In these two reapportionment cases, the courts below have struck down as unconstitutional the weighted voting plans which had been proposed to correct the conceded malapportionment of the Boards of Supervisors of Washington and Saratoga Counties.
*248In the Washington County case, the plaintiffs are residents, taxpayers and property owners of the Town of Kingsbury and, in the Saratoga County case, the plaintiffs are property owners and taxpayers of the City of Saratoga Springs. In each case, they instituted these actions seeking (1) a declaratory judgment that the apportionment of the Board of Supervisors of their respective county was unconstitutional and (2) an order directing the board to submit a valid plan of apportionment. It is not disputed that, at present, as prescribed by section 150 of the County Law, the municipalities in each county are equally represented by one member on the Board of Supervisors, even though there is a great disparity in the populations of the several towns and cities.1
In the Washington County litigation, the court at Special Term held that the apportionment of the board and section 150 of the County Law, as applied, violated the one man-one vote rubric and were, accordingly, unconstitutional. The board was directed to prepare and submit a permanent plan of reapportionment but was permitted, in the interim, to function as it was presently constituted. The board thereupon adopted what it terms an ‘ ‘ Adjusted Weighted Voting Plan” which provides that each town is to be represented on the board by at least one supervisor who will be entitled to cast one vote for every 279 persons residing in the town, up to a maximum of 15 votes. The membership of the board would be enlarged to allow for additional supervisors from those towns with populations large enough to warrant more than 15 votes. Thus, Kingsbury, the largest town, would be represented by three supervisors who would each cast 13 votes, for a total of 39. Dresden, Hampton and Putnam, the smallest towns, would each be represented by one supervisor who would cast two votes and the most votes cast by any single member of the board would be the 14 allotted to the supervisor from Greenwich.
Shortly after the action was commenced in Saratoga County, its Board of Supervisors adopted a so-called “ Fractional-Weighted Voting Plan ” which, generally speaking, follows the *249same pattern as the one for Washington County. This plan provides that each town and city will be represented on the board by at least one supervisor who will be entitled to cast one vote for every 600 persons residing in the municipality, up to a maximum of 20 votes. The membership of the board would be enlarged to allow for an additional supervisor from Saratoga Springs which has a population large enough to warrant more than 20 votes. More specifically, Saratoga Springs would be represented by two supervisors who would each cast 14 votes for a total of 28, while Providence, Edinburg and Day, the smallest towns, would each be represented by one supervisor who would cast one vote; the most votes cast by any single member of the board would be the 16 allotted to the supervisor from the Town of Moreau.
The court at Special Term found each weighted voting plan unacceptable, on constitutional grounds, because, in its words, the plan, in practice, “virtually strips the smaller towns of a true voice on the board.” Each board was ordered to submit a plan other than one involving weighted voting and the Appellate Division affirmed both orders.2
There is no doubt that, as presently constituted, both Boards of Supervisors are malapportioned. Equal representation on the boards of municipalities with populations that vary from a few hundred to many thousands does not satisfy the “ one person, one vote ” principle announced in Reynolds v. Sims (377 U. S. 533) and, although the United States Supreme Court has not as yet passed upon the question (see, e.g., Dusch, v. Davis, 387 U. S. 112; Avery v. Midland County, 406 S. W. 2d 422 [Tex.], cert, granted 388 U. S. 905), we have expressly held that the rule of the Sims case applies to local ‘ ‘ elective legislative bodies exercising general governmental powers ”. (Seaman v. Fedourich, 16 N Y 2d 94, 101; see, generally, Weinstein, The Effect of the Federal Reapportionment Decisions on Counties and Other Forms of Municipal Government, 65 Col. L. *250Rev. 21.) Tlio present imbalance on tlio boards is directly attributable to the County Law which provides that the supervisors of the several cities and towns in each county, without regard to population differences, “ shall constitute the board of supervisors of the county” (§ 150) and that the board shall conduct its business ‘ ‘ by the affirmative vote of a majority of [its] total membership” (§ 153, subd. 4). Quite clearly, therefore, these sections of the County Law, as applied to Saratoga and Washington Counties, are violative of constitutional requirements. (See Michl v. Shanklin, 17 N Y 2d 906; cf. Graham v. Board of Supervisors of Erie County, 18 N Y 2d 672; see, also, McGill v. Board of Supervisors of Niagara County, 19 N Y 2d 860.) In the absence of a valid statute establishing the organization and composition of the Boards of Supervisors of those counties, the boards should be directed to reapportion themselves in accordance with the powers granted to them by the Municipal Home Buie Law (§ 10, subd. 1, par. [ii], cl. a, subcl. [1]).
