489 U.S. 688
109 S.Ct. 1433
103 L.Ed.2d 717
BOARD OF ESTIMATE OF CITY OF NEW YORK, et al.,  Appellants,v.Beverly MORRIS et al.  Frank V. PONTERIO, Appellant,  v.  Beverly MORRIS, Joy Clarke Holmes and Joanne Oplustil.
Nos. 87-1022, 87-1112.
Argued Dec. 7, 1988.
Decided March 22, 1989.


Syllabus

New York City's Board of Estimate consists of the mayor and two other members elected citywide, each of whom casts two votes, plus the elected presidents of the city's five boroughs, each of whom casts one vote.  Appellees, residents and voters of Brooklyn, the most populous borough, charging that the city charter's sections governing the board's composition are inconsistent with the Equal Protection Clause of the Fourteenth Amendment, brought suit in the District Court, which concluded that the board was a nonelective, nonlegislative body not subject to the rule established by Reynolds v. Sims, 377 U.S. 533, 84 S.Ct. 1362, 12 L.Ed.2d 506, and other reapportionment cases.  The Court of Appeals reversed, finding that the board's selection process must comply with the reapportionment cases' so-called "one-person, one-vote" requirement, since its members ultimately are chosen by popular vote.  On remand, the District Court determined that applying the Abate v. Mundt, 403 U.S. 182, 91 S.Ct. 1904, 29 L.Ed.2d 399, population per representative methodology to the disparate borough populations produced a total deviation of 132.9% from voter equality among the electorates, and that the city's explanations for this range neither required nor justified such a gross deviation.  The Court of Appeals affirmed, holding, inter alia, that the presence of citywide representatives did not warrant departure from the Abate methodology and, thus, that the District Court's finding of a 132.9% deviation was correct.
Held:  The Board of Estimate's structure is inconsistent with the Equal Protection Clause of the Fourteenth Amendment because, although the boroughs have widely disparate populations, each has equal representation on the board.  Pp. 692-703.
(a) Board membership elections are local elections subject to review under the prevailing reapportionment doctrine.  The board, composed of officials who become members as a matter of law upon their elections, has a significant range of fiscal and legislative functions common to municipal governments, including assisting in the formulation of the city's budget, and controlling land-use, contract, and franchise powers.  That the citywide members enjoy a 6-to-5 voting majority does not render the board's composition constitutional, since the borough presidents control the outcome of board decisions anytime the citywide members do not vote together and always control budgetary decisions because the mayor has no vote on such matters. Moreover, the Reynolds- Abate approach should not be put aside in favor of the theoretical Banzhaf Index—which produces a standard deviation of 30.8% for nonbudget matters and a larger figure for budget items by mathematically calculating a voter's power to determine the outcome of an election—since the latter approach tends to ignore partisanship, race, voting habits, and other characteristics having an impact on general  lection outcomes. Pp. 692-699.
(b) The presence of citywide members is a major component to be factored into the process of determining the deviation between more or less populous boroughs.  This approach—which yields a standard deviation of 78%—recognizes that voters in each borough vote for, and are represented by, both their borough president and the citywide members, thus departing from the lower courts' approach which treated the five boroughs as single-member districts, each with a representative having a single vote.  Pp. 699-701.
(c) The city's proffered governmental interests—that the board is essential to the successful government of New York City, is effective, and accommodates natural and political boundaries as well as local interests—do not suffice to justify a 78% deviation from the one-person, one-vote ideal, particularly because the city could be served by alternative ways of constituting the board that would minimize the discrimination in voting power.  Pp. 701-703.
831 F.2d 384 (CA2 1987) affirmed.
WHITE, J., delivered the opinion of the Court, in which REHNQUIST, C.J., and MARSHALL, O'CONNOR, SCALIA, and KENNEDY, JJ., joined.  BRENNAN, J., filed an opinion concurring in part and concurring in the judgment, in which STEVENS, J., joined, post, p. 703.  BLACKMUN, J., filed an opinion concurring in part and concurring in the judgment, post, p. 703.
Peter L. Zimroth, New York City, for appellants.
Richard David Emery, New York City, for appellees.
Justice WHITE delivered the opinion of the Court.


