This is a petition for a writ of mandamus brought in the Superior Court. G. L. (Ter. Ed.) c. 213, § 1A (see St. 1941, c. 180); c. 249, § 5. The petitioner is a resident and legal voter of the city of Cambridge. The respondents are the duly appointed and qualified board of election commissioners of said city. See St. 1921, c. 239, as finally amended with respect to § 3 thereof by St. 1939, c. 432; Kidder v. Mayor of Cambridge, 304 Mass. 491. The petitioner seeks an order that the respondents conduct the municipal election in Cambridge in 1941 in accordance with the provisions of G. L. (Ter. Ed.) c. 43, as amended, particularly §§ 56-63 thereof, describing the present form of government of said city and known as Plan B, on the ground that the form of government adopted by said city in 1940, known as Plan E, described in G. L. (Ter. Ed.) c. 43, §§ 93-116, added to said chapter by St. 1938, c. 378, § 15, and referring therein to G. L. (Ter. Ed.) c. 54A, inserted in the General Laws by St. 1938, c. 341, § 1, involving proportional representation, is in violation of the Constitution of the Commonwealth and of the Constitution of the United States and therefore an election conducted in accordance with such plan would violate and interfere with the “petitioner’s right to vote and have his vote counted.”
Rightly no contention is made that the petitioner is not a proper party to bring the petition. See Brewster v. Sherman, 195 Mass. 222; Brooks v. Secretary of the Commonwealth, 257 Mass. 91, 94-95, and cases cited; Cape Cod Steamship Co. v. Selectmen of Provincetown, 295 Mass. 65, 69; Fitzgerald v. Selectmen of Braintree, 296 Mass. 362. Compare Police Commissioner of Boston v. Boston, 279 Mass. 577, 585-586. And the petition is properly brought against the respondents, since by statute the duty of conducting a *305municipal election in the city of Cambridge is committed to the board of election commissioners. St. 1921, c. 239, as finally amended by St. 1939, c. 432. G-. L. (Ter. Ed.) c. 50, § 1; c. 54, § 11 (as amended by St. 1938, c. 341, § 6), §§ 31, 40, 48, 53, 65 as amended. See Fitzgerald v. Selectmen of Braintree, 296 Mass. 362.
The case comes before us upon a report of the trial judge at the request of the parties without decision by him. The report is irregular. Such a judge, unlike a justice of this court (see G. L. [Ter. Ed.] c. 211, § 6; Liggett Drug Co. Inc. v. License Commissioners of North Adams, 296 Mass. 41, 44), has power to report a case at law without decision only “after verdict, or after a finding of the facts by the court,” or “where there is agreement as to all the material facts.” G. L. (Ter. Ed.) c. 231, § 111; St. 1939, c. 257. Scaccia v. Boston Elevated Railway, 308 Mass. 310. The report in the present case purports to be made “upon the pleadings.” Obviously there has been no “verdict,” and there has been no “finding of the facts by the court,” though, since all the allegations of fact in the petition are admitted by the answer and there are no allegations of fact in the answer, a finding of facts by the court would have been largely, if not wholly, perfunctory. Compare Attorney General v. Loomis, 225 Mass. 372, 373. And there is not in form an “agreement as to all the material facts,” although there is in substance an agreement upon the facts alleged in the petition. The “agreement as to all the material facts” that can be the basis of a report without decision, however, is an agreement constituting a case stated. Frati v. Jannini, 226 Mass. 430, 431. And in view of the principles particularly applicable to a case stated (see Bartlett v. Tufts, 241 Mass. 96, 99; G. L. [Ter. Ed.] c. 231, § 126; United States Fidelity & Guaranty Co. v. English Construction Co. 303 Mass. 105, 108-109; compare Everett v. Canton, 303 Mass. 166, 167) — however unimportant in the present case — a report “upon the pleadings,” even in the circumstances of- < this case, cannot be treated as a report upon an “agreement as to all the material facts” in accordance with the principle that the “character of a pleading or other paper *306put upon the files of the court must be determined from its essential substance and not from the title, name or description attached to it.” E. S. Parks Shellac Co. v. Jones, 265 Mass. 108, 110. Boston v. Santosuosso, 302 Mass. 169, 175. Nor, in accordance with this principle, can the report be treated as made “after a finding of the facts by the court.” The report, therefore, must be discharged and the case stand for further hearing in the Superior Court. Atlantic Maritime Co. v. Gloucester, 228 Mass. 519, 523, 528. However — as was done in the case last cited — since the case has been fully argued on the merits and the public interest requires a speedy disposition thereof, and since as matter of law upon the facts appearing in the record but one conclusion can be reached — without intending to establish any general rule of practice — we deem it “appropriate that a statement ... [of this conclusion] be made now for the guidance of the Superior Court upon its further hearing.” Page 524. The present case in this aspect is materially different from John Gilbert Jr. Co. v. C. M. Fauci Co., ante, 271, where a judge of the Superior Court attempted to report an interlocutory ruling made by another judge of that court in an equity case. See G. L. (Ter. Ed.) c. 214, § 30. Compare c. 214, § 31; c. 231, § 112.
