Original actions, authorized by Amendment No. 23 to the state Constitution, were filed by Nabors Shaw, of Poinsett county; L. H. Autry and J. Lee Bearden, of Mississippi county; and Girard P. Shofner, of Pulaski county. Each named the Governor, Secretary of State, and Attorney General, as respondents. It was alleged in the petitions that these officers, who constitute a board of reapportionment, erred in the result certified to the Secretary of State January 21, 1941.
In Cause No. 6357 — Shaw v. Adkins, et als. — it is asserted that Poinsett's population of 37,670 exceeds that of either White, Benton, St. Francis, Hempstead, Miller. *Page 858 or Lonoke county, each of which was given two representatives, while but one was assigned to Poinsett.
Cause No. 6358 — Autry, et als., v. Adkins, et als. — alleges that in assigning two representatives each to Benton, Craighead, Crittenden, Garland, Hempstead, Lonoke, Miller, Phillips, St. Francis, Washington, and White counties, and in assigning but three to Mississippi county, the board acted arbitrarily and in disregard of the county's population of 80,217. James Terry and Harry W. Haines, and twenty-seven other citizens of Mississippi county, intervened in Cause No. 6258. They adopted the Autry-Bearden complaint and made other allegations.
In Cause No. 6376 — Shofner v. Adkins, et als. — it is alleged that Pulaski county, with a population of 156,085, is entitled to eight representatives instead of seven as assigned by the board.
Royce Weisenberger intervened in all three cases and seeks to show that under any method of reapportionment Hempstead county is entitled to two representatives, as now assigned.
The board of apportionment assigned to each of the following counties one representative: Arkansas, Ashley, Baxter, Boone, Bradley, Calhoun, Carroll, Chicot, Clark, Clay, Cleburne, Cleveland, Columbia, Conway, Crawford, Cross, Dallas, Desha, Drew, Faulkner, Franklin, Fulton, Grant, Greene, Hot Spring, Howard, Independence, Izard, Jackson, Johnson, LaFayette, Lawrence, Lee, Lincoln, Little River, Logan, Madison, Marion, Monroe, Montgomery, Nevada, Newton, Ouachita, Perry, Pike, Poinsett, Polk, Pope, Prairie. Randolph, Saline, Sevier, Scott, Searcy, Sharp, Stone, Van Buren, Woodruff, and Yell.
To each of the following counties two representatives were given: Benton, Craighead, Crittenden, Garland, Hempstead, Lonoke, Mifler, Phillips, St. Francis, Washington, and White.
To each of the following counties three representatives were assigned: Jefferson, Mississippi, Sebastian, and Union. *Page 859
Pulaski county was given seven representatives.
The board adopted 19,492 as the basis of population for representative.1
Amendment No. 23 required the board to make its first apportionment within ninety days from January 1, 1937, "and. . . thereafter, on or before February 1 immediately following each federal census, the board shall reapportion the state for both representatives and senators.2 . . ."
Section two of the amendment provides that the house of representatives shall consist of 100 members. Each county existing at the time of apportionment shall have at least one representative, "and . . . the remaining numbers shall be equally distributed (as nearly as practicable) among the more populous counties of the state, in accordance with a ratio to be determined by the population of said counties as shown by the federal census next preceding any apportionment hereunder."
The board correctly assigned one representative to each county. Of the remaining 25, eleven went to Benton, Craighead, Crittenden, Garland, Hempstead, Lonoke, Miller, Phillips, St. Francis, Washington, and White counties; eight went to Jefferson, Mississippi, Sebastian, and Union counties, and six went to Pulaski, in the proportion heretofore shown.
Was this distribution "in accordance with a ratio to be determined by the population [of the more populous counties] as shown by the federal census"?