1
The Board of Estimate of the City of New York consists of three members elected citywide, plus the elected presidents of each of the city's five boroughs.  Because the boroughs have widely disparate populations—yet each has equal representation on the board—the Court of Appeals for the Second Circuit held that this structure is inconsistent with the Equal Protection Clause of the Fourteenth Amendment.  We affirm.


2
Appellees, residents and voters of Brooklyn, New York City's most populous borough, commenced this action against the city in December 1981.1  They charged that the city's charter sections that govern the composition of the Board of Estimate2 are inconsistent with the Equal Protection Clause of the Fourteenth Amendment as construed and applied in various decisions of this Court dealing with districting and apportionment for the purpose of electing legislative bodies.  The District Court dismissed the complaint, 551 F.Supp. 652 (EDNY 1982), on the ground that the board was not subject to the rule established by Reynolds v. Sims, 377 U.S. 533, 84 S.Ct. 1362, 12 L.Ed.2d 506 (1964), its companion cases, and its progeny, such as Abate v. Mundt, 403 U.S. 182, 91 S.Ct. 1904, 29 L.Ed.2d 399 (1971), because in its view the board is a nonelective, nonlegislative body.  The Court of Appeals reversed.  707 F.2d 686 (CA2 1983).  Because all eight officials on the board ultimately are selected by popular vote, the court concluded that the board's selection process must comply with the so-called "one person, one vote" requirement of the reapportionment cases.  The court remanded to the District Court to ascertain whether this compliance exists.  Bifurcating the proceedings, the District Court determined first, that applying this Court's methodology in Abate v. Mundt, supra, to the disparate borough populations produced a total deviation of 132.9% from voter equality among these electorates, 592 F.Supp. 1462 (EDNY 1984);  and second, that the city's several explanations for this range neither require nor justify the electoral scheme's gross deviation from equal representation.  647 F.Supp. 1463 (EDNY 1986).  The court thus found it unnecessary to hold that the deviation it identified was per se unconstitutional.


3
The Court of Appeals affirmed.  831 F.2d 384 (CA2 1987). Tracing the imperative of each citizen's equal power to elect representatives from Reynolds v. Sims to Abate v. Mundt and beyond, the court endorsed the District Court's focus on population per representative.  The court held that the presence of the citywide representatives did not warrant departure from the Abate approach and that the District Court's finding of a 132% deviation was correct.  Without deciding whether this gross deviation could ever be justified in light of the flexibility accorded to local governments in ordering their affairs, the Court of Appeals, agreeing with the District Court, held inadequate the city's justifications for its departure from the equal protection requirement that elective legislative bodies be chosen from districts substantially equal in population, especially since alternative measures could address the city's valid policy concerns and at the same time lessen the discrimination against voters in the more populous districts.  We noted probable jurisdiction in both Nos. 87-1022 and 87-1112, 485 U.S. 986, 108 S.Ct. 1288, 99 L.Ed.2d 498 (1988).3


4
As an initial matter, we reject the city's suggestion that because the Board of Estimate is a unique body wielding non-legislative powers, board membership elections are not subject to review under the prevailing reapportionment doctrine.  The equal protection guarantee of "one person, one vote" extends not only to congressional districting plans, see Wesberry v. Sanders, 376 U.S. 1, 84 S.Ct. 526, 11 L.Ed.2d 481 (1964), not only to state legislative districting, see Reynolds v. Sims, supra, but also to local government apportionment.  Avery v. Midland County, 390 U.S. 474, 479-481, 88 S.Ct. 1114, 1117-1118, 20 L.Ed.2d 45 (1968); Abate v. Mundt, supra, 403 U.S., at 185, 91 S.Ct., at 1906.  Both state and local elections are subject to the general rule of population equality between electoral districts.  No distinction between authority exercised by state assemblies, and the general governmental powers delegated by these assemblies to local, elected officials, suffices to insulate the latter from the standard of substantial voter equality.  See Avery v. Midland County, supra, 390 U.S., at 481, 88 S.Ct., at 1118.  This was confirmed in Hadley v. Junior College Dist. of Metropolitan Kansas City, 397 U.S. 50, 90 S.Ct. 791, 25 L.Ed.2d 45 (1970):


5
"[W]henever a state or local government decides to select      persons by popular election to perform governmental      functions, the Equal Protection Clause of the Fourteenth      Amendment requires that each qualified voter must  e given an      equal opportunity to participate in that election, and when      members of an elected body are chosen from separate      districts, each district must be established on a basis that      will insure, as far as is practicable, that equal numbers of      voters can vote for proportionally equal numbers of      officials."  Id., at 56, 90 S.Ct., at 795.