The present form of government of the city of Cambridge is in accordance with Plan B as described in G. L. (Ter. Ed.) c. 43, §§ 56-63, inclusive, as amended. See Cunningham v. Mayor of Cambridge, 222 Mass. 574; Mayor of Cambridge v. Cambridge, 228 Mass. 249; Ellis v. Civil Service Commission, 229 Mass. 147; Shannon v. Mayor of Cambridge, 231 Mass. 322; School Committee of Cambridge v. Mayor & City Council of Cambridge, 233 Mass. 6; McLaughlin v. Mayor of Cambridge, 253 Mass. 193; Duggan v. Third District Court of Eastern Middlesex, 298 Mass. 274.
These facts appear from the record: On “the fifth day of November, A.D. 1940, there was conducted in the city of Cambridge a referendum upon the question of a proposed change of city charter from the present Plan B form of government to the Plan E form of government as promul*307gated under the provisions of G. L. (Ter. Ed.) c. 43, §§93 to 116 and G. L. (Ter. Ed.) c. 54A.” As “a result of said referendum 25,873 votes were cast in favor of the proposed change and 18,310 votes were cast against said proposal and 7,505 exercised no choice.” As “a result of said vote the respondents, acting in their capacity as the election commissioners of the city of Cambridge, propose to conduct an election in November of 1941 in accordance with the provisions of the Plan E form of charter as contained in G. L. (Ter. Ed.) c. 43, together with the attendant proportional representation method of voting, as contained in G. L. (Ter. Ed.) c. 54A.” There is no contention that the Plan E form of charter was not adopted in accordance with the applicable statutory provisions, or that, if such adoption is not ineffective for the reasons urged by the petitioner, an election in accordance therewith should not be held in November, 1941. See G. L. (Ter. Ed.) c. 43, §§ 2-15, 45; St. 1938, c. 378, §§2-5; G. L. (Ter. Ed.) c. 54A, § 2, as appearing in St. 1938, c. 341, § 1, and as amended by St. 1938, c. 378, § 17.
The Plan E form of government is particularly described in G. L. (Ter. Ed.) c. 43, §§ 93-116 (added to G. L. [Ter. Ed.] c. 43 by St. 1938, c. 378, § 15). See also §§ 31, 36, as amended by said c. 378, §§ 12, 13. Said § 31, as so amended, provides that the “school committee shall consist of the mayor, who shall be the chairman, and six members elected at large. . . . After the adoption of Plan E by a city, the six members other than the mayor shall be elected at large for terms of two years each by proportional representation as hereinafter provided.” Section 96 provides that in a city having more than seven wards at the time of the adoption of the plan the city council shall consist of nine members. Cambridge then had more than seven wards. See St. 1939, c. 507. This section provides also that all of the members of the council “shall, at each regular municipal election, be elected at large for terms of two years each by proportional representation as hereinafter provided.” Section 115 provides that, except “as otherwise provided in sections ninety-three to one hundred and sixteen, inclusive, of this *308chapter, the provisions of sections nine to sixteen, inclusive, of chapter fifty-four A relative to proportional representation shall apply with respect to municipal elections in any city adopting this plan.” Section 115 (see also c. 54A, § 16 [b]) provides also for alternative methods of “counting the voters’ first choices,” but it appears from the record that the respondents propose to conduct the election in November, 1941, in accordance with the provisions of c. 54A, and the parties make no contention based upon the possibility of using an alternative method. It is, therefore, unnecessary for the purposes of this case to consider any of the possible alternative methods.