If the problem is considered but casually the responding impression is that the "more populous counties" should be grouped in the order of their population, thus permitting familiar mathematical computations to be applied and a definite result ascertained. But it is not that simple. A somewhat similar provision of *Page 860 the federal Constitution3 has been productive of arithmetical and algebraic perplexities since Daniel Webster's plan of 1832 proved to be unworkable in practice because it did not always give the right total.4
According to Professor Huntington (see footnote No. 4), a mathematical study of the problem made in 1921 showed that there are five methods which are workable, and which avoid what the author referred to as the "paradoxes." The approved concepts are: (1) Method of major fractions. (2) Method of equal proportions. (3) Method of harmonic mean. (4) Method of smallest divisors. (5) Method of greatest divisors.
In a preliminary discussion of the five methods, Professor Huntington says:
"To meet realistically the actual situation in Congress when an apportionment bill is up for debate, the emphasis is shifted from the process of computation to the test of fairness which the final result should satisfy. The fairness of the final result, not the technical process of achieving this result, is regarded as the important *Page 861 thing. For example, suppose an actual apportionment bill proposes to give Alabama nine seats, Arizona one, Arkansas seven, etc., in a house of any given size (say 435). The fundamental question which Congress has to face is this: Does the distribution proposed in the bill put each state as nearly as may be on a par with every other state, or would the bill be `improved' by transferring a seat from such-and-such a state to such-and-such another state?
"To answer this question, Congress must decide what goal or aim it has in mind when discussing proposed `improvements' in a given bill. It is generally agreed that Congress, consciously or unconsciously, has had two principal aims in view: First, to equalize the `congressional districts' among the several states; and secondly, to equalize the `individual shares' among the several states. What the modern mathematical theory has done is to establish clearly the relations between these two aims and give the possible methods listed above.
"The mathematical facts are as follows: The method of smallest divisors and the method of greatest divisors fail on both these aims; the method of major fractions fails on the first aim; the method of harmonic mean fails on the second aim; the method of equal proportions achieves both aims.
"In view of these facts, the method of equal proportions was approved by two scientific bodies: The Advisory Committee to the Director of the Census, in 1921; and the National Academy of Sciences, in 1929."
Apportionment methods referred to by Professor Huntington are discussed in "Congressional Apportionment," by Laurence F. Schmeckebier. The book was copyrighted in 1941 by The Brookings Institution. At page 12 it is said: "While these methods are all mathematically correct, each one starts with a different premise and the results may be different. . . . Two of the modern methods — major fractions and equal proportions — are recognized by statute. The other three methods — harmonic mean, smallest divisors, and greatest divisors *Page 862 — have been discussed in committees and in the literature, but have never received statutory recognition."5
The problem is to divide 25 representatives among the more populous counties "in accordance with a ratio to be determined by the population of said counties." It was recognized by those who framed our Constitution that a mathematically exact division would be impossible because there are no fractional representatives; hence, in the Constitution there is authority for making the apportionment "as nearly as practicable."
First, the ratio must be ascertained. The total population of 1,949,387 divided by 100 shows this factor to be 19,494, minus. The result is termed the natural ratio. But there has been assigned to each county one representative, and 75 times 19,494 gives 1,462,050. This, taken from total population, leaves 487,337. If we divide the remainder by 25 — a number equal to the unassigned representatives — the result is 19,494, the natural ratio.
According to Schmeckebier, no modern method of apportioning representatives uses any ratio in determining the result. A ratio, he says, is often referred to, but it is obtained after the apportionment is made from a so-called priority list. All modern methods — equal proportions, major fractions, harmonic mean, smallest divisors, and greatest divisors — assign the representatives to each state, in the case of congressional action, and to each county, in the case of state procedure, by means of priority lists, which indicate the apportionment to be made from the definite number — in Congress, ordinarily 435, and in Arkansas definitely 100. As the federal Constitution provides that one representative shall be assigned to each state, no question of priority *Page 863 would exist if the house consisted of 48 members. Each state obtains one representative, regardless of its population. Therefore, the priority list begins with the forty-ninth member of the house, and when completed it shows which states would receive additional members for any size house. As applied to reapportionment in Arkansas, the priority list begins with the member which we may designate as 76. In reality, priorities relate only to 25 members. Under our constitutional provision, the division of these 25 representatives is in accordance with a ratio to be determined by the population of such counties, exclusive of the remaining 75; hence, the priority list must be compiled and the ratios ascertained.
