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A Formula To Achieve One-Person, One-Vote Reapportionment

Jun 18, 2009
There is a paradox in the one-person, one-vote principle.

Reapportioning solely on the basis of persons counted in the census makes district vote totals vary to an unacceptable degree.

But reapportioning solely on the basis of votes cast makes district populations vary to an unacceptable degree.

BOTH people and votes are needed to reapportion in a manner that truly implements the one-person, one-vote principle.

The solution to the paradox requires neither an inductive nor a deductive approach, but an "abductive" one. An age-old dictum must be disproved: we can -- in fact must -- mix apples (people) and oranges (votes).

Consider the following formula:

Congressional District* Population
According To The Last Census

divided by

The Average Of The Total Vote Cast
In The Congressional District
In The Previous Two Congressional
General Election Years**


The Average Of The Total Votes Cast
In A Precinct In The Previous Two
Congressional General Election Years



The "derived precinct populations" would be the building blocks for constructing districts. Their physical boundaries, etc., would be exactly the same as those of existing precincts. When added up, there is nothing "abstract" whatsoever about the derived precinct populations. More on that in a moment.

The formula, it must be emphasized, does not omit the actual population. (See in the formula's first column "Congressional District Population According to the Last Census"). In comparing one congressional district to another, the ineligibles are absolutely, definitely counted.

The mechanics of the formula are not intuitively obvious to many readers. Hence, I offer this clarifying, hypothetical case:

Assume a congressional district has a population of 800,000 people.*** Assume, furthermore, that the average turnout in the last two congressional general election years was 400,000 votes. The contents of the first column in the formula would be:

Congressional District Population
According To The Last Census
= 800,000

divided by

The Average Of Total Votes Cast
In The Congressional District
In The Previous Two Congressional
General Election Years
= 400,000

We come to the second column of the formula: "The Average Of The Total Votes Cast In A Precinct In The Previous Two Congressional General Election Years." Let us assume that the entire congressional district consists of only five precincts. Moreover, assume that our task is to build two state house districts from those five precincts. Finally, assume the averages of the total votes cast in the two elections in question were the following:

Precinct 1. 50,000 votes.
Precinct 2. 100,000 votes.
Precinct 3. 80,000 votes.
Precinct 4. 20,000 votes.
Precinct 5. 150,000 votes.

Note that the total is 400,000 votes, the figure given in column 1 of the formula.

For obvious reasons, the first column in the formula will always be a figure greater than 1. In our example, that figure is: total census population (800,000) divided by votes cast (400,000) = 2.

The second and final calculation in the formula: multiply each precinct vote by 2. The result is the "derived precinct population." Thus,

Precinct 1. 2 x 50,000 = 100,000 Derived Precinct Population.
Precinct 2. 2 x 100,000 = 200,000 Derived Precinct Population.
Precinct 3. 2 x 80,000 = 160,000 Derived Precinct Population.
Precinct 4. 2 x 20,000 = 40,000 Derived Precinct Population.
Precinct 5. 2 x 150,000 = 300,000 Derived Precinct Population.

Note that the five precincts' vote total is 400,000. We saw that number before, at the bottom of column 1 in the formula.

Now, note something most readers probably will not anticipate:

The total of the derived precinct populations is 800,000, the number shown at the top of column 1 in the formula. In other words, the total of the derived precinct populations equals the "real" population total presented in the census.

What happened is this: precincts with large numbers of ineligibles -- servicemen, aliens, prisoners, students, etc. -- did not receive undue representation relative to other precincts. What the formula accomplishes is not the elimination but the spreading around of ineligibles over all the precincts in a congressional district.

As mentioned, our task is to build two state house districts. If we put precincts 1 and 5 together, we have a district composed of (1) 400,000 derived population, and (2) 200,000 votes. That decision leaves us no choice for the second district: precincts 2, 3, and 4. They form a district composed of (1) 400,000 derived population, and (2) 200,000 votes, identical to the first district. What could be more equitable than that? People and votes? Apples and oranges?

The essence of the formula: the votes-cast element checks the population element WITHIN congressional districts. The population component checks the votes-cast component AMONG congressional districts.

Those checks and their resulting balance are the one-person, one-vote principle in action.


*Why are congressional districts used as the basic population unit? Other units, such as counties, could be employed. Answer: federal courts and other bodies, both governmental and nongovernmental, closely scrutinize congressional districts as to their equality of populations and communities of interest. Assuming those districts have been properly drawn, the formula would build reapportionment on an established, legal, and just consensus. Reapportionment outside the United States, such as in the European Union, may find that other units of population are more appropriate. The basic logic of the formula, however, remains valid.
** Why use more than one election year for a votes-cast figure? Turnout can vary significantly from year to year due to local political and weather conditions. To reduce extreme turnout deviations up or down, the formula takes two general elections and averages them.
***The real number is about 650,000. I am simplifying things so that you will not need a calculator.
About the Author
Thomas Belvedere is the pseudonym of a top consultant to senators, representatives, governors, and the media. An accredited expert witness in federal court, he has a Ph.D. in political science. He authored "The Source of Terrorism: Middle Class Rebellion" available at http://www.booklocker.com/.
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