APPENDIX TO OPINION OF
MR. JUSTICE HARLAN.The Inadequacy op Arithmetical Formulas as Measures op the Rationality op Tennessee’s Apportionment.
Two of the three separate concurring opinions appear to concede that the Equal Protection Clause does not guarantee to each state voter a vote of approximately equal weight for the State Legislature. Whether the existing Tennessee apportionment is constitutional is recognized to depend only on whether it can find “any possible justification in rationality” (ante, p. 265); it is to be struck down only if “the discrimination here does not fit any pattern” (ante, p. 258).
One of the concurring opinions, that of my Brother Stewart, suggests no reasons which would justify a finding that the present distribution of state legislators is unconstitutionally arbitrary. The same is true of the majority opinion. My Brother Clark, on the other hand, concludes that “the apportionment picture in Tennessee is a topsy-turvical of gigantic proportions” (ante, p. 254), solely on the basis of certain statistics presented in the text of his separate opinion and included in a more extensive Table appended thereto. In my view, that analysis is defective not only because the “total representation” formula set out in footnote 7 of the opinion (ante, p. 255), rests on faulty mathematical foundations, but, more basically, because the approach taken wholly *341ignores all other factors justifying a legislative determination of the sort involved in devising a proper apportionment for a State Legislature.
In failing to take any of such other matters into account and in focusing on a particular mathematical formula which, as will be shown, is patently unsound, my Brother Clark’s opinion has, I submit, unwittingly served to bring into bas-relief the very reasons that support the view that this complaint does not state a claim on which relief could be granted. For in order to warrant holding a state electoral apportionment invalid under the Equal Protection Clause, a court, in line with well-established constitutional doctrine, must find that none of the permissible policies and none of the possible formulas on which it might have been based could rationally justify particular inequalities.
I.
At the outset, it cannot be denied that the apportionment rules explicitly set out in the Tennessee Constitution are rational. These rules are based on the following obviously permissible policy determinations: (1) to utilize counties as electoral units; (2)' to prohibit the division of any county in the composition of electoral districts; (3) to allot to each county that has a substantial voting population — at least two-thirds of the average voting population per county — a separate “direct representative” ; (4) to create “floterial” districts (multicounty representative districts) made up of more than one county; and (5) to require that such districts be composed of adjoining counties.1 Such a framework unavoidably *342leads to unreliable arithmetic inequalities under any mathematical formula whereby the counties’ “total representation” is sought to be measured. It particularly results in egregiously deceptive disparities if the formula proposed in my Brother Clark’s opinion is applied.
That formula computes a county’s “total representation” by adding (1) the number of “direct representatives” the county is entitled to elect; (2) a fraction of any other seats in the Tennessee House which are allocated to that county jointly with one or more others in a “floterial district”; (3) triple the number of senators the county is entitled to elect alone; and (4) triple a fraction of any seats in the Tennessee Senate which are allocated to that county jointly with one or more others in a multicounty senatorial district. The fractions used for items (2) and (4) are computed by allotting to each county in a combined district an equal share of the House or Senate seat, regardless of the voting population of each of the counties that make up the election district.2
*343This formula is patently deficient in that it eliminates from consideration the relative voting power of the counties that are joined together in a single election district. As a result, the formula unrealistically assigns to Moore County one-third of a senator, in addition to its direct representative {ante, p. 255), although it must be obvious that Moore’s voting strength in the Eighteenth Senatorial District is almost negligible. Since Moore County could cast only 2,340 votes of a total eligible vote of 30,478 in the senatorial district, it should in truth be considered as represented by one-fifteenth of a senator. Assuming, arguendo, that any “total representation” figure is of significance, Moore’s “total representation” should be 1.23, not 2.3
The formula suggested by my Brother Clark must be adjusted regardless whether one thinks, as I assuredly do not, that the Federal Constitution requires that each vote be given equal weight. The correction is necessary simply to reflect the real facts of political life. It may, of course, be true that the floterial representative’s “function *344is to represent the whole district” {ante, p. 256). But can it be gainsaid that so long as elections within the district are decided not by a county-unit system, in which each county casts one vote, but by adding the total number of individual votes cast for each candidate, the concern of the elected representatives will primarily be with the most populous counties in the district?
II.
I do not mean to suggest that any mathematical formula, albeit an “adjusted” one, would be a proper touchstone to measure the rationality of the present or of appellants’ proposed apportionment plan. For, as the Table appended to my Brother Clark’s opinion so conclusively shows, whether one applies the formula he suggests or one that is adjusted to reflect proportional voting strength within an election district, no plan of apportionment consistent with the principal policies of the Tennessee Constitution could provide proportionately equal “total representation” for each of Tennessee’s 95 counties.