6
These cases are based on the propositions that in this country the people govern themselves through their elected representatives and that "each and every citizen has an inalienable right to full and effective participation in the political processes" of the legislative bodies of the Nation, State, or locality as the case may be.  Reynolds v. Sims, 377 U.S., at 565, 84 S.Ct., at 1378.  Since "[m]ost citizens can achieve this participation only as qualified voters through the election of legislators to represent them," full and effective participation requires "that each citizen have an equally effective voice in the election of members of his . . . legislature."  Ibid.  As Daniel Webster once said, "the right to choose a representative is every man's portion of sovereign power."  Luther v. Borden, 48 U.S. (7 How.) 1, 30, 12 L.Ed. 581 (1849) (statement of counsel).  Electoral systems should strive to make each citizen's portion equal.  If districts of widely unequal population elect an equal number of representatives, the voting power of each citizen in the larger constituencies is debased and the citizens in those districts have a smaller share of representation than do those in the smaller districts.  Hence the Court has insisted that seats in legislative bodies be apportioned to districts of substantially equal populations.  Achieving " 'fair and effective representation of all citizens is . . . the basic aim of legislative apportionment,' [Reynolds, supra ], [377 U.S.] at 565-566 [84 S.Ct., at 1383-1384] and [it is] for that reason that [Reynolds ] insisted on substantial equality of populations among districts."  Gaffney v. Cummings, 412 U.S. 735, 748, 93 S.Ct. 2321, 2329, 37 L.Ed.2d 298 (1973).


7
That the members of New York City's Board of Estimate trigger this constitutional safeguard is certain.  All eight officials become members as a matter of law upon their various elections. New York City Charter § 61 (1986).  The mayor, the comptroller, and the president of the city council, who constitute the board's citywide number, are elected by votes of the entire city electorate.  Each of these three cast two votes, except that the mayor has no vote on the acceptance or modification of his budget proposal.  Similarly, when residents of the city's five boroughs the Bronx, Brooklyn, Manhattan, Queens, and Richmond (Staten Island)—elect their respective borough presidents, the elections decide each borough's representative on the board.  These five members each have single votes on all board matters.


8
New York law assigns to the board a significant range of functions common to municipal governments.4  Fiscal responsibilities include calculating sewer and water rates, tax abatements, and property taxes on urban development projects.  The board manages all city property;  exercises plenary zoning authority;  dispenses all franchises and leases on city property; fixes generally the salaries of all officers and persons compensated through city moneys;  and grants all city contracts.  This array of powers, which the board shares with no other part of the New York City government, are exercised through the aforementioned voting scheme:  three citywide officials cast a total of six votes;  their five borough counterparts, one vote each.


9
In addition, and of major significance, the board shares legislative functions with the city council with respect to modifying and approving the city's capital and expense budgets. The mayor submits a proposed city budget to the board and city council, but does not participate in board decisions to adopt or alter the proposal.  Approval or modification of the proposed budget requires agreement between the board and the city council. Board votes on budget matters, therefore, consist of four votes cast by two at-large members;  and five, by the borough presidents.


10
This considerable authority to formulate the city's budget, which last fiscal year surpassed $25 billion, as well as the board's land use, franchise, and contracting powers over the city's 7 million inhabitants, situate the board comfortably within the category of governmental bodies whose "powers are general enough and have sufficient impact throughout the district" to require that elections to the body comply with equal protection strictures.  See Hadley v. Junior College Dist., 397 U.S., at 54, 90 S.Ct., at 794.


11
The city also erroneously implies that the board's composition survives constitutional challenge because the citywide members cast a 6-to-5 majority of board votes and hence are in position to control the outcome of board actions.  The at-large members, however, as the courts below observed, often do not vote together;  and when they do not, the outcome is determined by the votes of the borough presidents, each having one vote.  Two citywide members, with the help of the presidents of the two least populous boroughs, the Bronx and Staten Island, will prevail over a disagreeing coalition of the third citywide member and the presidents of the three boroughs that contain a large majority of the city's population. Furthermore, because the mayor has no vote on budget issues, the citywide members alone cannot control board budgetary decisions.


