A Short Story about the Reapportionment of Congress and the 1990 Census

Margo Anderson, Department of History, UW-Milwaukee, Milwaukee, WI 53201

Stephen E. Fienberg, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213

Progress, far from consisting in change, depends on retentiveness…. Those who cannot remember the past are condemned to fulfil it.

George Santayana, 1905-06

Those who are familiar with the “equal proportions” formula used to reapportion the U.S. House of Representatives each decade are aware how sensitive it is to small changes in states’ population data. In 1990 this sensitivity took on new significance as statisticians and politicians debated the merits of adjusting the decennial census data to correct for the differential undercount. The “official” apportionment results from the 1990 census were published in December of 1990, and the repportionment of Congressional seats among the states proceeded on the basis of those data. Adjusted census results were released in July of 1991. These data would have changed the reapportionment of Congress and shifted two seats in the House: one each from the states of Wisconsin and Pennsylvania to the states of California and Arizona. Adding to the complexity of the debates about which set of data to use, and in the midst of the ensuing litigation between New York City and the U.S. Department of Commerce, the Census Bureau discovered a computer coding error in the adjusted data estimates and issued “revised adjusted data” in January 1992.

Several years later, an allegation regarding the effects of this computer error arose which claimed that using the revised adjusted data, adjustment would have only moved one seat in Congress (from Wisconsin to California). The allegation appears to have moved from the Department of Commerce (and perhaps the Census Bureau itself) to the lawyers at the Justice Department to statisticians at University of California at Berkeley, and then on to the U.S. Congress. As it traveled, the allegation received more and more attention and took on mythical proportions, and has played a major role in the political controversies surrounding plans for the 2000 census. Here we expose the origins of the myth and suggest reasons why others failed to rebut in public what turns out to have been an erroneous allegation.

Background:

The Republican Congress and the Clinton administration have been embroiled in controversy over the use of sampling for the 2000 census since the plans were formally announced in early 1996. House Republicans have opposed the administration plan and have advocated a “traditional enumeration” with increased efforts to find and count everyone. They claim that the administration plans for incorporating sampling into the design would permit manipulation of the count for the benefit of Democrats and would jeopardize the quality of the “traditional enumeration.” The Census Bureau and the Clinton administration promote the 2000 plan as thoughtful and innovative methods within the time honored tradition of counting, that will improve the accuracy of the overall count.⁽¹⁾

In the context of this partisan controversy, opponents of adjusting the census have looked back at the 1990 experience for guidance, and have retrieved the story of the “computer error.” In this version of the story, the effort to adjust the census in 1990 was misguided, because the adjustment methodology is not accurate enough to apportion Congress properly. After correction for the computer error, in this view, Arizona would not have deserved a seat in Congress at the expense of Pennsylvania. Luckily, the story goes, in July 1991, the hero of the day, Secretary of Commerce Robert Mosbacher, rightly rejected the adjusted data, because he suspected that the sampling technique and bureau implementation were fundamentally flawed. As House Census Subcommittee Chair Dan Miller (R-FL) put it in opinion piece in the Washington Post (June 26, 1998, “Playing Politics with the Census”), “…if sampling had been used in the 1990 census, Pennsylvania would have mistakenly lost a seat in Congress to Arizona. This error was not even caught until early 1992.”

This charge has been repeated in the media. For example:

1. “Will You be Counted in 2000? Census Plans to ‘Sample’ May Lead to Big Errors,” Investor’s Business Daily, July 8, 1998, pp. 1, 32:

A computer programming error . . . overstated the undercount by a million people and probably would have given a congressional seat to Arizona that belonged to Pennsylvania.

The charge appears to derive from earlier charges in papers, Congressional testimony and court filings, and we provide a sample of these statements below:

2. November 1995, Brief for the Federal Petitioners, before the United States Supreme Court, Wisconsin v. City of New York, 517 U.S. 1 (1996), pp. 4, 18-19.

It was subsequently determined, however, that as a result of certain errors (including a computer processing error), that estimate [of 2.1%] overstated the undercount; the Census Bureau represented at the trial in this case that the undercount was 1.6% of the population….

If Secretary Mosbacher had authorized the particular adjustment proposed for his consideration in July 1991, and those adjusted figures had been made the basis for a reapportionment of Representatives among the States, the result would have been a loss of one Representative each for Wisconsin and Pennsylvania and a gain of one Representative each for California and Arizona. See Pet. App. 250-151. Subsequently, however, the Census Bureau determined that its initial estimate of the net undercount had been substantially overstated. See page 4, supra. The Bureau then released corrected adjusted figures for each State. See CAPE Report, Att. 4. We have been informed by the Department of Commerce that if the method of equal proportions (see page 3, supra) is applied to the corrected adjusted census figures, Wisconsin would lose a Representative and California would gain one (as compared to the current apportionment), but the number of Representatives allotted to Arizona and Pennsylvania would remain unchanged.

3. Kenneth Wachter and David Freedman, Testimony on Plans for Census 2000, House Committee on Government Reform and Oversight, 29 February 1996.