The method of election and particularly of counting the votes under Plan E is, in outline, as follows: Nominations are to be made by petitions each signed by not less than fifty registered voters; c. 43, § 110. There is to be a separate form of ballot for each body to be elected; c. 43, § 112. Ballots are to be printed in as many lots as there are candidates for election to such body. In the first lot the candidates are to be arranged in alphabetical order, and in each succeeding lot the first name in the preceding lot. is to be placed last. Sets of ballots to be used at the several polling places are to be made up by combining ballots from the different lots; c. 43, § 113; c. 54A, § 5. Each voter is to mark his choices of candidates by a number indicating, respectively, his first and succeeding choices, in the order of his preference, and may mark as many choices as he pleases; c. 43, § 112. There is to be a central counting place to which the ballots are to be delivered and at which they are to be publicly counted, and there is provision for a director of the count; c. 43, § 113; c. 54A, § 6. The ballots are to be placed in envelopes and sealed at the several polling places and the ballot receptacles are to be assembled at the central counting place in an order of polling places to be determined by lot; c. 43, § 113; c. 54A, § 8.
The ballots are to be counted under the supervision of the director of the count; c. 43, § 115; c. 54A, § 9. Said *309§ 9 provides in part as follows: “(b) Each candidate shall be credited with one vote for every valid ballot that is sorted to him as first choice, or otherwise credited to him as hereinafter provided, and no ballot shall ever be credited to more than one candidate at the same time, (c) A ‘ quota ’ is the smallest number of votes which any candidate must receive in order to be assured of election without more candidates being elected than there are offices to be filled. It shall be determined by dividing the total number of valid ballots by one more than the total number of candidates to be elected and adding one to the result, disregarding fractions. Whenever at any stage of the counting the number of ballots credited to a candidate becomes equal to the quota, he shall be declared elected, and no ballots in excess of the quota shall be credited to him except as provided in rule (f) [^providing for a minor contingency] or (1) of this section, (d) The ballots shall be sorted according to the first choices marked on them, the ballots from each polling place being handled together, and those from different polling places being handled in the order of polling places determined under the provisions of section eight, (e) If a candidate is elected while the ballots are being sorted according to first choices, any subsequent ballots which show him as first choice shall each be credited to the second choice marked on it, or, if the second choice also has been elected, to the next choice marked on it for a candidate not yet elected. . . . (g) When all the ballots have been thus sorted and credited to the first available choices marked .on them, every candidate who is credited with fewer ballots than the number of signatures required for his nomination shall be declared defeated, (h) All the ballots of the candidates thus defeated shall be transferred, each to the candidate indicated on it as next choice among the continuing candidates. A ‘continuing candidate’ is a candidate not as yet either elected or defeated. . . . (i) When all the ballots of the candidates thus defeated have been transferred, the one candidate who is then lowest on the poll shall be declared defeated and all his ballots transferred in the same way. (j) Thereupon the candidate who *310is then lowest shall be declared defeated and all his ballots similarly transferred; and in like manner candidates shall be declared defeated one at a time and all their ballots transferred. ... (1) Whenever candidates to the number to be elected have received the quota, any transfer of ballots in progress when the last quota was reached shall be completed, but immediately thereafter all continuing candidates shall be declared defeated and the election shall be at an end. Whenever all ballots of all defeated candidates have been transferred, and it is impossible to defeat another candidate without reducing the continuing candidates below the number still to be elected, all the continuing candidates shall be declared elected and the election shall be at an end.”
It is apparent that the provisions of Plan E for proportional representation involve the following significant features. (We speak, for convenience, of the election of members of the municipal council — nine in number — though the same principles are applicable to the election of members of the school committee other than the mayor —■ six in number. And we assume the number of votes to be cast to be fifty thousand — though the applicable principles are the same irrespective of the number of votes.)
1. Limited voting — that is, though nine members of the municipal council are to be elected, each voter is permitted to have counted only a vote for one such member. The right of the voter, however, is somewhat enlarged by the applicable principles of preferential voting hereinafter referred to.
2. Preferential voting — that is, each voter, though entitled to have only a vote for one candidate counted, is entitled to express as many relative choices or preferences as he sees fit, and, if his vote is not counted for the candidate of his first choice, to have it counted for another candidate for whom he has expressed a choice, in the order of preference shown by him upon his ballot.
