Consequential Miscounts

Analysis of Apportionment Sensitivity to Population Miscounts

The impact of population miscounts on the apportionment of representation is greatly magnified by having too few Representatives, thereby creating a powerful incentive for some states to game the census process.

As explained in this website, the House of Representatives is in egregious violation of the Constitution’s one-person-one-vote equality requirement as a result of there being too few Representatives. A consequent inequity is that relatively small variations or miscounts in the states’ populations can produce inordinately huge percentage changes in some of the states’ House delegation sizes.

For example, if the state of New York had conjured up 89 additional residents for their 2020 population census, it could have kept all 27 of its Representatives.¹ Instead, its House delegation was reduced by one (and it therefore also lost a Presidential Elector). In other words, New Yorkers lost 3.7% of their representation due to an infinitesimal (0.00044%) shortfall in their state’s reported population total! The resulting ratio of representation change, or “Δ”, to population Δ is over 8,400! And whether New York was 89 residents short, or just one, the result would have been the same, as close doesn’t count in apportionment math!

The reason that a tiny shortfall in population can produce such a consequential change in representation is that a 50-state republic with 330 million inhabitants needs far more than 435 Representatives in order to produce mathematically equitable apportionment solutions. If the number of Representatives were greatly increased, then any changes in the states’ populations would produce proportionately commensurate changes in the sizes of their House delegations.

Moreover, because of how apportionment math works, all the states are algebraically interconnected. Even though New York’s 2020 census had increased from its previous census, it nonetheless lost a Representative because some other states had even greater population increases. Such outcomes are an inevitable result of the zero-sum game created by fixing the number of Representatives at 435 rather than allowing the House to grow along with the population (as was intended by the founders).

Population Adjustments and Apportionment

Relative to the apportionment of 435 Representatives, this analysis explains why relatively minor adjustments in the states’ population totals produce disproportionately large changes in some of the states’ delegation sizes. It will also show that the resulting changes in delegation sizes would be smaller and more equitable if the House were much larger. This will be demonstrated by comparing apportionments that result from the official 2020 population census² to apportionments that would result from an alternative, or adjusted, population census.

Post-Enumeration Survey

To create that alternative population census, we will make relatively small adjustments to the official 2020 population census. In order to create a plausible alternative population scenario, those adjustments will be based on the estimated overcounts and undercounts of “household population” provided by the Census Bureau’s “Post-Enumeration Survey” (PES) Report.³ Released in June of 2022, the PES Report provides a statistically derived estimate of the 2020 census miscount for each state. As explained by the Census Bureau:

“The purpose of the Post-Enumeration Survey is to measure the accuracy of the census by independently surveying a sample of the population. The survey estimates the proportion of people and housing units potentially missed or counted erroneously in the census.”⁴

As illustrated in the chart below, the PES Report’s estimated household population miscounts range from -5% to +6.8%.

Figure 1

For example, as shown above, the Census Bureau estimates that Rhode Island’s household population was overcounted by 4.6%, whereas Tennessee’s population was undercounted by roughly the same percentage. And though New York’s official census was 89 residents short of keeping all their Representatives, the PES data reveals that its population census had actually been inflated by several hundred thousand!

Why are there population miscounts? “Erroneous enumerations include duplicates as well as people who were but should not have been counted” is one unreassuring explanation offered by the PES Report. Another reason is that, in those cases where the census data was deemed to be inadequate, the population numbers were imputed (i.e., conjectured) from other data sources.

With respect to the Census Bureau’s estimated miscounts, the PES Report explains that they are derived from data samples along with a statistical analysis thereof. Consequently, their estimates are subject to a probability distribution with respect to whether the actual values could be smaller or larger than the mean values illustrated above. Moreover, according to their report, in only 14 states did the Census Bureau collect enough survey data for their estimates to be deemed statistically significant (indicated by the darker bars in the chart above).