12
The city's primary argument is that the courts below erred in the methodolog  by which they determined whether, and to what extent, the method of electing the board members gives the voters in some boroughs more power than the voters in other boroughs. Specifically, the city focuses on the relative power of the voters in the various boroughs to affect board decisions, an approach which involves recognizing the weighted voting of the three citywide members.


13
As described by the Court of Appeals, 831 F.2d, at 386, n. 2 (the city's description is essentially the same, Brief for Municipal Appellants 35-36), the method urged by the city to determine an individual voter's power to affect the outcome of a board vote first calculates the power of each member of the board to affect a board vote, and then calculates voters' power to cast the determining vote in the election of that member.  This method, termed the Banzhaf Index, applies as follows:  552 possible voting combinations exist in which any one member can affect the outcome of a board vote.  Each borough president can cast the determining vote in 48 of these combinations (giving him a "voting power" of 8.7%), while each citywide member can determine the outcome in 104 of 552 combinations (18.8%).  A citizen's voting power through each representative is calculated by dividing the representative's voting power by the square root of the population represented;  a citizen's total voting power thus aggregates his power through each of his four representatives—borough president, mayor, comptroller, and council president.  Deviation from ideal voting power is then calculated by comparing this figure with the figure arrived at when one considers an electoral district of ideal population.  Calculated in this manner, the maximum deviation in the voting power to control board outcomes is 30.8% on nonbudget matters, and, because of the mayor's absence, a higher deviation on budget issues.


14
The Court of Appeals gave careful attention to and rejected this submission.  We agree with the reasons given by the Court of Appeals that the population-based approach of our cases from Reynolds through Abate should not be put aside in this litigation.  We note also that we have once before, although in a different context, declined to accept the approach now urged by the city.  Whitcomb v. Chavis, 403 U.S. 124, 91 S.Ct. 1858, 29 L.Ed.2d 363 (1971).  In that case we observed that the Banzhaf methodology "remains a theoretical one" and is unrealistic in not taking into account "any political or other factors which might affect the actual voting power of the residents, which might include party affiliation, race, previous voting characteristics or any other factors which go into the entire political voting situation."  Id., at 145-146, 91 S.Ct., at 1870.


15
The personal right to vote is a value in itself, and a citizen is, without more and without mathematically calculating his power to determine the outcome of an election, shortchanged if he may vote for only one representative when citizens in a neighboring district, of equal population, vote for two;  or to put it another way, if he may vote for one representative and the voters in another district half the size also elect one representative.  Even if a desired outcome is the motivating factor bringing voters to the polls, the Court of Appeals in this case considered the Banzhaf Index an unrealistic approach to determining whether citizens have an equal voice in electing their representatives because the approach tends to ignore partisanship, race, and voting habits or other characteristics having an impact on election outcomes.


16
The Court of Appeals also thought that the city's approach was "seriously defective in the way it measures Board members' power to determine the outcome of a Board vote."  831 F.2d, at 390.  The difficulty was that this method did not reflect the way the board actually works in practice;  rather, the method is a theoretical explanation of each board member's power to affect the outcome of board actions.  It may b  that in terms of assuring fair and effective representation, the equal protection approach reflected in the Reynolds v. Sims line of cases is itself imperfect, but it does assure that legislators will be elected by, and represent citizens in, districts of substantially equal size. It does not attempt to inquire whether, in terms of how the legislature actually works in practice, the districts have equal power to affect a legislative outcome.  This would be a difficult and ever-changing task, and its challenge is hardly met by a mathematical calculation that itself stops short of examining the actual day-to-day operations of the legislative body.  The Court of Appeals in any event thought there was insufficient reason to depart from our prior cases, and we agree.5


