The first official Census took place in 1790 and was conducted under Secretary of State Thomas Jefferson; it was taken by U.S. marshals on horseback and counted approximately 3.6 million inhabitants.
The original legal purpose of the Census was to determine the number of seats each state gets in the House of Representatives. Article I, Section 2 of the U.S. Constitution mandates that an apportionment of representatives among the states must be carried out every ten years. Over the years, the amount of data collected has increased and we now also do the decennial census to
- gain a better understanding of where people live and establish patterns of settlement, and
- help determine the allocation of federal funds for community services, such as school lunch programs, and new construction, such as highways and hospitals.
As a result of the 2020 census, more than \$675 billion per year will be distributed to local, state and tribal governments for many purposes, including those just listed.
The Census is an expensive undertaking—estimates for the cost of administering the 2020 census are roughly \$15.6 billion, or about \$108 per U.S. housing unit.
The Census is also a big employer—the Bureau hired about 500,000 temporary workers across the country to help with the count. Historically, the Census was one of the first big employers for women.
What is (re)apportionment?
It is the process of (re)allocating the 435 House seats to the states.
Any method of apportionment for the House must consider three key variables:
- the number of House seats;
- the number of U.S. states;
- the apportionment population (as reported by the Census Bureau) of each state.
The first congressional apportionment (in 1790) involved 15 states, and 105 House seats. To illustrate how we think about this—the population of Virginia was 630,560 at the time and the U.S. population was 3,615,920. Thus, one could say that the ideal number of seats for Virginia would be (630,560 ÷ 3,615,920) × 105 = 18.310. Of course, this is a problem, as the number of House seats must be an integer. Should we round up? Round down? An apportionment method will tell you how to do this rounding.
The choice of method was not determined in the Constitution and so each decade a method had to be proposed in Congress and work through the legislative process. Following the first census, a bill was passed by both House and Senate and delivered to President George Washington for his signature into law; this bill included the proposal to adopt an apportionment method developed and supported by Alexander Hamilton. President Washington used the veto power to veto this bill, this was the very first presidential veto. Subsequently, a method developed by Jefferson was passed into law. It gave one more seat to Virginia (19) than did Hamilton’s (18). Virginia’s gain, incidentally, came paired with the loss of a seat to Delaware.
Several methods have been used throughout U.S. history, and other methods have been devised and debated by Congress but ultimately never adopted.
The Apportionment Act of 1941 fixed the method to be used—the Hill-Huntington method (also called Method of Equal Proportions)—as well as fixing the House size of 435 (with exceptions), at least until another law replaces this law. The map shows predictions for the change in seats from the 2020 Census, and the final numbers will be in effect for the 2024 and 2028 presidential elections.
When the reapportioning algorithm is implemented, each state receives one Representative, as required by the Constitution, and the remaining seats are distributed using the Hill-Huntington method. Essentially, a ranked list is created that indicates which states will receive the 51st-435th House seats.
Biographical factets: Joseph Hill was the Chief statistician at the Census Bureau and mathematician Edward Huntington taught at Williams and Harvard and served as MAA president, AAAS (American Association for the Advancement of Science) president, and AMS vice president!
And, on to redistricting…
One could say that the fun only begins AFTER reapportionment, as the redistricting process unfolds. Of course, there is a year’s worth of lectures possible on redistricting. I will limit myself to one short paragraph.
In listening to the January 29 edition of NPR’s “Politics with Amy Walter” conversation with Dave Wasserman, I learned that we are self-sorting geographically—in 1992, 38% of Americans lived in “landslide” districts and in 2020 it was 58%. Consistent with this, and as compared to 2011, there are more Republican trifecta states (now 23 versus 22 in 2011) and also more Democratic trifectas (now 15 versus 11 in 2011). This observation certainly implies we might see more partisan gerrymandering than last time. Many people—including many politicians—push for the redistricting process to be in the hands of commissions (as opposed to state legislatures). In the about-to-begin redistricting round, we have some states (including CO, MI, NY, OH, UT and VA) that have moved to commissions; some of these commissions are structured to be powerful, some less so. The strength in redistricting that a trifecta can bring is intertwined, of course, with who is in charge of redistricting in the state as well as with state laws and guidelines. All I can say is…….tighten your seatbelts.
The promised update on the Census
Oops, that turned into a lecture. I miss teaching.
My original goal when I sat down to write this was to provide an update on the status of the Census.
Census results are not all published at one time. This is what was supposed to happen:
For a variety of reasons—including delays due to the COVID pandemic—the Census numbers for reapportionment that were expected in December of 2020 were not delivered on time. On January 28, 2021, the Census Bureau issued a statement announcing an April 30 delivery date.
In Congress, there are efforts to enforce the timeline. Senator Brian Schatz (HI), together with Alaska Senators Lisa Murkowski and Dan Sullivan, will very soon (and depending on when you read this, maybe already has) reintroduce(d) the 2020 Census Deadline Extensions Act. This bipartisan bill reinforces the Census Bureau’s April 30 target date for the delivery of reapportionment data. The AMS has endorsed this bill.
Obviously, the March 31 date for redistricting data delivery will also not be met. The Census Bureau announced on February 12 that it will deliver the redistricting data to all states (and to the public) by September 30, 2021. According to that announcement, other support products that states will use during their redistricting process have already been delivered.
During the previous administration, work at the Census Bureau had become increasingly politicized. This eventually resulted in the resignation of its Director, Steven Dillingham, whose departure was applauded in the statistics community. During her confirmation hearing to become commerce secretary, Gina Raimondo stated her intention to depoliticize the Census, stating “The experts and statisticians at the Census Bureau are top notch, so I, once confirmed, intend to rely on them.”
One last thing: President Trump issued an executive order on June 21, 2020 that laid out a plan to violate the U.S. Constitution by excluding undocumented immigrants from the 2020 Census. And, on January 20, 2021, one of President Biden’s first executive orders overturned the Trump order.
And, finally, a very short note on why should mathematicians specifically care about all this?
Each step in the decennial three-step process—census, reapportionment, redistricting—involves mathematics and statistics; ensuring sound methodologies are used is important to the mathematical sciences community.
The Census uses sophisticated statistical methods and—for the first time—differential privacy to protect Census data. The American Statistical Association was founded in 1839 in part to support an accurate and reliable census. Data sets released by the Census Bureau, which is the nation’s largest statistical agency, are used by researchers across many fields and ensuring good quality data are released is also a priority for us.
Reapportionment is a fun math problem. You can find lots on the internet about the many apportionment methods. It is an important problem not only in apportionment of our Congress—countries that have legislatures elected via proportional representation use an apportionment method, an apportionment method must be used to calculate win/loss ratios for sports teams, and apportionment methods are used by insurance companies when two or more insurance policies are taken out on a property.
And, as most of you will know, there are mathematicians and statisticians around the country whose research focuses on redistricting and who have served the public by providing expertise to courts and line-drawers.
 For additional information, see Michael L. Balinski and H. Peyton Young, Fair Representation: Meeting the Ideal of One Man, One Vote (New Haven, CT: Yale University Press, 1982)