Therefore, though these estimated miscounts can be used to calculate a hypothetical apportionment population, they are not sufficient to definitively determine what the actual apportionment population should have been. However, it is reasonable to assume that these PES adjustments suggest a very probable, if not a more probable, population scenario. (It would be preferable if the US Census Bureau adjusted the 2020 Population Census to reflect the results of their PES Report, and made those results public, but it is unlikely that they will do so voluntarily.)

Alternate Population Scenario

We used the PES estimates to create an alternate adjusted population scenario by calculating the estimated overcount or undercount (as applicable) for each state’s household population, and subtracting or adding that to the total apportionment population. Because household population comprises approximately 97% of the total apportionment population,⁵ this calculation provides a very plausible adjusted population estimate. (The remaining components comprising the population totals were not addressed by the PES Report.)

The methodology we used to create the adjusted population census can be easily explained with an example. The PES Report estimated that Colorado’s Census Count (Household Population) of 5,647,000 was overcounted by 2.19%, which is equal to 121,019 residents. To create our adjusted population total, that overcount was subtracted from Colorado’s total apportionment population of 5,782,171 to arrive at an adjusted total census of 5,661,152 (a 2.09% decrease). This methodology is fully explained in Appendix 1 which also provides the results for every state.

The Analysis

We now have two apportionment population scenarios: The official population census, and the alternative one derived from the PES miscount estimates. Each of those population scenarios will be used to determine the apportionment of the following two House sizes:

The current size of 435 Representatives. These calculations are shown in Appendix 2.
And 6,692 Representatives, a size which complies with the intended version of Article the first of the Bill of Rights. These calculations are shown in Appendix 3.

The result is four different apportionment scenarios. To illustrate this with an example, the table below provides the resulting analysis for the state of Colorado.

As shown in the table above, though Colorado’s total census population was decreased by only 2.1%, that would have resulted in a 12.5% reduction in the size of its delegation (at a House size of 435). That is a representation Δ to population Δ multiple of nearly six!

As it turns out, when there are only 435 Representatives, a similar pattern is repeated across all the states: Relatively small changes in a state’s population usually produce a disproportionately large or small change in its representation, as shown in Appendix 4 and illustrated in the chart below.

In the chart below, the percentage change in each state’s total population is indicated with a small scarlet diamond (◆). And relative to the 435-Representative scenario, the resulting percentage changes in the states’ delegation sizes are indicated by the dark gray bars. Note that a total of six states would have either gained or lost a Representative as a result of these population adjustments. Specifically, three Representatives that should have been apportioned to Florida, Tennessee and Texas were instead allotted to Colorado, Minnesota and Rhode Island.

Figure 2

This analysis makes apparent the seemingly capricious outcomes that result from apportioning only 435 Representatives. For example, reducing Rhode Island’s population by 4.6% reduces its representation by 50%! That’s a 11x ratio of representation Δ to population Δ. And increasing Tennessee’s population by 4.9% increases its representation by 11%. That’s a 2.3x ratio of representation Δ to population Δ. And though Arkansas and Hawaii had even larger population adjustments (+5.16% and -6.16%, respectively), that would not have changed either state’s delegation size! If that doesn’t seem equitable, it’s because it isn’t.

Because we have so few Representatives, the apportionment process effectively becomes a lottery relative to how the last few Representatives are allotted: Relatively minor population variations, or miscounts, will likely result in a jackpot prize for a few states, to the detriment of several other states. This places an extraordinary, if not unreasonable, burden on the Census Bureau to produce nearly flawless population counts.

Contrast those outcomes with the 6,692-Representative scenario, indicated by the light yellow bars, in which the impact of the population changes on representation is spread across 36 states. Returning to the example of Colorado: Whereas a population decrease of 2.1% would result in a 12.5% reduction in its delegation size when apportioning 435, at a House size of 6,692, its delegation would be reduced by only 2.6%. Another example is Hawaii, which loses 6.7% of their delegation as a result of its 6.2% decrease in apportionment population. And Rhode Island loses only 4.5% of its delegation, which is almost equal to its population decrease of 4.6%. The point is, when the number of Representatives is sufficiently large, most of the states’ percentage changes in representation will closely approximate their percentage changes in population (as would be expected). And therefore, any miscounts will not result in disproportionately large misallocations of representation.