We now know that if Secretary of Commerce Mosbacher had decided to use the statistically adjusted numbers as 1990 Census counts, a seat in the House of Representatives would have been shifted from Pennsylvania to Arizona by an error in a computer program. . . . The coding error epitomizes the problems of statistical adjustment in 1990. . . . In 1990, the complexity of their modeling systems made it hard for the Bureau to detect big mistakes and uncertainties, until long after critical decisions had been made. .
. .Unfortunately, the Bureau’s plans for Census 2000 add further layers of complexity onto the complications of 1990, and leave the final numbers even more vulnerable to statistical error.

4. David Freedman, Technical Report No. 455, April 20, 1996, Planning for the Census in the Year 2000, p. 18, commenting on the PES in the 1990 census:

To summarize: when we corrected the Loss Function Analysis to take PES errors into better account, we found that the adjusted figures may be more accurate — or the census. The difference in accuracy may be statistically significant, or just at the chance level: conclusions are driven by assumptions, not by data. A more rudimentary loss function analysis: the proposed adjustment for 1990 would have moved two seats in Congress. After correction for the coding error, but not the other measured errors, only one seat moves. Much of the adjustment is due to error.

Where did the allegation come from?

To our knowledge, the November 1995 Justice Department statement quoted above is the first public statement that alleged that the correction of the coding error would have changed the apportionment of Congress. We have not found evidence that the charge was ever raised in any of the earlier court documents from the litigation surrounding the 1990 census. The error itself was discussed at the district court trial in May 1992 which considered whether Secretary Mosbacher’s decision was “arbitrary and capricious” and hence should be reversed. At the time the Justice Department did not claim that it affected the apportionment of the House. In 1993, District Judge Joseph McLaughlin upheld the authority of Mosbacher’s decision, and New York City appealed the ruling. In 1994, the Second Circuit Court of Appeals reversed McLaughlin and called for further proceedings at the district court level. In response, several states, including Wisconsin, Oklahoma and Pennsylvania filed briefs before the Supreme Court in 1995 asking for the court to take the case and reverse the Court of Appeals. But, significantly, the briefs filed in spring 1995 did not claim that the computer error would have affected apportionment, not even the filings from the state of Pennsylvania. Hence one must look to a close reading of the November 1995 Justice Department brief to reveal how the allegation emerged.

How apportionment works:

The apportionment of Congress on its face is a deceptively simple process. As stated in the Constitution, “Representatives….shall be apportioned among the several States which may be included within this Union, according to their respective Numbers…” The federal government takes a decennial census which produces population counts for the 50 states. Each state is guaranteed one seat. Congress sets the size of the House, currently at 435 members. Thus the task of apportionment is to allocate seats 51 to 435 among the states “according to their respective numbers.” Ross Burson, demographer for the state of Missouri, has prepared a spreadsheet and explanation for calculating the allocations using the current apportionment formula, known as the method of equal proportions. The spreadsheet is available on the web, www.iupui.edu/it/ibrc/SDC/apportionment.html. As Burson explains,

This method assigns seats in the House of Representatives according to a “priority” value. The priority value is determined by multiplying the population of a State by a “multiplier.” For example, following the 1990 census, each of the 50 states was given one seat out of the current total of 435. The next, or 51st seat, went to the State with the highest priority value and thus became that State’s second seat. This continued until all 435 seats had been assigned to a state.

This is how it is done.

Equal Proportions Method

P – represents a State’s total population

n – represents the number of seats a State would have if it gained a seat (because all states automatically received one seat the next seat gained is seat two, and the next “seat three,” and the next “seat four,” and so on.) The multiplier equals (1 divided by (the square root of n(n-1))
[which is called the reciprocal of the geometric mean]. Computing these values is quite easy using a PC and a good spreadsheet package.

Actual calculation of the apportionment is tedious but relatively simple. On multiplies each state’s population by the multipliers for n = 2 to n
= the possible number of seats for the largest state, say 60, generating a list of “priority numbers.” Then one sorts the priority numbers in descending order, and draws a line at the 435th seat. States receive as many seats as they have priority numbers above the line. See Table A, the official apportionment of the House at the 1990 census,⁽²⁾ and Table 1, the calculation of the apportionments for seats just above and below the 435th seat.

To evaluate the claim that the correction of the computer error in the adjusted data would have shifted a seat in Congress, one must recalculate the priority numbers derived from the apportionment formula using the adjusted and corrected adjusted data. Table 2 lists the July 1991 adjusted state totals plus the overseas population from Table A.
Table 3 lists the adjusted data corrected for the computer error, that is, the January 1992 corrected adjusted state totals plus the overseas population from Table A.⁽³⁾Tables 4 and 5 provides the calculation of the apportionments for seats just above and below the 435th seat for the adjusted and corrected adjusted apportionment data. Contrary to the allegation, both sets of data shift seats to California and Arizona at the expense of Wisconsin and Pennsylvania.