By the method of equal proportions6 as applied to Arkansas' representation in Congress, seven congressmen would be retained. By the method of major fractions, Michigan, now having 17 congressmen, would gain one, and Arkansas would be the corresponding loser.
A great deal has been written, by those engaged in the task of testing apportionments, regarding absolute and relative differences. The absolute difference between two numbers is obtained by subtracting the smaller from the larger. The relative difference is the percentage by which the larger exceeds the smaller, and is obtained by dividing the smaller amount into the difference. An illustration given by Schmeckebier is: If a piece of property costing $500 is sold for $600 and another piece of property costing $1,000 is sold for $1,100, the absolute difference in the profit is the same in each case — $100. But the relative difference in one case is 500 divided into 100, or 20 per cent.; in the other case it is 1,000 divided into 100, or 10 per cent.
The following table shows population of earth of the state's 75 counties according to the 1930 and the 1940 censuses: *Page 864
POPULATION OF ARKANSAS BY COUNTIES
Population Population County 1940 1930 County 1940 1930
Arkansas ........ 24,437 22,300 Lee ........... 26,810 26,637 Ashley .......... 26,785 25,151 Lincoln ....... 19,709 20,250 Baxter .......... 10,281 9,519 Little River .. 15,932 15,515 Benton .......... 36,148 35,253 Logan ......... 25,967 24,110 Boone ........... 15,860 14,937 Lonoke ........ 29,802 33,759 Bradley ......... 18,097 17,494 Madison ....... 14,531 13,334 Calhoun ......... 9,636 9,752 Marion ........ 9,464 8,876 Carroll ......... 14,737 15,820 Miller ........ 31,874 30,586 Chicot .......... 27,452 22,646 Mississippi ... 80,217 69,289 Clark ........... 24,402 24,932 Monroe ........ 21,133 20,651 Clay ............ 28,386 27,278 Montgomery .... 8,876 10,768 Cleburne ........ 13,134 11,373 Nevada ........ 19,869 20,407 Cleveland ....... 12,570 12,744 Newton ........ 10,881 10,564 Columbia ........ 29,822 27,320 Ouachita ...... 31,151 29,890 Conway .......... 21,536 21,949 Perry ......... 8,392 7,695 Craighead ....... 47,200 44,740 Phillips ...... 45,970 40,683 Crawford ........ 23,920 22,549 Pike .......... 11,786 11,792 Crittenden ...... 42,473 39,717 Poinsett ...... 37,670 29,695 Cross ........... 26,046 25,723 Polk .......... 15,832 14,857 Dallas .......... 14,471 14,671 Pope .......... 25,682 26,547 Desha ........... 27,160 21,814 Prairie ....... 15,304 15,187 Drew ............ 19,831 19,928 Pulaski ...... 156,085 137,727 Faulkner ........ 25,880 28,381 Randolph ...... 18,319 16,871 Franklin ........ 15,683 15,762 St. Francis ... 36,043 33,394 Fulton .......... 10,253 10,834 Saline ........ 19,163 15,660 Garland ......... 41,664 36,031 Scott ......... 13,300 11,803 Grant ........... 10,477 9,834 Searcy ........ 11,942 11,056 Greene .......... 30,204 26,127 Sebastian ..... 62,809 54,426 Hempstead ....... 32,770 30,847 Sevier ........ 15,248 16,364 Hot Spring ...... 18,916 18,105 Sharp ......... 11,497 10,715 Howard .......... 16,621 17,489 Stone ......... 8,603 7,993 Independence .... 25,643 24,225 Union ......... 50,461 55,800 Izard ........... 12,834 12,872 Van Buren ..... 12,518 11,962 Jackson ......... 26,427 27,943 Washington .... 41,114 39,255 Jefferson ....... 65,101 64,154 White ......... 37,176 38,269 Johnson ......... 18,795 19,289 Woodruff ...... 22,133 22,682 Lafayette ....... 16,851 16,934 Yell .......... 20,970 21,313 Lawrence ........ 22,651 21,663
Since priority lists are used in each of the five so-called modern methods of apportionment, it is essential to show the steps by which these lists are prepared. They are obtained by multiplying the population of each county successively by the multipliers applicable to the second representative, the third representative — and so on. It should be pointed out, however, that a different series of multipliers is used for each of the methods.