A metaphorical way of thinking about these two different House sizes is to imagine apportioning, to the fifty states, 435 bowling balls versus 6,692 marbles. It is intuitively easy to understand why thousands of marbles can be allocated far more proportionately than allocating a few hundred bowling balls. Moreover, when allocating the marbles, small adjustments in all the states’ population totals will generally produce approximately similar changes in each state’s allocation of marbles. In contrast, when reallocating bowling balls based on the same population adjustments, most of the states would be unaffected, with the aggregate impact of those adjustments being disproportionately consolidated into just a few states.

The Incentives to Game the System

Zooming out, there is an important larger issue relative to the population census miscounts: The way the federal system is currently structured, there are two powerful incentives for the states to game the system which, in combination, turn the census into a very high stakes zero-sum game. The first incentive, as explained above, is the potential for a state to gain (or avoid losing) a significant portion of their House delegation (and of their Electoral College delegation) when the total number of Representatives is fixed at a relatively small number (i.e., 435).

The second incentive is the potential for gaining (or not losing) billions of federal dollars: The federal government will utilize the census data to determine how it distributes approximately $1.5 trillion annually to the states.⁶

Either of these are exceedingly powerful incentives for some states to game the system by engaging in strategies to maximize their reported census populations. But regardless of whether there is any deliberate fraud, minimizing the incentives to falsify the census results would help ensure the public’s trust in the census process.

The Partisan Bias

Even the appearance of bias can arouse public suspicion. For example, relative to the 435-Representative scenario described above, the analysis shows that three Representatives that were apportioned to three overcounted “blue” states⁷ should have been apportioned to three undercounted “red” states.⁸ By itself, this could be considered a statistically random outcome. Unfortunately, this pattern of overcounting the “blue” state populations, and undercounting the “red” state populations, is quite prevalent relative to the 2020 population census, as is apparent in the chart below.

The chart below is identical to the Household Population chart shown at the beginning of this article, except that each state’s political leaning is indicated relative to the Democrat or Republican party.⁹ For the sake of brevity, and in hopes of thwarting partisan sentiments, this analysis will generally reference the “blue” or “red” states.

Figure 3

Based on two different measures, the estimates provided by the PES Report reveal a significant bias in the 2020 population census that predominantly favors the blue states to the detriment of the red states. The first measure is the percentage of states that had overcounted or undercounted populations. The data indicate that 75% of the blue states were likely to have been overcounted, whereas 66.7% of the red states were likely to have been undercounted.

The second measure is the averages of those miscounts, which are similarly skewed in favor of the blue states: The average overcount of the blue states is 2.6% which is more than double that of the red states (at 1.1%). And the average percentage undercount of the red states is nearly triple the blue states’ average. (All of these measures are provided in the table in the chart.)

To summarize, nearly 75% of the blue states were overcounted, the average of which was 2.6%. And the red state statistics are nearly the converse of those: Approximately 67% of them were undercounted, the average of which was over 2%.

Statistically Significant

Even allowing for the fact that these miscounts are based on statistical sampling and, therefore, each state’s mean estimate is subject to a probability distribution, this analysis shows that the 2020 census was broadly skewed to favor one political party over the other. That notwithstanding, a second analysis was done to include only those 14 states which, according to the PES Report, the Census Bureau collected enough data to calculate statistically significant miscount estimates. Those states are identified by the solid bars in the following chart (which otherwise illustrates the exact same data as in the preceding chart).
Figure 4

To summarize, 86% of these blue states were overcounted, the average of which was 4.5%. And again, the red state statistics are nearly the converse of those: Approximately 71% of these were undercounted, the average of which was nearly 4%. The table below compares this blue state bias to the overall blue state bias of the 50 states (from Figure 3).