The grounds, in substance, upon which the petitioner contends that Plan E is unconstitutional as depriving him *311of Ms "right to vote and have his vote counted” are these: (1) that he is deprived of a right to vote and have his vote counted in the municipal election in the city of Cambridge equal to that of a duly qualified voter in other cities of the Commonwealth; (2) that, even apart from such a comparison, limited voting is unconstitutional as depriving him of his right to vote and have his vote counted for nine members of the council; and (3) that preferential voting, particularly the method of counting votes under Plan E, deprives him of his right to vote and have his vote counted.
The question of the constitutionality of the statutes providing for the Plan E form of government must be considered in accordance with certain long established and frequently stated principles. These principles were stated in Lowell Co-operative Bank v. Co-operative Central Bank, 287 Mass. 338, 343-344, as follows: "All rational presumptions are made in favor of the validity of every legislative enactment. Perkins v. Westwood, 226 Mass. 268, 271, and cases cited. Commonwealth v. Leach, 246 Mass. 464. This court is concerned only with the power of the Legislature to enact laws, the question of their expediency or the policy behind them being matters purely within the legislative discretion. German Alliance Ins. Co. v. Kansas, 233 U. S. 389, 413. It was said by Mr. Justice Hughes in Chicago, Burlington & Quincy Railroad v. McGuire, 219 U. S. 549, at page 569: ‘The scope of judicial inquiry in deciding the question of power is not to be confused with the scope of législative considerations in dealing with the matter of policy. Whether the enactment is wise or unwise, whether it is based on sound economic theory, whether it is the best means to achieve the desired result, whether, in short, the legislative discretion within its prescribed limits should be exercised in a particular manner, are matters for the judgment of the legislature, and the earnest conflict of serious opinion does not suffice to bring them within the range of judicial cognizance.’” See also Slome v. Chief of Police of Fitchburg, 304 Mass. 187, 189-190, and cases cited; Attorney General v. Secretary of the Commonwealth, 306 Mass. 25, 30; Mueller v. Commissioner of Public Health, 307 Mass. 270, *312275. Furthermore, it was said by this court more than one hundred years ago, speaking by Chief Justice Shaw, in Commonwealth v. Blackington, 24 Pick. 352, 355-356: “It is however hardly possible too often to repeat the familiar sentiment, that although this power of deciding on the constitutionality of legal enactments, is one clearly vested in the judicial department, it is to be resorted to and exercised with great caution and deliberation, and it is always to be presumed that a coordinate branch of the government has acted within the limits of its constitutional authority, until the contrary shall clearly and satisfactorily appear. ... In construing this constitution, it must never be forgotten, that it was not intended to contain a detailed system of practical rules, for the regulation of the government or people in after times; but that it was rather intended, after an organization of the government, and distributing the executive, legislative and judicial powers, amongst its several departments, to declare a few broad; general, fundamental principles, for their guidance and general direction.” And it was said by the Court of Appeals of the State of New York in Johnson v. New York, 274 N. Y. 411, 430, in dealing with a statute providing for proportional representation: “We must always be careful in approaching a constitutional question dealing with principles of government, not to be influenced by old and familiar habits, or permit custom to warp our judgment. We must not shudder every time a change is proposed.”
First. Under, the Constitution of the Commonwealth.
The petitioner, in support of his contention that Plan E violates the Constitution of the Commonwealth, relies upon art. 1 and art. 9 of the Declaration of Rights thereof which are as follows: “All men are born free and equal, and have certain natural, essential, and unalienable rights; among which may be reckoned the right of enjoying and defending their lives and liberties; that of acquiring, possessing, and protecting property; in fine, that of seeking and obtaining their safety and happiness” (art. 1); “All elections ought *313to be free; and all the inhabitants of this commonwealth, having such qualifications as they shall establish by their frame of government, have an equal right to elect officers, and to be elected, for public employments” (art. 9).