17
Having decided to follow the established method of resolving equal protection issues in districting and apportionment cases, the Court of Appeals then inquired whether the presence of at-large members on the board should be factored into the process of determining the deviation between the more and less populous boroughs.  The court decided that they need not be taken into account because the at-large members and the borough presidents respond to different constituencies. The three at-large members obviously represent citywide interests; but, in the Court of Appeals' judgment, the borough presidents represent and are responsive to their boroughs, yet each has one vote despite the dramatic inequalities in the boroughs' populations.  Consideration of the citywide members might be different, the court explained, "[i]f the at-large bloc was not simply a majority, but a majority such that it would always and necessarily control the governing body, and the district representatives play a decidedly subsidiary role. . . ."  831 F.2d, at 389, n. 5.  Like Judge Newman in concurrence, however, the court noted that this was decidedly not true of the Board.6


18
The Court of Appeals then focused on the five boroughs as single-member districts, electing five representatives to the Board, each with a single vote.  Applying the formula that we have utilized without exception since 1971, see Abate v. Mundt, 403 U.S., at 184 and n. 1, 91 S.Ct., at 1906 and n. 1;  Gaffney v. Cummings, 412 U.S., at 737, 93 S.Ct., at 2323;  Brown v. Thomson, 462 U.S. 835, 103 S.Ct. 2690, 77 L.Ed.2d 214 (1983), the Court of Appeals agreed with the District Co rt that the maximum percentage deviation from the ideal population is 132.9%.7


19
We do not agree with the Court of Appeals' approach.  In calculating the deviation among districts, the relevant inquiry is whether "the vote of any citizen is approximately equal in weight to that of any other citizen," Reynolds v. Sims, 377 U.S., at 579, 84 S.Ct., at 1390, the aim being to provide "fair and effective representation for all citizens," id., at 565-566, 84 S.Ct., at 1383-1384.  Here the voters in each borough vote for the at-large members as well as their borough president, and they are also represented by those members.  Hence in determining whether there is substantially equal voting power and representation, the citywide members are a major component in the calculation and should not be ignored.8


20
Because of the approach followed by the District Court and the Court of Appeals, there was no judicial finding concerning the total deviation from the ideal that would be if the at-large members of the board are taken into account.  In pleadings filed with the District Court, however, appellees indicated, and the city agreed, that the deviation would then be 78%.  See App. 47, 206, 375-376.  This deviation was confirmed at oral argument.9  Tr. of Oral Arg. 14-15, 39-40.  And as to budget matters, when only two citywide members participate, the deviation would be somewhat larger.  We accept for purposes of this case the figure agreed upon by the parties.


21
We note that no case of ours has indicated that a deviation of some 78% could ever be justified.  See Brown v. Thomson, supra, 462 U.S., at 84 -847, 103 S.Ct., at 2697-2699;  Connor v. Finch, 431 U.S. 407, 410-420, 97 S.Ct. 1828, 1831-1837, 52 L.Ed.2d 465 (1977);  Chapman v. Meier, 420 U.S. 1, 21-26, 95 S.Ct. 751, 763-766, 42 L.Ed.2d 766 (1975);  Mahan v. Howell, 410 U.S. 315, 329, 93 S.Ct. 979, 987, 35 L.Ed.2d 320 (1973).  At the very least, the local government seeking to support such a difference between electoral districts would bear a very difficult burden, and we are not prepared to differ with the holding of the courts below that this burden has not been carried.  The city presents in this Court nothing that was not considered below, arguing chiefly that the board, as presently structured, is essential to the successful government of a regional entity, the City of New York.  The board, it is said, accommodates natural and political boundaries as well as local interests.  Furthermore, because the board has been effective it should not be disturbed.  All of this, the city urges, is supported by the city's history.  The courts below, of course, are in a much better position than we to assess the weight of these arguments, and they concluded that the proffered governmental interests were either invalid or were not sufficient to justify a deviation of 132%,10 in part because the valid interests of the city could be served by alternative ways of constituting the board that would minimize the discrimination in voting power among the five boroughs.11  Their analysis is equally applicable to a 78% deviation, and we conclude that the city's proffered governmental interests do not suffice to justify such a substantial departure from the one-person, one-vote ideal.


22
Accordingly the judgment of the Court of Appeals is


23
Affirmed.


24
Justice BRENNAN, with whom Justice STEVENS joins, concurring in part and concurring in the judgment.


25
I agree with the opinion of the Court except insofar as it holds that the Court of Appeals should have taken the at-large members of the board into account in calculating the deviation from voter equality.  For the reasons given by the Court of Appeals, I would exclude those members from this calculation.


