delivered the opinion of the Court.

Georgia’s 1962 Senatorial Reapportionment Act1 appor- . tions the 54 seats of the Georgia Senate among the State’s *435159 counties. The 54 senatorial districts created by the Act are drawn, so far as possible, along existing , county lines; Thirty-three of the senatorial districts are made up of from one to eight counties each,2 and voters in these districts elect their senators by a district-wide vote. The remaining 21 senatorial districts are allotted in groups of from two to seven among the seven most populous counties, but voters in these districts do not elect a senator by a district-wide vote; instead they join with the voters of the other districts of the county in electing all the county’s senators by á county-wide vote.

The appellees, registered voters of Georgia, brought this action in the District Court for the Northern District of Georgia against the Secretary of State of Georgia and local election officials seeking a decree that the requirement of county-wide voting in the seven multi-district counties violates the Equal Protection Clause of the Fourteenth Amendment. A three-judge court granted appellees’ motion for summary judgment, stating that “The statute causes a clear difference in the treatment accorded voters in each of the two classes of senatorial districts. It is the same law applied differently to dif*436ferent" persons. The voters select their own senator in one class of districts. In the other they do not. They must join with others in selecting a group of senators and their own choice of a senator may be nullified by what voters in other districts of the group desire. This difference is a discrimination as between voters in the two classes. . . . The statute here is nothing more than a classification of voters in senatorial districts on the basis of homesite, to the end that some are allowed to select their representatives while others are not. It is an invidious discrimination tested by any standard.” 228 F. Supp. 259, 263. We noted probable jurisdiction, 379 U. S. 810. We reverse.

Only last Term, in our opinion in Reynolds v. Sims, 377 U. S. 533, decided after the decision below, we rejected the notion that equal protection necessarily requires the formation of single-member districts. In discussing the impact on bicameralism of the equal-protection standards, we said, “One body could be composed of single-member districts while the other could have at least some multi-member districts.” 377 U. S., at 577. (Emphasis supplied.) Again, in holding that a State might legitimately desire to maintain the integrity of various political subdivisions, such as counties, we said: “Single-member districts may be the rule in one State, while another State might desire to achieve some flexibility by creating multi-member or floterial districts. Whatever the means of accomplishment, the overriding objective must-be substantial equality of population among the various districts, so that the vote of any citizen is approximately equal in weight to that of any other citizen in the State.” 377 U. S., at 579. (Emphasis supplied.)

It is not contended that there is not “substantial equality of population” among the 54 senatorial districts. The equal protection argument is focused solely upon the question whether county-wide voting in the seven multi-*437district counties results in denying the residents therein a vote “approximately equal in weight to that of” voters resident in the single-member constituencies. Contrary to the District Court, we cannot say. that it does. There is .clearly no mathematical disparity. Fulton County, the State’s largest constituency, has a population nearly seven times larger than that of a single-district constituency and for that reason elects seven senators. Every Fulton County voter, therefore, may vote for seven senators to represent his interests in the legislature. But the appellees assert that this scheme is defective because county-wide voting in multi-district counties could, as a matter of mathematics, result in the nullification of the unanimous choice of the voters of a district, thereby thrusting upon them a senator for whom no one in the district had voted. But this is only a highly hypothetical assertion3 that, in any event, ignores the practical reali*438ties of representation in a multi-member constituency. It is not accurate to treat a senator from a multi-district county as the representative of only that district within the county wherein he resides. The statute uses districts in multi-district counties merely as the basis of residence for candidates, not for voting or representation. Each district’s senator must be a resident of that district, but since his tenure depends upon the county-wide electorate he must be vigilant to serve the interests of all the people in the county, and not merely those of people in his home district; thus in. fact he is the county’s and not merely the district’s senator. If the weight of the vote of any voter in a Fulton County district, when he votes for seven senators to represent him in the Georgia Senate, is not the exact equivalent of that of a. resident of a single-member constituency, we cannot say that his vote is not “approximately equal in weight to that of any other citizen in the State*”