The petitioner cites in support of his contention generally the case of Attorney General v. Suffolk County Apportionment Commissioners, 224 Mass. 598, relating to the election of representatives to the General Court. In that case it was said at pages 601-602: “The right to vote is a fundamental personal and political right. The equal right of all qualified to elect officers is one of the securities of the Declaration of Bights, arts. 1-9. Unlawful interference with the right to vote, whether on the part of public officers or private persons, is a private wrong for which the law affords a remedy, although it may also have significant political results. Capen v. Foster, 12 Pick. 485. Lamed v. Wheeler, 140 Mass. 390. The right of every voter to participate in the election of representatives to the General Court ‘equally, as nearly as may be/ with all his fellows is secured by the twenty-first amendment to the Constitution. An act of the Legislature limiting or in any way interfering with this right would be invalid. See Kinneen v. Wells, 144 Mass. 497.” The petitioner rightly does not rely in the present case upon said art. 21 of the Amendments, relating to the election of representatives, or art. 22 thereof relating to the election of senators, both of which are superseded by art. 71 of the Amendments. All of these Amendments relate to the election of officers created by the Constitution. Constitution, Part II, c. 1, §§ 2, 3. See Donovan v. Suffolk County Apportionment Commissioners, 225 Mass. 55; McGlue v. County Commissioners, 225 Mass. 59, 64; Brophy v. Suffolk County Apportionment Commissioners, 225 Mass. 124; Merrill v. County Commissioners, 257 Mass. 184; Attorney General v. Secretary of the Commonwealth, 306 Mass. 25; Graham v. Special Commissioners of Suffolk County, 306 Mass. 237. And rightly the petitioner does not rely upon art. 14 of the Amendments providing that in “all elections of civil officers by the people of this commonwealth, whose election is provided for by *314the constitution, the person having the highest number of votes shall be deemed and declared to be elected." A member of the municipal council of the city of Cambridge is not an officer “whose election is provided for by the constitution." Such election is provided for by statute under constitutional authority. See Constitution, Part II, c. 1, § 1, art. 4; art. 2 of the Amendments; Cunningham v. Mayor of Cambridge, 222 Mass. 574, 576-577; Young v. City Council of Waltham, 243 Mass. 288; Sullivan v. Lawson, 267 Mass. 438, 439-440; Wood v. Election Commissioners of Cambridge, 269 Mass. 67, 69; Goodale v. County Commissioners, 277 Mass. 144, 149.
A. Plan E, as applied to the city of Cambridge, is not unconstitutional on the ground that thereunder an inhabitant of the city who is a duly qualified voter therein does not have a right to vote for a member of the municipal council and to have his vote counted equal to the rights respectively of inhabitants of other cities in the Commonwealth, who are duly qualified voters, to vote for municipal officers of their cities.
The case of Graham v. Roberts, 200 Mass. 152, and the reasoning of the court therein, are substantially decisive on this point. It was there said, pages 153-154, after quoting from art. 9 of the Declaration of Rights: “The petitioners seem to construe this article not only as applying generally to elections of municipal officers, but as meaning that the inhabitants of different cities in different parts of the Commonwealth shall all have an equal right to elect the same number and kind of municipal officers, and to be elected to the same offices, as the inhabitants of any other city in the Commonwealth. This is not the true construction of the article. While all inhabitants having the prescribed qualifications have absolutely equal rights in reference to the election of the officers of the State government, the Constitution recognizes the fact that a proper application of the principle of local self-government may call for the election of different officers, and for their election in different ways, in different cities of the Commonwealth. Article 2 of the Articles of Amendment is in part as follows: 'The General Court shall have full power and authority to *315erect and constitute municipal or city governments, in any corporate town or towns in this Commonwealth, and to grant to the inhabitants thereof such powers, privileges, and immunities, not repugnant to the Constitution, as the General Court shall deem necessary or expedient for the regulation and government thereof, . . . Provided, that no such government shall be erected or constituted in any town not containing twelve thousand inhabitants, nor -unless it be with the consent, and on the application of a majority of the inhabitants of such town, present and voting thereon/ etc. This recognizes the right and duty of the General Court to determine what powers, privileges, and immunities should be granted to any city for the regulation and government of it, and secures to the inhabitants the right to give or withhold their consent to the establishment of the new municipal government. This makes it plain that different cities may be established with different kinds of government, different officers, and different modes of electing them.” See also Opinion of the Justices, 138 Mass. 601, Larcom v. Olin, 160 Mass. 102, and Cole v. Tucker, 164 Mass. 486, cited in the Graham case.