26
Justice BLACKMUN, concurring in part and concurring in the judgment.


27
I, too, would affirm the judgment below and share many of the Court's reasons for doing so.


28
I agree with the majority that measuring the degree of voter inequality in these cases requires inclusion of the at-large members of the Board of Estimate.  I also suspect the Court is correct in rejecting the Banzhaf Index here.  But, as the Court itself notes, ante, at 698, under the Index the deviation from voter equality measures 30.8% for nonbudget matters, and a still larger figure for budget issues.  Even this measure of voter inequality is too large to be constitutional and, for the reasons given by the District Court, 647 F.Supp. 1463 (EDNY 1986), cannot be justified by the interests asserted by the city.



1
 Appellants in No. 87-1022 are New York City, the city's board of Estimate, the board's eight members, and intervenor-defendant, Robert Straniere, a New York State Assembly member   Frank Ponterio, a resident of Staten Island, and an intervening defendant below, is the appellant in No. 87-1112.


2
 Section 61 of the New York City Charter (1986) reads: "Membership.  The mayor, the comptroller, the president of the council, and the presidents of the boroughs shall constitute the board of estimate."  Section 62 reads:  "Voting in the Board.  a. As members of the board of estimate, the mayor, the comptroller and the president of the council shall each be entitled to cast two votes, and the president of each borough shall be entitled to cast one vote.  b. Except as otherwise provided in this charter or by law, the board shall act by resolution adopted by a majority of the whole number of votes authorized to be cast by all the members of the board. . . .  d. A quorum of the board shall consist of a sufficient number of members thereof to cast six votes, including at least two of the members authorized to cast two votes each." Section 120(d) provides that the mayor may not vote as a board member when the adoption or modification of his proposed budget is at issue.


3
 The municipal appellants and intervenor-appellant Straniere served and filed notices of appeal on October 15, 1987, and November 6, 1987, respectively.  Intervenor-appellant Pontiero served and filed his notice of appeal on December 16, 1987.


4
 The District Court correctly observes that the board's powers are set forth in the city charter, state legislation, and the New York City Administrative Code.  Plaintiffs-appellees submitted to the District Court the following list of board powers:
"A. The Board of Estimate exclusively
"i. determines the use, development and impr vement of property owned by the City;
"ii. approves standards, scopes and final designs of capitol [sic ] projects for the City;
"iii. negotiates and enters into all contracts on behalf of the City;
"iv. negotiates and approves all franchises that are granted by the City;
"v. grants leases of City property and enters into leases of property for City use;
"vi. sets the rates for purchases of water from the City;
"vii. sets the charges for sewer services provided by the City;
"viii. approves or modifies all zoning decisions for the City;  and
"ix. sets tax abatements.
"B. The Board of Estimate acting in conjunction with the New York City Council
"i. recommends and approves the expense budget of the City without the participation of the Mayor;
"ii. recommends and approves the capital budget of the City without the participation of the Mayor;
"iii. periodically modifies the budgets of the City;
"iv. confers with the City Council when agreement on the budget between the two bodies is not reached;
"v. overrides mayoral vetoes of budget items without the participation of the Mayor;  and
"vi. holds hearings on budgetary matters.
"C. The Board of Estimate also
"i. administers the Bureau of Franchises;
"ii. administers the Bureau of the Secretary;
"iii. holds public hearings on any matter of City policy within its responsibilities whenever called upon to do so by the Mayor or in its discretion for the public interest;
"iv. holds hearings on tax abatements that are within the discretion of City administrative agencies;  and
"v. makes recommendations to the Mayor or City Council in regard to any matter of City policy."  Statement of Facts Pursuant to Local Rule 9(g) in No. 8-CV-3920 (EDNY), App. 44-46.
See also W.H.K. Communications Associations, Inc., The Structure, Powers, and Functions of New York City's Board of Estimate (1973), App. 54 (Kramarsky Study).