The pattern suggested by the appellants in Exhibits “A” and “B” attached to their complaint is said to be a “fair distribution” which accords with the Tennessee Constitution, and under which each of the election districts represents approximately equal voting population. But even when tested by the “adjusted” formula, the plan reveals gross “total representation” disparities that would make it appear to be a “crazy quilt.” For example, Loudon County, with twice the voting population of Humphreys County would have less representation than Humphreys, and about one-third the representation of Warren County, which has only 73 more voters. Among the more populous counties, similar discrepancies would appear. Although Anderson County has only somewhat over 10% more voters than Blount County, it would have *345approximately 75% more representation. And Blount would have approximately two-thirds the representation of Montgomery County, which has about 13% less voters.4
III.
The fault with a purely statistical approach to the case at hand lies not with the particular mathematical formula used, but in the failure to take account of the fact that a multitude of legitimate legislative policies, along with circumstances of .geography and demography, could account for the seeming electoral disparities among counties. The principles set out in the Tennessee Constitution are just some of those that were deemed significant. Others may have been considered and accepted by those entrusted with the responsibility for Tennessee’s apportionment. And for the purposes of judging constitutionality under the Equal Protection Clause it must be remembered that what is controlling on the issue of “rationality” is not what the State Legislature may actually have considered but what it may be deemed to have considered.
For example, in the list of “horribles” cited by my Brother Clark (ante, p. 255), all the “underrepresented” counties are semiurban: all contain municipalities of over 10,000 population.5 This is not to say, however, that the *346presence of any such municipality within a county necessarily demands that its proportional representation be reduced in order to render it consistent with an “urban versus rural” plan of apportionment. Other considerations may intervene and outweigh the Legislature’s desire to distribute seats so as to achieve a proper balance between urban and rural interests. The size of a county, in terms of its total area, may be a factor.6 Or the location within a county of some major industry may be thought to call for dilution of voting strength.7 Again, the combination of certain smaller counties with their more heavily populated neighbors in senatorial or “floterial” districts may result in apparent arithmetic inequalities.8
More broadly, the disparities in electoral strength among the various counties in Tennessee, both those relied upon by my Brother Clark and others, may be *347accounted for by various economic,9 political,10 and geographic 11 considerations. No allegation is made by the appellants that the existing apportionment is the result of any other forces than are always at work in any legislative process; and the record, briefs, and arguments in this Court themselves attest to the fact that the appellants could put forward nothing further at a trial.
By disregarding the wide variety of permissible legislative considerations that may enter into a state electoral apportionment my Brother Clark has turned a highly complex process into an elementary arithmetical puzzle. *348It is only by blinking reality that such an analysis can stand and that the essentially legislative determination can be made the subject of judicial inquiry.
IV.
Apart from such policies as those suggested which would suffice to justify particular inequalities, there is a further consideration which could rationally have led the Tennessee Legislature, in the exercise of a deliberate choice, to maintain the status quo. Rigidity of an apportionment pattern may be as much a legislative policy decision as is a provision for periodic reapportionment. In the interest of stability, a State may write into its fundamental law a permanent distribution of legislators among its various election districts, thus forever ignoring shifts in population. Indeed, several States have achieved this result by providing for minimum and maximum representation from various political subdivisions such as counties, districts, cities, or towns. See Harvey, Reapportionments of State Legislatures — Legal Requirements, 17 Law & Contemp. Probs. (1952), 364, 368-372.
It is said that one cannot find any rational standard in what the Tennessee Legislature has failed to do over the past 60 years. But surely one need not search far to find rationality in the Legislature’s continued refusal to recognize the growth of the urban population that has accompanied the development of industry over the past half decade. The existence of slight disparities between rural areas does not overcome the fact that the foremost apparent legislative motivation has been to preserve the electoral strength of the rural interests notwithstanding shifts in population. And I understand it to be conceded by at least some of the majority that this policy is not *349rendered unconstitutional merely because it favors rural voters.
Once the electoral apportionment process is recognized for what it is — the product of legislative give-and-take and of compromise among policies that often conflict— the relevant constitutional principles at once put these appellants out of the federal courts.