In Cole v. Tucker, 164 Mass. 486, where the constitutionality of a statute providing for the use of official ballots in the election of city officers was involved, it was said in holding that the statute was not unconstitutional because inapplicable to towns: “There is nothing in the Constitution which requires that the laws regulating elections for city and town officers shall be uniform throughout the Commonwealth ... In matters which concern the form of holding elections for city and town officers, in the absence of anything in the Constitution prescribing the manner in which such elections shall be held, we are of opinion that the provisions need not be the same for all the cities and towns of the Commonwealth.” Pages 489-490. The Graham case related primarily to the manner of election, particularly the form of ballot to be used. But it was there said that there “is no constitutional restriction upon the power of the General Court to fix the qualifications of city officers.” Page 156. Article 2 of the Amendments restricts the powers of *316the General Court in creating cities out of towns. See Attorney General v. Methuen, 236 Mass. 564, 570-578. This restriction, however, has “no relevancy to the modifications from time to time of the form of city charter when once the transmutation from town to city has been made.” Cunningham v. Mayor of Cambridge, 222 Mass. 574, 576. In that case, relating to a Plan B charter provided for under general laws upon adoption by the city, it was said that it “is not beyond the power vested by the Constitution in the General Court, to establish several models for the government of cities, and to provide that one or another of these may become operative in any city (with the exception of Boston), already chartered, by the voters at an election held in due form, without further legislative intervention.” Page 577. See also Sullivan v. Lawson, 267 Mass. 438, where a statute- creating a board of police to be appointed by the Governor with the advice and consent of the Council was considered. It was said in that case at pages 439-440: “The power to grant a charter as a city rests wholly in the Legislature under our constitution. Art. 2, Amendments to the Constitution, Larcom v. Olin, 160 Mass. 102. The Legislature may grant such powers as it sees fit and may take away or modify powers once granted when in its opinion the public welfare so requires.” And years before the decision of this case the statute providing for a board of police for the city of Boston appointed in like manner was sustained as constitutional under said art. 2 of the Amendments, and the Constitution, Part II, c. 1, § 1, art. 4. Commonwealth v. Plaisted, 148 Mass. 375. In. that case the court said at pages 386-387: “The several towns and cities are agencies of government largely under the control of the Legislature. The powers and duties of all the towns and cities, except so far as they are specifically provided for in the Constitution, are created and defined by the Legislature, and we have no doubt that it has the right in its" discretion to change the powers and duties created by itself, and to vest such powers and duties in officers appointed by the Governor, if in its judgment the public good requires this, instead of leaving such officers to be *317elected by the people or appointed by the municipal authorities.” See also Broadhurst v. Fall River, 278 Mass. 167, 170-171. In the case of Goodale v. County Commissioners, 277 Mass. 144, 149, it was said to be “well settled that cities established under art. 2 of the Amendments to the Constitution may have different kinds of government, different officers and different modes of electing them.” See also Opinion of the Justices, 138 Mass. 601, 603; 303 Mass. 631, 638. It is not to be thought that these decisions and statements were made without recognition of the provisions of art. 1 and art. 9 of the Declaration of Rights. Indeed, the more specific of these articles, art. 9, was quoted in Graham v. Roberts, 200 Mass. 152, 153-154, and therein construed with a statement that the Constitution “recognizes the fact that a proper application of the principle of local self-government may call for the election of different officers, and for their election in different ways, in different cities of the Commonwealth.” The article was also referred to in Cole v. Tucker, 164 Mass. 486, 487-488.
General Laws (Ter. Ed.) c. 43, first enacted as St. 1915, c. 267, authorizing different forms of city charters, provides not only for different officers in different cities but also for different ways of electing them. Plan A, §§ 46-55, and Plan D, §§ 79-92, each provides for a mayor and a city council elected at large; Plan B, §§ 56-63, for a mayor, and a city council elected in part by districts and in part at large; and Plan C, §§ 64-78, for a council elected at large. And there are charters whereunder all the members of the city council are elected by districts. We are not aware that the constitutional validity of these differences in the officers to be elected and in the manner of electing them has ever been challenged on the ground of lack of equality among the duly qualified voters of the several cities with respect to their rights to vote for municipal officers and to have their votes counted. Indeed, the petitioner assumes the validity of Plan B, although under this plan, unlike other plans, the duly qualified voters of a city are not all permitted thereby to vote for all the members of the governing body.