Major fractions and equal proportions, having been recognized as the two methods generally approved, the three other processes will not be analyzed, although tables showing results under each are included in this opinion. *Page 865
Major Fractions. — The priority list is obtained by dividing the population of each county successively by the arithmetic mean between succeeding representatives.7 The priority list obtained by the process shown in the seventh footnote (major fractions) is made use of in this way: Assign the seventy-sixth representative (first disposed of in the additional group of 25) to the county having the highest number in the priority list, the second to the next highest number in the priority list, and so on until the full 25 have been disposed of Pulaski county, having the highest number in the priority list,8 would receive the first additional representative, and Miller county would be recipient of the twenty-fifth representative. The order of assignment is shown by the figures inclosed within parentheses, following priority numbers. (See table identified as footnote 8.) For instance, Pulaski county, in stead of having its seven representatives assigned successively, receives the first, second, fourth, seventh, twelfth, and twenty-second of the 25 to be assigned, and other counties, as shown by the figures inclosed in parentheses in tabulations appear as footnotes 8, 10, 11, 12, and 13, receive additional representatives in the numerical order shown. *Page 866
Equal Proportions. — The priority list is obtained by dividing the population of each county by the geometric mean of successive numbers of representatives.9 The *Page 867 priority list obtained by the process shown in the ninth footnote (equal proportions) is made use of in the manner explained as pertaining to major fractions. The priority list and other data for use in the equal proportions method are shown as the tenth footnote.10
Other Methods. — Footnotes 11, 12, and 13 are priority lists and other data for harmonic mean method, smallest divisors method, and greatest divisors method.11,12,13
Proof of product obtained under the two methods discussed in detail — major fractions and equal proportions — may be shown in the following manner, the result in each case being the same:
Lonoke county has a population of 29,802, and has two house members. Theoretically each represents a population of 14,901. Mississippi county has a population of 80,217 and has three members. Each, therefore, represents a population of 26,739. In theory each Mississippi county member represents 11,838 more constituents than does each of Lonoke's members, the differential being 79.4 per cent. If one member should be taken from Lonoke county and given to Mississippi county, each of Mississippi's four members would represent 20,054 persons and Lonoke's one remaining member would represent 29,802, an absolute difference of 9,748, or 48.6 per cent. against Lonoke. The disparity difference against Mississippi county at present is much larger than the disparity against Lonoke county if the latter is reduced to one member.
Union county's population is 50,461. It has three members, each of whom, theoretically, represents a *Page 868 constituency of 16,820. Ponisett's population is 37,670. The county has one house member, and this member, in theory, represents 20,850 more in population than do each of Union county's members, the differential being 124.0 per cent. If one member should be taken from Union and assigned to Poinsett, the two Poinsett members will each represent 18,835 in population. Each of the remaining Union county members will represent a *Page 869 population of 25,231 — an absolute difference of 6,396. The percentage against Union county in its relation to Poinsett would then be 34.0, as compared with a former percentage of 124.0 against Poinsett.
