Compromise split the difference: proportional representation in the House, equal in the Senate.

To keep that compromise, the House would need to expand as the nation’s population grew and new states joined the Union. Between 1789 and 1913, the size of the U.S. House gradually grew from 65 seats to 435 seats, where it remains today.

2. How are seats doled out to the states?

As required by the U.S. Constitution, every 10 years the U.S. Census counts all the residents in each state. Under the current rules, add in designated residents overseas and you get each state’s apportionment population.

The apportionment population of every state, however, has never been a whole-number multiple of an ideal district size. And because a state can’t be assigned with say, 1.5 representatives, some rounding is needed.

The census since 1941 has used the Hill method of equal proportions, which rounds these fractions on the geometric mean of the two nearest whole numbers. This provides a slightly lower threshold for smaller states than the normal arithmetic mean. Take Rhode Island after the 2010 Census. Its quotient was about 1.486; the geometric mean of 1 and 2 is 1.414; Rhode Island’s quotient, then, was rounded up; and it receives two seats in the U.S. House for the next decade.

3. What’s so special about 435 seats?

The 1920 Census showed that the United States was no longer a majority rural country. As more people lived in urban areas, their representatives sought to add seats to the House to give adequate representation to growing cities. But House members from rural areas in 1921 defeated a measure to enlarge the House from 435 to 483 seats.

The House has remained frozen at 435 seats since then — except in 1959 to accommodate the admission of Alaska and Hawaii. But after the 1960 Census, Congress reverted the House to 435 members. To accommodate a new seat for Alaska and two for Hawaii, the mathematics of the Hill method meant that Massachusetts, Missouri and Pennsylvania had to give up one seat each to make room for the representatives from Alaska and Hawaii.

4. Which state would give up a seat for D.C. or for Puerto Rico?

That brings us to today. If we use the current method for apportioning seats and the census’s resident population estimates, 37 states would keep the same number of representatives as they had after 2010. Seven states would lose a seat (Illinois, Michigan, Minnesota, New York, Pennsylvania, Rhode Island and West Virginia); five states would gain a seat (Arizona, Colorado, Florida, North Carolina and Oregon); Texas would gain two.

Based on the 2018 Census estimates, the District has 702,455 — more people than either Wyoming or Vermont. If the District were a state, it would receive one House member. Puerto Rico has an estimated 3.2 million residents, earning it four House seats.

But if the House won’t expand beyond 435 seats, other states would have to pony up the extra seats for D.C. and Puerto Rico. Based on the Hill method and these estimates, if Congress just adds the District’s one seat, it would come from California’s 2018 delegation, which would drop from 53 seats to 52.

To add just Puerto Rico’s four seats, then Alabama, Arizona, California and Ohio would give up one seat each. And if both the District and Puerto Rico gained seats, then those four states plus Colorado would each lose one seat.

5. So why not make the House bigger?

Congress could amend the Apportionment Act of 1941 to expand the size of the House.

In that case, how large should the House be? Right before the House was frozen at 435 in 1921, one common benchmark was to increase the House size so that no state would lose any seats.

For none of the 50 states to lose any seats based on 2018 population estimates, the House would need to be increased to 447 seats. In doing so, the seven states that would have lost a seat would not. Seven other states would also gain one seat from their 2010 apportionment (Arizona, California, Colorado, Montana, North Carolina, Oregon and Virginia), one state would gain two seats (Florida), and one state would gain three seats (Texas).

With the return of an adjustable size of the House, if the District and/or Puerto Rico were also included, none of the above states would lose any seats. Adding only the District’s one seat would bring the size of the House to 448 seats; adding only Puerto Rico’s four seats would increase it to 451. Including both D.C. and Puerto Rico as states would bring the total size of the U.S. House to 452 seats.

The math and politics of admitting the District or Puerto Rico as states are complex. But they also offer a chance to reconsider the frozen size of the U.S. House.

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Jeffrey W. Ladewig is an associate professor of political science at the University of Connecticut.