In reversing the District Court we should emphasize that the equal-protection claim below was based upon an alleged infirmity that attaches to the statute on its face. Agreeing with appellees’ contention that the multi-mem-ber constituency feature of the Georgia scheme was per se bad, the District Court entered the decree on summary judgment. We treat the question as presented in that *439context, and our opinion is not to be understood to say that in all instances or under all circumstances such a system as Georgia has will comport with the dictates of . the Equal Protection Clause. It might well be that, designedly or otherwise, a multi-member constituency apportionment scheme, under the circumstances of a particular casé, would operate to minimize or cancel out the voting strength of racial or political elements of the voting population. When this is demonstrated it will be time enough to consider whether the system still passes constitutional muster. This question, however, is not presented by the record before us. It is true that appel-lees asserted in one Short paragraph of their brief in this Court that the county-wide election method was resorted to by Georgia in order to minimize the strength of racial and political minorities in the populous urban counties. But appellees never seriously pressed , this point below and offered no proof to support it,, the District Court did not consider or rule on its merits, and in oral argument here counsel for appellees stressed that they do not rely on this argument. The record thus does not contain any substantiation of the bald assertion in appellees’ brief. Since, under these circumstances, this issue has "not been formulated to bring it into focus, and the evidence has not been offered or appraised to decide it, our holding has no bearing on that' wholly separate question.” Wright v. Rockefeller, 376 U. S. 52, 58.

Reversed.

concurring.

Under the compulsion of last Term’s reapportionment decisions I join the opinion and judgment of the Court, but with one reservation. There is language in today’s opinion, unnecessary to the Court’s resolution of this case, that might be taken to mean that the constitutionality of *440state legislative apportionments must, in the last analysis, always be judged in terms of simple arithmetic.

As this Court embarks on the difficult business of putting flesh on the bones of Reynolds v. Sims, 377 U. S. 533, and its companion decisions of last June, I desire expressly to reserve for a case which squarely presents the issue, the question of whether the principles announced in those decisions require such a sterile approach to the concept of equal protection in the political field.

dissenting.

Georgia — whose political hierarchy was long constructed on the county-unit* basis — has made an important change. The Georgia Constitution was amended to read:

“The Senate shall consist of 54 members. The General Assembly shall have authority’to create, rearrange and change senatorial districts and to provide for the election of Senators from each senatorial district, or from several districts embraced within one county, in such manner as the General Assembly may deem advisable.” (Italics added.) Art. III, § II, par. I.

, The “senatorial district” is thus made the unit in the election of senators. But the Senatorial Reapportionment Act provides in relevant part:

“Each Senator must be a resident of his own senatorial district and'shall be elected by the voters of his own district, except that the Senators from those senatorial districts, consisting of less than one county shall be elected by all the voters of the county in which such senatorial district is located.”

Thus “senatorial districts” are put into two classifications: first, those, comprising one or more counties; sec*441ond, those consisting of less than one county. The “equal protection” problem under the Fourteenth Amendment arises by reason of the fact that all electors of the districts in the first group choose their own senators, while the electors of the districts in the second group must share the choice of their senators with all the other electors in their county. I agree with the District Court: . . voters in some senatorial districts cannot be treated differently from voters in other senatorial districts. The statute here is nothing more than a classification of voters in senatorial districts on the basis of. homesite, to the end that some are allowed to select their representatives while others are not.” 228 F. Supp. 259, 263.

There are seven senatorial districts within Fulton County:

District 34 containing 82,195 voters.

District 35 containing 82,888 voters.

District 36 containing 79,023 voters.

District 37 containing 78,540 voters.

District 38 containing 78,953 voters.

District 39 containing 79,713 voters.

District 40 containing 74,834 voters.

There are three senatorial districts in De.Kalb County:

District 41 containing 75,117 voters.

District 42 containing 95,032 voters.

District 43 containing 86,633 voters.

As appellees point out, even if a candidate for one of those districts obtained all of the votes in that district, he could still be defeated by the foreign vote, while he would of course be elected if he were running in á district in the first group. I have no idea how this weighted voting might produce prejudice race-wise, religion-wise, politics-wise. But to allow some candidates to be chosen by the electors in their districts and others to be defeated by the voters of foreign districts is in my view an “invidi*442ous discrimination” — the test of unequal protection under the Fourteenth Amendment. Baker v. Carr, 369 U. S. 186, 244. I had assumed we had settled this question in Gray v. Sanders, 372 U. S. 368, 379, where we said: “Once the geographical unit for which a representative is to be chosen is designated, all who participate in the election are to have an equal vote — ^whatever their race, whatever their sex, whatever their occupation, whatever their income, and wherever their home may be. in that geographical unit. This is required by the Equal Protection Clause of the Fourteenth Amendment.”