By either of the five methods Lonoke and Union counties each lose a representative, and by either Poinsett gains. *Page 870
By the method of smallest divisors Pulaski county would lose one member, while by the method of greatest divisors it would gain two. According to either of the other three methods, Pulaski's representation would be unchanged.
By four of the five methods Mississippi county gains a member, while under the smallest divisor method its representation remains static. *Page 871
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By the method of smallest divisors Ouachita and Greene counties would each gain a member, but under either of the other four methods there would be no changes.
By the method of greatest divisors Hempstead and Miller counties would each lose a member, while under either of the other four systems these counties would not be affected.
These results are presented in the following table. It shows assignment of the 25 additional representatives by counties according to the apportionments of 1937 and 1941. Also, there is shown results obtained by the five apportionment methods discussed in this opinion:
RESULTS OBTAINED BY DIFFERENT METHODS
County Pop. 1937 Major Equal Harmonic Smallest Greatest 1941 Apprtmnts. Frctns. Prptns. Mean Divisors Divisors
Pulaski .... 156,085 6 6 6 6 5 8 Mississippi . 80,217 2 3 3 3 2 3 Jefferson ... 65,101 2 2 2 2 2 2 Sebastian ... 62,809 2 2 2 2 2 2 Union ....... 50,461 2 1 1 1 1 1 Craighead ... 47,200 1 1 1 1 1 1 Phillips .... 45,970 1 1 1 1 1 1 Crittenden .. 42,473 1 1 1 1 1 1 Garland ..... 41,664 1 1 1 1 1 1 Washington .. 41,114 1 1 1 1 1 1 Foinsett .... 37,670 0 1 1 1 1 1 White ....... 37,176 1 1 1 1 1 1 Benton ...... 36,148 1 1 1 1 1 1 St. Francis . 36,043 1 1 1 1 1 1 Hempstead ... 32,770 1 1 1 1 1 0 Miller ...... 31,874 1 1 1 1 1 0 Ouachita .... 31,151 0 0 0 0 1 0 Greene ...... 30,204 0 0 0 0 1 0 Columbia .... 29,822 0 0 0 0 0 0 Lonoke ...... 29,802 1 0 0 0 0 0 ___________________________________________________________________________ TOTALS 25 25 25 25 25 25
It is not our purpose to assert that all possible methods of computation have been tested, or to say that in certain circumstances relating to population gains or losses a more equitable apportionment could not be made. We have given earnest consideration to discussions by authorities who have been classed as experts. That the methods of major fractions and equal proportions give uniform results when applied to Arkansas is *Page 873 significant. The fact that the National Academy of Sciences has given its indorsement to the method of equal proportions in preference to other systems is highly persuasive. This method, therefore, is adopted by us, with the result that Lonoke and Union counties each lose a representative, and Mississippi and Poinsett each gain a member.
The board of apportionment's findings in respect of house membership, while remarkably accurate in the main, must be revised to the extent indicated. It is so ordered.
1 The 1940 census gave Arkansas a population of 1,949,387. This number divided by 100 (representatives from all counties) yields 19,494 minus, instead of 19,492.
2 See Bailey, Lieutenant Governor, v. Abington, 201 Ark. 1072,145 S.W.2d 176, 149 S.W.2d 573.
3 Constitutional provisions dealing with the subject are the third clause of 2 of article, and the Fourteenth Amendment. The third clause of 2, art. 1, is: "Representatives and direct taxes shall be apportioned among the several states which may be included in this union according to their respective numbers, which shall be determined by adding to the whole number of free persons, including those bound to service for a term of years, and excluding Indians not taxed three-fifths of other persons. . . ." The pertinent part of 2 of the Fourteenth Amendment, adopted to meet conditions brought about by abolition of slavery, is: "Representatives shall be apportioned among the several states according to their respective numbers, counting the whole number of persons in each state, excluding Indians not taxed." [January 8, 1941, President Roosevelt transmitted to congress a message in compliance with the provisions of 22(a) of the Act approved June is, 1929, "providing for the fifteenth and subsequent decennial censuses, and for the apportionment of representatives in congress." In the message it was stated that the director of the census had included all Indians in the tabulation of total population, "since the Supreme Court has held that all Indians are now subject to federal taxation." (Superintendent v. Commissioner, 295 U.S. 418,55 S. Ct. 820, 79 L. Ed. 1517.) The secretary of commerce addressed an inquiry to Attorney General Jackson regarding the status of Indians in respect of the census. The attorney general (November 28, 1940) replied that an opinion by him would not be determinative, since neither the congress nor the courts would be bound by it.]