The relevant provisions of the Tennessee Constitution are Art. II, §§ 5 and 6:
“Sec. 5. Apportionment of representatives — The. number of Representatives shall, at the several periods of making the enumeration, be apportioned among the several counties or districts, according to the *342number of qualified voters in each; and shall not exceed seventy-five, until the population of the State shall be one million and a half, and shall never exceed ninety-nine; Provided, that any county having two-thirds of the ratio shall be entitled to one member.
“Sec. 6. Apportionment o/ senators. — The number of Senators shall, at the several periods of making the enumeration, be apportioned among the several counties or districts according to the number of qualified electors in each, and shall not exceed one-third the number of representatives. In apportioning the Senators among the different counties, the fraction that may be lost by any county or counties, in the apportionment of members to the House of Representatives, shall be made up to such county or counties in the Senate, as near as may be practicable. When a district is composed of two or more counties, they shall be adjoining; and no counties shall be divided in forming a district.”
This formula is not clearly spelled out in the opinion, but it is necessarily inferred from the figures that are presented. Knox County, for example, is said to have a “total representation” of 7.25. It *343elects (1) three direct representatives (value 3.00); (2) one representative from a two-county district (value .50); (3) one direct senator (value 3.00); and (4) one senator in a four-county district (value .75). See Appendix to opinion of Mr. Justice Clark, ante, pp. 262-264.
If this “adjusted” formula for measuring “total representation” is applied to the other “horribles” cited in the concurring opinion {ante, p. 255), it reveals that these counties — which purportedly have equal “total representation” but distinctly unequal voting population — do not have the same “total representation” at all. Rather than having the same representation as Rutherford County, Moore County has only about 40% of what Rutherford has. Decatur County has only 55% of the representation of Carter County. While Loudon and Anderson Counties are substantially underrepresented, this is because of their proximity to Knox County, which outweighs their votes in the Sixth Senatorial District and in the Eighth Floterial District.
These disparities are as serious, if not more so, when my Brother Clark’s formula is applied to the appellants’ proposal. For example, if the seven counties chosen by him as illustrative are examined as they would be represented under the appellants’ distribution, Moore County, with a voting population of 2,340, is given more electoral strength than Decatur County, with a voting population of 5,563. Carter County (voting population 23,302) has 20% more “total representation” than Anderson County (voting population 33,990), and 33% more than Rutherford County (voting population 25,316).
Murfreesboro, Rutherford County (pop. 16,017); Elizabethton, Carter County (pop. 10,754); Oak Ridge, Anderson County (pop. 27,387). Tennessee Blue Book, 1960, pp. 143-149.
For example, Carter and Washington Counties are each approximately 60% as large as Maury and Madison Counties in terms of square miles, and this may explain the disparity between their “total representation” figures.
For example, in addition to being “semi-urban,” Blount County is the location of the City of Alcoa, where the Aluminum Company of America has located a large aluminum smelting and rolling plant. This may explain the difference between its “total representation” and that of Gibson County, which has no such large industry and contains no municipality as large as Maryville.
For example, Chester County (voting population 6,391) is one of those that is presently said to be overrepresented. But under the appellants’ proposal, Chester would be combined with populous Madison County in a “floterial district” and with four others, including Shelby County, in a senatorial district. Consequently, its total representation according to the Appendix to my Brother Clark’s opinion would be .19. (Ante, p. 262.) This would have the effect of disenfranchising all the county’s voters. Similarly, Rhea County’s almost 9,000 voters would find their voting strength so diluted as to be practically nonexistent.
For example, it is primarily the eastern portion of the State that is complaining of malapportionment (along with the Cities of Memphis and Nashville). But the eastern section is where industry is principally located and where population density, even outside the large urban areas, is highest. Consequently, if Tennessee is apportioning in favor of its agricultural interests, as constitutionally it was entitled to do, it would pecessarily reduce representation from the east.
For example, sound political reasons surely justify limiting the legislative chambers to workable numbers; in Tennessee, the House is set at 99 and the Senate at 33. It might have been deemed desirable, therefore, to set a ceiling on representation from any single county so as not to deprive others of individual representation. The proportional discrepancies among the four counties with large urban centers may be attributable to a conscious policy of limiting representation in this manner.
For example, Moore County is surrounded by four counties each of which has sufficient voting population to exceed two-thirds of the average voting population per county (which is the standard prescribed by the Tennessee Constitution for the assignment of a direct representative), thus qualifying for direct representatives. Consequently Moore County must be assigned a representative of its own despite its small voting population because it cannot be joined with any of its neighbors in a multicounty district, and the Tennessee Constitution prohibits combining it with nonadjacent counties. See note 1, supra.