*318No question is raised in the present case as to the power of the General Court to prescribe different qualifications of voters for voting for municipal officers in the city of Cambridge from those prescribed for voters for voting for such officers in other cities of the Commonwealth. Plan E does not deal with the subject of the qualifications of voters thereunder. But the petitioner contends that the power of the General Court to provide for the election of different officers in that city from the officers to be elected in other cities, and to prescribe different qualifications for such officers and different ways of electing them, does not extend to restricting the voters of said city to voting and having their votes counted for a lesser number of candidates relative to the number to be chosen than is permitted in other cities — that is, that such a restriction denies to a duly qualified voter in said city the right to vote and have his vote counted conferred by art. 1 of the Declaration of Rights, and particularly his “equal right to elect officers” guaranteed by art. 9 thereof. It is unnecessary to decide whether either of these articles has any application to the participation of a duly qualified voter in a city in the election of persons to statutory municipal offices in said city. In Cole v. Tucker, 164 Mass. 486, 487-488, however, it was assumed that the principles stated in said art. 9 “apply to elections for city and town officers.” See also Opinion of the Justices, 160 Mass. 586, 592. In any event this article is to be read in the light of the principle already stated “that different cities may be established with different kinds of government, different officers, and different modes of electing them.” Graham v. Roberts, 200 Mass. 152, 154. Since there is no constitutional objection, on the ground of denial to an inhabitant of the Commonwealth, duly qualified to vote, of “an equal right to elect officers,” to differences among the several cities of the Commonwealth in the number, power and qualification of municipal officers, in the selection of such officers by election or appointment (see Commonwealth v. Plaisted, 148 Mass. 375, 386-387) or by election at large or by districts, or in the manner in which candidates are nominated *319(Graham v. Roberts, 200 Mass. 152, 155-156, where the statute provided for preliminary election for nominations), all of which matters affect in some degree the right to elect officers, there is no sound ground for contending that a difference among the several cities resulting from the adoption by one of them of a form of government providing for proportional representation involving limited and preferential voting is constitutionally objectionable on the ground of inequality in the right of duly qualified voters to elect officers among the several cities of the Commonwealth. H Plan E providing for such proportional representation is open to constitutional objection, it must be by reason of such objection as applied to the inhabitants of Cambridge who are duly qualified voters therein irrespective of differences between this form of government and the forms of government of other cities of the Commonwealth.
B. Plan E, as applied to the city of Cambridge, is not unconstitutional by reason of the provision therein for limited voting, considered apart from the provision for preferential voting hereinafter dealt with.
The substance of this provision for limited voting is that, at an election at large of members of the municipal council, each duly qualified voter is permitted to cast a vote for only one candidate for election to such council, though there are nine positions therein to be filled, and that an aggregate number of votes for such a candidate equal to the prescribed “quota,” which is slightly more than one tenth of the total number of votes cast, will insure the election of such a candidate ■— though a lesser number of votes may elect a candidate if there are not nine candidates receiving more votes than he received. Each voter, therefore, can participate effectively in the election of only one member of the municipal council. Under the provision for limited voting a voter has a more restricted right to vote but a greater likelihood that his vote will be effective in the election of a candidate than if he were permitted to vote for a number of candidates equal to the number of positions to be filled and the result were determined in *320accordance with the ordinary principles of majority or plurality voting.
We assume in favor of the petitioner that under our form of government as a whole and particularly those provisions of the Constitution that guarantee “equal protection of equal laws without discrimination or favor based upon unreasonable distinctions ” (see Brest v. Commissioner of Insurance, 270 Mass. 7, 14; Opinion of the Justices, 303 Mass. 631, 643; Constitution, Part II, c. 1; § 1, art. 4; Declaration of Rights, arts. 1, 6, 7), whatever may be the scope of art. 9 guaranteeing to all inhabitants of the Commonwealth “an equal right to elect officers” (see Opinion of the Justices, 160 Mass. 586, 592; Cole v. Tucker, 164 Mass. 486, 487-488; Graham v. Roberts, 200 Mass. 152, 154), the General Court, notwithstanding its broad power to provide different forms of government for different cities already discussed, cannot deny to a duly qualified voter in a city a right to vote for municipal officers thereof equal to that of other such voters' in said city, or at least in the same subdivision thereof — a distinction not here material.