The Supreme Court recently observed that all of the constitutional principles which govern the apportionment of state legislatures are not necessarily applicable to the organization of local governments. In Sailors v. Board of Educ. (387 U. S. 105, 110), the court remarked:
“ Viable local governments may need many innovations, numerous combinations of old and new devices, great flexibility in municipal arrangements to meet changing urban conditions. We see nothing in the Constitution to prevent experimentation.”
And, in Dusch v. Davis (387 U. S. 112, supra), the court approved Virginia Beach’s “ experimentation ” in local government. The City of Virginia Beach had consolidated with an adjoining county, which was both rural and urban, under a borough form of government. A plan was adopted, by which all of the members of the City Council were elected at large, it being provided, however, that at least one councilman was required to reside in each of the city’s seven boroughs. This plan was said to properly “ reflect a detente between urban and rural communities that may be important in resolving the complex problems *251of the modern megalopolis” (387 U. S., at p. 117; see, also, Matter of Blaikie v. Power, 13 N Y 2d 134, opp. dsmd. 375 U. S. 439).
It might appear, on first impression, that the modified weighted voting plans before us were designed to accomplish almost the same objective as the scheme underlying the Virginia Beach plan — namely, to assure that sparsely populated areas have a voice in the councils of government. However, as we noted in the Graham case (18 N Y 2d 672, 674, supra), any method of allocating votes among representatives in proportion to population is liable to have hidden ‘ inherent defects ’ Although the small towns in a county would be separately represented on the board, each might actually be less able to affect the passage of legislation than if the county were divided into districts of equal population with equal representation on the board and several of the smaller towns were joined together in a single district. (See Banzhaf, Weighted Voting Doesn’t Work: A Mathematical Analysis, 19 Rutgers L. Rev. 317.) The significant standard for measuring a legislator’s voting power, as Mr. Banzhaf points out, is not the number or fraction of votes which he may cast but, rather, his “ ability * * * , by his vote, to affect the passage or defeat of a measure ” (19 Rutgers L. Rev., at p. 318). And he goes on to demonstrate that a weighted voting plan, while apparently distributing this voting power in proportion to population, may actually operate to deprive the smaller towns of what little voting power they possess, to such an extent that some of them might be completely disenfranchised and rendered incapable of affecting any legislative determinations at all (19 Rutgers L. Rev., at pp. 325-338).
Of course, in any weighted voting scheme, those representatives who cast the larger aggregates of votes can be expected to have greater influence with their colleagues than representatives with only a single vote. We find nothing unconstitutional in a disparity of influence among the various members of a county board of supervisors. In every legislature there will be some members who, because of particular expertise, wealth, political office, a reputation for probity and the like, will be found to exercise more sway than others In the passage or defeat of legislation and, when weighted voting is employed, *252such influence might well attach to the representatives from the larger constituencies who cast the larger aggregates of votes.
The principle of one man-one vote is violated, however, when the power of a representative to affect the passage of legislation by his vote, rather than by influencing his colleagues, does not roughly correspond to the proportion of the population in his constituency. Thus, for example, a particular weighted voting plan would be invalid if 60% of the population were represented by a single legislator who was entitled to cast 60% of the votes. Although his vote would apparently be weighted only in proportion to the population he represented, he would actually possess 100% of the voting power whenever a simple majority was all that was necessary to enact legislation. Similarly, a plan would be invalid if it was mathematically impossible for a particular legislator representing say 5% of the population to ever cast a decisive vote. Ideally, in any weighted voting plan, it should be mathematically possible for every member of the legislative body to cast the decisive vote on legislation in the same ratio which the population of his constituency bears to the total population. Only then would a member representing 5% of the population have, at least in theory, the same voting power (5%) under a weighted voting plan as he would have in a legislative body which did not use weighted voting — e.g., as a member of a 20-member body with each member entitled to cast a single vote. This is what is meant by the one man-one vote principle as applied to weighted voting plans for municipal governments. A legislator’s voting power, measured by the mathematical possibility of his casting a decisive vote, must approximate the power he would have in a legislative body which did not employ weighted voting.