5
 Similarly, we reject appellant Ponterio's submission, which disagrees with both the Court of Appeals and the city. Ponterio puts aside a citizens' theoretical ability to cast a tie-breaking vote for their representative and focuses only on each borough representative's tie-breaking power on the board. Brief for Appellant Ponterio in No. 87-1112, pp. 17-23.  The formula suffers from the criticisms applicable to the Banzhaf Index generally.  Ponterio's argument in some ways is also inconsistent with our insistence that the equal protection analysis in this context focuses on representation of people, not political or economic interests.  See, e.g., Reynolds v. Sims, 377 U.S. 533, 561, 562, 84 S.Ct. 1362, 1381, 1382, 12 L.Ed.2d 506 (1964);  Dunn v. Blumstein, 405 U.S. 330, 336, 92 S.Ct. 995, 999, 31 L.Ed.2d 274 (1972).


6
 The Court of Appeals writes:  "Though the appellant Board insists on referring to 'an at-large majority voting bloc,' in fact there is no such 'bloc.'  Rather, this supposed 'bloc' consists of three persons having two votes each who are free to, and do, vote on different sides of various issues.  Only if all three vote together are they bound to carry the day.  Furthermore, on certain budget issues, on which the mayor does not vote, the at-large members cannot win a vote without the support of a borough president.  It follows that there is no majority-at-large voting bloc bound to control the Board and that this case is far removed from the hypotheticals offered by the Board and Amicus Banzhaf."  831 F.2d, at 389, n. 5 (citation omitted).


7
 That percentage is the sum of the percentage by which Brooklyn, the city's most populous district (population 2,230,936), exceeds the ideal district population (1,414,206), and the percentage by which Staten Island, the least populous (352,151), falls below this ideal.  Queens' population was stipulated to be 1,891,325;  Manhattan's, 1,427,533;  and the Bronx's, 1,169,115.  The parties stipulated, therefore, that the city's total population is 7,071,030.  See App. to Juris. Statement in No. 87-1112, pp. 9-10, 11.


8
 Appellees point out that in Avery v. Midland County, 390 U.S. 474, 88 S.Ct. 1114, 20 L.Ed.2d 45 (1968), we struck down a county apportionment scheme consisting of four district representatives and one at-large member without considering the effect of the at-large representative.  In that case, however, we were not faced with the task of determining the disparity in voting power among districts of different population;  the issue before the Court was whether our decision in Reynolds v. Sims, requiring that state legislatures be apportioned on the basis of population, applied as well to local government legislative bodies.  390 U.S., at 478-479, 88 S.Ct., at 1116-1118.  Nothing in Avery even remotely suggests that the impact of at-large representatives is to be ignored in determining whether an apportionment scheme violates the Equal Protection Clause.


9
 At oral argument in this Court, the city conceded this point:
"QUESTION:  . . . If we use the Abate method and took the three at-large officers and factored them into the analysis, what would the population deviation be?  Or can we not determine that based on this record?  Mr. ZIMROTH [counsel for the city]:  It depends on how you factor them in.  There's one way of factoring them in which would divide the number of city-wide votes proportionately among all of the counties [sic ]. . . .If you use that method, you come up with a number of 76 [sic ] percent. . . . [T]hat's the answer to your question.  That's the result you get if you use that methodology."  Tr. of Oral Arg. 14-15.  Appellees' counsel also stated that the deviation "came to 78 percent when you allocated that way."  Id., at 39-40.  Although Ponterio rejected the 78% figure in the District Court, he did so only in reliance on his modified Banzhaf test.  For reasons already stated, that reliance is misplaced.


10
 We note also that we are not persuaded by arguments that explain the debasement of citizens' constitutional right to equal franchise based on exigencies of history or convenience.  See Reynolds, 377 U.S., at 579-580, 84 S.Ct., at 1390-1391 ("Citizens, not history or economic interests, cast votes");  see also Maryland Committee for Fair Representation v. Tawes, 377 U.S. 656, 675, 84 S.Ct. 1429, 1439, 12 L.Ed.2d 595 (1964);  Lucas v. Forty-Fourth Colorado General Assembly, 377 U.S. 713, 738, 84 S.Ct. 1459, 1474, 12 L.Ed.2d 632 (1964).


11
 We are not presented with the question of the constitutionality of the alternative board structures suggested by the District Court and the Court of Appeals.