Why then did the Justice Department write in its November 1995 brief that the “corrected adjusted census figures” changed the apportionment of House seats compared to the original adjusted data? The answer is that the Justice Department, or whoever did the calculations for it, mistakenly used a fourth set of state population data, likely those data which were released by the Census Bureau Committee on Adjustment of Postcensal Estimates (CAPE) in July 1992.⁽⁴⁾ Tables 6 and 7 list the CAPE state population totals plus the overseas population and the apportionment of seats just above and below the 435th seat for the CAPE data. The apportionment of the House using the CAPE data would have moved one seat from Wisconsin to California.

The changes in the CAPE adjusted census results derived from revision of the post strata used to calculate the adjusted population counts. The original PES design had 1392 post strata. The CAPE program reduced the post strata to 357 to eliminate empty cells, reduce the need for smoothing, and use the revised data for post censal estimates and developing sampling frames over the decade. Thus, the CAPE numbers were never intended as corrected replacements for the original adjusted counts to be used for apportionment.

The larger issue is why the myth of the impact of the computer error continues. Here we suggest that the tediousness of the task of actually calculating House apportionments with the four different data sets deterred even the numerically minded from examining the issue too closely. Further, the claim that the Census Bureau is inept and cannot be trusted is nicely supported by pointing to this computer error. And finally, of course, there is the fact that the apportionment formula is very sensitive. A population shift of one person can change the apportionment of the House. Unfortunately, that one person could as easily have been the results of an error in the actual census enumeration instead of in the adjustment process. After all, about 1 in 10 people in the U.S. was either omitted from the census or erroneously enumerated in 1990.

It is quite natural, as Santayana notes, to use of past to guide the future, and thus to look to the 1990 census experience for guidance on the possibility of adjusting the census in 2000. That historical analysis, however, must get the story straight. Brown, et al., most recently have presented yet another variation on the myth: “Errors in the PES-the coding error being the dominant factor-would have moved a congressional seat from Pennsylvania to Arizona.” Yet they also cite a report that points out the error with regard to this myth. ⁽⁵⁾

A more accurate statement looking back to what happened in 1990 would be: “Changing the post strata usef for adjustment in 1990 after the fact could have shifted a seat in Congress.” And, we might add, “so did deciding to include the overseas population in the state apportionment counts.”

This history lesson about the “computer error” and its implications suggests two morals:

1. Politicians and statisticians should agree upon the rules of the game before the census is taken and then stick to them.

2. Observers should check the numbers carefully to be sure they support their claims.

Notes

1. The debate hit the national news in the summer of 1997. Republicans attached to the flood relief bill for the Dakotas a rider banning the use of sampling in the 2000 census. The President vetoed the flood relief bill and after several months of negotiation, Congress and the President compromised on language in the appropriations bill. That compromise created a Census Board to monitor plans for and administration of the 2000 Count and permitted accelerated legal challenges to the bureau plans. In 1998 Speaker of the House Newt Gingrich and the Southeastern Legal Foundation filed separate lawsuits in federal court against the Clinton administration in an effort to block key aspects of the 2000 Census Plan. In January 1999, the Supreme Court ruled in the suits (Department of Commerce v. U.S. House, 119 S. Ct. 765 (1999)) that the current statutory language of Title 13 of the U.S. Code prevents sampling for purposes of apportioning seats in the House of Representatives. The decision removed one piece of the sampling plan for the census, the phase known as sampling for nonresponse followup (NRFU). The decision did not reach the question of whether the bureau could or should use a sample post enumeration survey to develop corrections of the count for overcounts, undercounts and miscounts, and thus the sampling controversy continues.

2. There is one further wrinkle one must take into account when calculating the priority numbers for the seats, namely that, as shown in Table A, the apportionment population is the resident population plus the United States population abroad allocated back to their home state. In 1990, the decision to add the overseas population to the resident population had the effect of shifting a House seat from Massachusetts to Washington. The issue was litigated in Franklin v. Massachusetts, 505 U.S. 788
(1992). See also Allan Schirm, “The Effects of Census Undercount Adjustment on Congressional Apportionment,” JASA, 86 (1991), pp. 526-41.

3. The July 1991 and January 1992 adjusted census counts for states are available in Defendant’s Exhibit 21, Memorandum for Charles D. Jones from John R. Thompson, February 5, 1992, New York v. Department of Commerce. For background, see Margo Anderson and Stephen E. Fienberg,
Who Counts? The Politics of Census Taking in Contemporary America (New York: Russell Sage, 1999). For the entire set of official and adjusted 1990 census data, see http://tier2.census.gov/pl94171/pl94index.htm.

4. Howard Hogan, “The 1990 Post-Enumeration Survey: Operations and Results,” JASA, 88 (1993): 1047-60.

5. Lawrence D. Brown, Morris L. Eaton, David A. Freedman, Stephen P. Klein, Richard A. Olshen, Kenneth W. Wachter, Martin T. Wells, and Donald Ylvisaker, “Statistical Controversies in Census 2000”, 39
Jurimetrics J. 347-375 (1999). See note 105, citing http://lib.stat.cmu.edu/~fienberg/DonnerReportsFinal.