4 Edward v. Huntington, Department of Mathematics, Harvard University: "A Survey of Methods of Apportionment in Congress." Seventy-sixth Congress, 3d session. Senate Document No. 304, p. 1.
5 The permanent apportionment section of the census act of June 18, 1929 (46 Stat. L. 26), provides that the President shall report to congress apportionments of representatives by three methods: (1) By the method used at the last preceding census, (2) by the method of major fractions, and (3) by the method of equal proportions. . . . The method last used before 1930 was that of major fractions. After the census of 1930 the methods of major fractions and equal proportions gave the same result. (The act of 1929 was amended by the Act of Apr. 25, 1940 — 54 Stat. L. 162 — but the act of 1940 made no change in the methods to be reported. It merely changed the date on which the report should be made.)
6 Schmeckebier, "Congressional Apportionment," p. 233.
7 Arithmetic mean mathematics, denotes a quantity having an intermediate value between several others from which it is derived and of which it expresses the mean value. Usually, unless otherwise specified, it is the one simple average formed by adding the quantities together in any order and dividing by their number. For example: All counties have one representative. If any county is entitled to another representative, the assignment of such would be a succeeding representative. In such case the arithmetic mean would be obtained by adding one (the first representative) and two (the second representative) and dividing by their number (two), the result being one and one-half, known in the apportionment process as a divisor. Such divisors increase in arithmetical progression for each additional representative, the next divisors being 2 1/2, 3 1/2, etc. In saying that the i, priority list is obtained by dividing the population of each county by the arithmetic mean between succeeding representatives (the divisor), the equivalent is the same as though the population of each county were multiplied by the reciprocal of the divisor for the purpose of obtaining a multiplier. The process is demonstrated in this way: The effect of dividing any number by 2 1/2 can be duplicated by multiplying that number by the reciprocal of 2 1/2, which is 0.40. The following are multipliers used for succeeding representatives in obtaining the priority list: Second representative, .666,666,67; third representative, .400,000,00; fourth representative, .285,714,29; fifth representative, .222,222,22; sixth representative, .181,818,18; seventh representative, .153,846,15; eighth representative, .133,333,33.
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9 The geometric mean of two numbers is the square root of their product. For example, all counties have one representative. When a county is entitled to additional representation, the assignment would be the next successive number. In such case the geometric mean would be obtained by multiplying one (the first representative) by two (the second representative) and extracting the square root of their product, the result being 1.414,213,6. Such divisors increase in geometric progression for each additional representative, the next being 2.449,489,7. etc. In saying that the priority list is obtained by dividing the population of each county by the geometric mean of successive numbers of representatives (the divisor), the equivalent is the same as though the population of each county were multiplied by the reciprocal of the divisor for the purpose of obtaining the multiplier. The process is demonstrated in this way: The effect of dividing any number by 1.414,213,6 can be duplicated by multiplying that number by the reciprocal of 1.414,213,6, which is 0.707,106,78. The following are multipliers used for succeeding representatives in obtaining the priority list: second representative, .707,106,78; third representative, .408,248,29; fourth representative, .288,675,13; fifth representative, .223,606,80; sixth representative, .182,574,19; seventh representative, .154,303,35; eighth representative, .133,630,62.
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