Unfortunately, it is not readily apparent on its face whether either of the plans before us meets the constitutional standard. Nor will practical experience in the use of such plans furnish relevant data since the sole criterion is the mathematical voting: power which each legislator possesses in theory — i.e., the indicia of representation — and not the actual voting power he possesses in fact — i.e., the indicia of influence. In order to measure the mathematical voting power of each member of these county boards of supervisors and compare it with the proportion of the population which he represents, it would be necessary to *253have the opinions of experts based on computer analyses. The plans, then, are of doubtful constitutional validity and to establish the facts one way or another would, in all likelihood, be most expensive. In our view, it was incumbent upon the boards to come forward with the requisite proof that the plans were not defective. (See, e.g., Connor v. Johnson, 265 F. Supp. 492, 493-494, affd. 386 U. S. 483; Swann v. Adams, 263 F. Supp. 225, 226.) Since this was not done, the courts below correctly determined that the plans were invalid.
It is true that, in Johnson v. City of New York (274 N. Y. 411, 430), our court declared that reapportionment legislation “ should not be declared unconstitutional unless it clearly appears to be so; all doubts should be resolved in favor of the constitutionality of an act. ” However, that pronouncement must be judged in the light of the situation actually presented. The Johnson case involved the issue whether the so-called Hare System of Proportional Voting violated the constitutional provision that each voter was entitled to vote for “ all officers ” standing for election in a particular district. In the first place, the mechanics of the Hare System were fully understood by the court and, in the second place, there was no factual dispute about the operation of the system which could be resolved only by resort to higher mathematics and at great expense. The case turned on the interpretation to be accorded the words “ all officers ”, and the court was simply not convinced by the arguments, of those who attacked the plan, that the phrase — “all officers ” — should be given a broad reading.
In the cases before us, on the other hand, there is no problem of interpretation or construction. If the smaller towns have been substantially deprived of the voting power to which they are entitled, the plans would unquestionably be violative of the one man-one vote principle. Consequently, the only issue calling for resolution is the factual one pertaining to the mathematical structure of the plans. At the very least, there is a significant possibility that the plans are actually defective, and yet the boards adopted them without obtaining the complicated and expensive mathematical analyses that would establish the facts one way or the other.
Under these circumstances, the boards are not entitled to rely on a presumption that their legislative acts are constitu*254tional. Such a presumption; — and that was the sort of presumption reflected in the Johnson case (274 N. Y. 411, supra) — is derived from the principle that it is improper for a court, in passing upon a constitutional question, to lightly disregard the considered judgment of a legislative body which is also charged with a duty to uphold the Constitution. With respect to weighted voting, however, a considered judgment is impossible without computer analyses and, accordingly, if the boards choose to reapportion themselves by the use of weighted voting, there is no alternative but to require them to come forward with such analyses and demonstrate the validity of their reapportionment plans.
We may not overlook the very real danger in these reapportionment cases of the courts being unnecessarily dragged into a “ mathematical quagmire (Baker v. Carr, 369 U. S. 186, 268 [per Frankfurter, J., dissenting]), understood only by experts using* computers. It is claimed that, if these counties were divided up into districts of equal population, the smaller towns would, of necessity, lose their identity because they would be combined with the larger industrial communities in the county, creating districts thereby lacking in mutual sentiments and interests. This result, -however, is not inevitable; we have barely crossed the threshold in exploring the variety of devices which may be employed, consistent with the constitutional mandate of one man-one vote, to assure that the points of view of the smaller towns in the county will be heard on the Board of Supervisors.
The order of the Appellate Division in each case should be modified so as to provide that the respective Board of Supervisors adopt and submit to the court at Special Term a constitutionally valid plan of reapportionment within 60 days from the date of entry of this court ^ order and, as so modified, affirmed, without costs.
. In Washington County, the town populations vary from 11,012 for Kings-bury to 426 for Dresden and, in Saratoga, the populations differ from about 16,000 for the City of Saratoga Springs to about 600 for the Town of Day.
. Although the Appellate Division granted permission to appeal to this court, such leave was unnecessary since the appeals lay as of right on the basis of the constitutional questions involved. (CPLR 5601, subd. [b], par. 1; see Graham v. Board, of Supervisors of Erie County, 18 N Y 2d 672; Michl v. Shanklin, 17 N Y 2d 906; see, also, CPLR 5520, subd. [b].)