ONE PERSON-ONE VOTE.

BEFORE THE READERS OF THIS JOURNAL

In the matter of equal representation in the House of Representatives

COMPLAINT AND PETITION OF THE MATHSEMANTIC MONITOR

Now comes the mathsemantic monitor (1), to publish this Complaint and Petition on the current method of apportionment of seats in the House of Representatives of the United States.

1. The complainant is also known as Edward MacNeal, a registered voter in the State of Pennsylvania.

2. The current method of apportioning seats in the House of Representatives of the United States violates the principle of one person-one vote.

3. The current method of apportioning seats in the House of Representatives of the United States violates the Fourteenth Amendment to the Constitution of the United States in that it does not apportion representatives among the several States in accordance with the whole number of persons in each state, nor as closely thereto as can easily be accomplished.

4. The current total number of seats (435) in the House of Representatives of the United States, adopted in 1911, and the method of apportioning them, adopted in 1929, lead to a larger population variation between the largest and smallest districts of representatives than is possible under an alternative method. (2)

Apportionment       Population per Seat (3)
Method           High        Low        Spread

Current          803,655     455,975    347,680
Alternative      699,999     401,828    298,171

5. The current method of apportioning seats in the House of Representatives of the United States, the so-called "method of equal proportions," does not even aim to make the populations of congressional districts as equal as possible. It concentrates instead on a procedure so mathematically complex as to defy the efforts of ordinary citizens to understand its impact. (4)

6. The alternative method used in paragraph #4 to apportion seats is completely transparent and aims directly at making the populations of congressional districts as equal as possible by minimizing the spread between the high and low population per seat. It can be calculated by most citizens. (5)

7. The application of the alternative method to the 1990 census would have resulted in the switch of only one seat (from Washington to Montana). (6) The national average population per seat (rounded to the nearest whole person) was 572,466. The shift would have reduced Montana's population per seat from 803,655 to 401,828 and increased Washington's from 543,105 to 610,993. (See table 1.) Thus congressional districts in Montana would have gone from being 231,189 people larger than the national average to 170,639 smaller, or 60,550 closer to the national average, while those in Washington would have gone from being 29,362 people smaller than the national average to 38,526 larger, or only 9,164 farther from the national average [9,165 in table 1 because calculated with full decimals].

8. A deviation of 9,165 from the national average is clearly closer than a deviation of 60,550. Therefore, the alternative method better satisfies the constitutionally required apportionment of representatives among the several States in accordance with the whole number of persons in each state.

9. Unless corrected, the deficiencies in the current method of apportioning seats in the House of Representatives of the United States may well lead to improper and constitutionally illegal apportionment based on the census for the year 2000.

10. The readers of this journal have a particular interest in, and knowledge of, the dangers of assigning meanings a priori to words or numbers by abstract definitions and the importance of assigning meanings to words and numbers in terms of their actual consequences in human use. (7)

WHEREFORE, the Mathsemantic Monitor respectfully petitions the readers of this journal to send copies of this article forthwith to the media, political officers, and others likely to be influential in hastening a correction of the current method of apportionment of seats in the House of Representatives of the United States.

Respectfully submitted,

The Mathsemantic Monitor

NOTES AND REFERENCES

1. Author of Mathsemantics: Making Numbers Talk Sense (New York: Viking, 1994).

2. For the history of the number of house seats and the methods adopted for apportioning them see "House Seats," the fifteenth article in this series, ETC, vol. 54, no. 4. The number of seats is set by the Apportionment Act of August 8, 1911. The current method of apportionment is statutorily imposed by Title 2 of the U.S. Code and was first used following the 1940 census (Allen L. Schirm, "The Effects of Census Undercount Adjustment on Congressional Apportionment," Journal of the American Statistical Association, vol. 86, no. 414, June 1941, p.527).

3. See table 1. The current figures are for Montana (high) and Wyoming (low). The alternative figures are for South Dakota (high) and Montana (low). The "spread" is merely the difference between the high and low populations per seat.

4. As noted in the first source cited in note 2: A book published by Congressional Quarterly Inc. for professional Washington says, "The method of equal proportions involves complicated mathematical calculations," and then describes it as follows:

In brief, each of the 50 states is initially assigned the one seat to which it is entitled by the Constitution. Then "priority numbers" for states to receive second seats, third seats, and so on are calculated by dividing the state's population by the square root of n(n-1), where "n" is the number of seats for that state. The priority numbers are then lined up in order and the seats given to the states with priority numbers until 435 are awarded.

The effect of first assigning one seat and then making calculations using the square root of any number, let alone one described as n(n-1), makes it impossible to judge from this description whether the method would give fair results or not. Thus the constitutional requirement that our "representatives shall be apportioned among the several states according to their respective numbers" is reduced to a mathematical-statistical puzzle that no ordinary citizen can understand.

[TABULAR DATA FOR TABLE 1 OMITTED]

5. The actual calculation for 1990, shown in table 1, and handled most efficiently with a computer using a spreadsheet program, goes like this (with explanatory comments in parentheses):

a. Divide the total U.S. population by 435 (to get the "national average" population per seat for 435 seats).

b. Divide the population of each state by the national average (calculating to several decimal places to get the "exact seats" each state should get were seats divisible into fractions).

c. Round the exact seats of each state to whole numbers both down and up (to get the only two choices that matter).

d. Divide the population of each state by the whole numbers of seats (both down and up, to determine the average population per seat that would result in each case).

e. Assign seats based on whichever rounding, down or up, comes closest to the national average, but never round downward to zero (an impermissible division in step 5.d anyway, hence ERR in table 1, so that each state gets at least one seat).

f. (To get exactly 435 seats when step 5.e reaches some other total [in 1990 it would have reached a total of 439], then) If step e totals to more than 435, switch the rounding from up to down for the state or states with the smallest rounding swing in population per seat. If step 3 totals to less than 435, switch the rounding from down to up in the same manner. (This ensures the least deviation possible from the national average.)

6. The penultimate paragraph of the earlier article on this subject in this series (see note 2) reads:

The paper that Gary Evans [who had brought the problem to my attention] sent me on this subject runs to 34 pages. Somehow carried back to my days of advising a staff on how to draft petitions, exhibits, and briefs for Civil Aeronautics Board proceedings, I dared write him that his good idea had to be boiled down so a judge could grasp its main points from a few short sentences that short tables instantly demonstrated, with no mathematical complications and nothing extraneous, and in not more than seven pages. Then, having involved myself to that extent, I had trouble sleeping until I'd worked out and sent to Gary a preliminary table that assured me a simplified version [of a proper allocation procedure] was possible.

The present article includes (table 1) the successor to that preliminary table and meets the promise of a simplified allocation procedure. I don't know why Gary Evans produced nothing further on the subject. Just possibly it had something to do with the fact that when he'd written his original proposal he resided in Montana but by the time I wrote to him he'd moved to the state of Washington.

7. Note that the exact number of seats merited in 1990 is 1.40 for Montana and 8.54 for Washington. Concentration on the decimals, the historic mistake, as if the essential meaning resided there, would lead one to expect that Montana's seats should be rounded down to one and Washington's rounded up to nine, which happens to agree in this respect with the current allocation that produces an unnecessarily large variation in population per seat. Hence looking to the decimals for the essential meaning, the historic approach taken, leads one astray. Concentration on developing a procedure that produces the least variation in population per seat, therefore the closest to one person-one vote, leads one to the alternative procedure proposed herein, which necessarily has that desired consequence.