This result is quite significant for two reasons. First, the fact that the analysis of the 14 states with statistically significant population miscounts has a bias even greater than that of all 50 states confirms that this bias generally pervades the entire 2020 population census.

And second, even when the analysis is limited to these 14 states, with the populations of the remaining states unchanged, the implications relative to the apportionment is quite consequential: If 435 Representatives were apportioned according to this scenario, then Florida and Texas would each have an additional Representatives while Minnesota and Rhode Island would each lose one. (See Appendix 5.)

A national problem

A population census of hundreds of millions of people is such a massive undertaking that some miscounting is inevitable even under the best of circumstances. However, in this case, the magnitude of the bias indicates that a much better understanding of the underlying causes is urgently needed.

One of those causes is the tremendous amount of money spent by some states to bolster their census results. For example, while California committed over $150 million to promote the collection of census data, the state of Texas failed to adequately fund such an effort.¹⁰ Not only did this probably cause Texas to forego an additional Representative, this reportedly cost the state billions of dollars in federal funding.¹¹

It is obviously a very good investment for a state to boost their census numbers, especially if such efforts utilize the expertise of high-priced consultants who understand how the Census Bureau extrapolates from available data. Even disregarding the possibility of dubious methods being employed, this degree of inconsistency from state to state, relative to how the census process is conducted, does not inspire confidence in the integrity of either the population census or the resulting apportionment of representation.

Regardless of the reasons for this conspicuous bias, when the results are so heavily skewed in this way, the public is likely to become mistrustful of the census process which, like the election process, should be very diligently guarded against accusations of fraud so as to maintain public trust. Whether these miscounts are due to insufficient resources, ineptitude, or fraud, they should not result in such consequential and inequitable changes in representation!

Reduce the Incentive to Game the System

The real story here is not about which political party may have done a better job of manipulating the census process. The real story is that by keeping the size of the House of Representatives fixed at small number for over a century, Congress has instituted a powerful incentive for states to game the census.

Working in tandem, the apportionment of representation and the allocation of federal funding are two overwhelmingly powerful inducements for states to manipulate the census. Greatly increasing the number of Representatives will virtually eliminate the first of those incentives. As shown with the 6,692-Representative scenario, any miscounts relative to the census will generally change a state’s representation by a commensurately small percentage. In contrast, under the current regime of 435, many states are incentivized to engage in an unseemly contest to win a jackpot prize in the national apportionment lottery. For example, by overstating its population by 4.6%, tiny Rhode Island doubled its House delegation, and increased its Electoral College delegation by 33%.

In the meantime, until the size of the House can be sufficiently increased to minimize such inequitable outcomes, a comprehensive audit should be conducted after each census. Overseen by a bipartisan congressional committee (perhaps utilizing an independent auditor), said audit should be informed by statistically-significant miscount estimates for all of the states, and also identify the root causes for any consequential miscounts. Using that data, the ideal remedy would be for Congress to correct the apportionment of representation. If that is not possible, it should at least be used to adjust the intrastate congressional district boundaries so that any overcounted areas are not also overrepresented. And, at a minimum, this adjusted census data should be used to correct the allocation of federal funds to the states.

At this point it should be recognized that the founders’ original design would have prevented these problems in two different ways. First, they had constructed counterbalancing incentives relative to the census count, as follows:.

Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers¹²

Under that arrangement, though a state would likely gain a Representative from a population overcount, it would also gain a greater share of the federal tax burden! Unfortunately, the 16^th Amendment eliminated this important counterbalance. Imagine how much different the census population totals would have been had the proportional allocation of federal taxes not been replaced by its opposite: An allocation of the federal spoils.

And the second way the founders hoped to prevent this problem was with the very first amendment proposed for the Bill of Rights, which was intended to require that the House forever grow along with the population. This would have ensured that relatively small miscounts of the states’ populations would not produce inordinately consequential and inequitable misallocations of representation.

As usual, the founders had it right in the first place!