The provision for limited voting, however, does not deny to any such duly qualified voter in the city of Cambridge a right to vote equal to that of any other such qualified voter. All the ballots are the same except for differences in the order in which the names of the candidates appear thereon — a difference that tends to eliminate any inequality that might result from a candidate’s having a particularly favorable position on the ballot. Each duly qualified voter has the same right to mark and cast his ballot as every other duly qualified voter. Each duly qualified voter has the same right as any other such voter to one and only one effective vote for a candidate. Doubtless the “right to elect” includes not only the right to deposit a ballot but also the right to have it counted in accordance with valid applicable statutory regulations. See O’Connell v. Mathews, 177 Mass. 518, 521; O’Brien v. Election Commissioners of Boston, 257 Mass. 332, 338. These regulations are the same for all duly qualified voters voting in a municipal election under Plan E. There is no inequality in this respect among *321the duly qualified voters in Cambridge unless by reason of the method of counting hereinafter considered in connection with preferential voting. Apart, at least, from the provision for such voting, all duly qualified voters in Cambridge have “an equal right to elect” members of the municipal council of the city “without discrimination or favor based upon unreasonable distinctions.” The provisions for limited voting treat all electors alike.
The objection of the petitioner to limited voting, however, goes beyond the objection to inequality among duly qualified voters of the city of Cambridge, already considered, to an objection to a denial of a right in such a voter to vote for as many candidates for the municipal council as there are positions therein to be filled. We are dealing here not with offices created by the Constitution but with offices created by statute under broad constitutional authority in the General Court to provide “for the election of different officers, and for their election in different ways, in different cities of the Commonwealth” as “a proper application of the principle of local self-government may call for.” See Graham v. Roberts, 200 Mass. 152, 154. A voter of a particular city, therefore, has no constitutional right to elect officers of a particular type. Moreover, the General Court has power to restrict the privilege of local self-government. It was said in Commonwealth v. Plaisted, 148 Mass. 375, 384-385, that “we cannot declare an act of the Legislature invalid because it abridges the exercise of the privilege of local self-government in a particular in regard to which such privilege is not guaranteed by any provision of the Constitution. While the Constitution recognizes our system of town governments as an inherent part of our general system of government, so that the Legislature could not abolish the town system without coming in conflict with some parts of its provisions, yet in most respects it leaves the power and duty of providing laws for the government of the towns and cities in the discretion of the Legislature.” Consequently the General Court has broad power to provide that officers of a city shall be appointed by the Governor rather than elected by *322the inhabitants of the city — to determine what officers of the city shall be so elected. Commonwealth v. Plaisted, 148 Mass. 375, 386-387. Broadhurst v. Fall River, 278 Mass. 167, 170-171.
• The broad power of the General Court to prescribe the form of government of a city, including the broad power • to determine what officers thereof shall be elected by its inhabitants, imports broad power in the General Court to prescribe the method of electing such officers. Where, at least, a statute does not deal with the qualifications of voters or deny to all such voters within the city an equal right to elect the officers thereof, the test of the constitutionality of the statute is whether it is reasonable within the authority conferred upon the General Court by the Constitution, Part II, c. 1, § 1, art. 4, to make reasonable laws, in the absence of any more specific provision of the Constitution dealing with the subject.
All doubts must be resolved in favor of the validity of the statute providing for Plan E. The provision therein for limited voting cannot be struck down as unconstitutional because unreasonable, unless it cannot be supported on any rational ground. We cannot say that the provision is lacking in such support. See Slome v. Chief of Police of Fitchburg, 304 Mass. 187, 189. The purpose of authorizing the election of officers of a city by the duly qualified voters therein is to permit such voters to be represented in the management of the affairs of the city. It cannot be said to be unreasonable — however wise or expedient — to permit minority groups of such voters selected in a reasonable manner to be represented in such management. This result, under other forms of city government, is effected, in some degree, by election of the city council by districts where one or more members of the council are elected for each of several territorial subdivisions of the city — a method of election that has long gone unquestioned in this Commonwealth as within the authority of the General Court, under art. 2 of the Amendments, to grant to the inhabitants of a city “such powers, privileges, and immunities, not repugnant to the constitution as the *323general court shall deem necessary or expedient for the regulation and government thereof.”- An analogy between such election by districts and election on the basis of proportional representation involving limited voting in a manner similar to that provided for by Plan E was recognized, though not without dissent, in Johnson v. New York, 274 N. Y. 411, 424, 432-433. Moreover, the principle of limited voting for the obvious purpose of permitting minority representation — that is, limitation of voters to voting for fewer candidates than the number of officers to be elected — has been embodied from time to time in a period of nearly fifty years in various statutes of the Commonwealth relating to the form of government of certain cities which, so far as appears in reports of this court, have not been questioned as to their constitutionality. See, for example: St. 1892, c. 355, § 10, repealed by St. 1896, c. 366; St. 1893, c. 473, § 2, repealed by St. 1899, c. 355; St. 1895, c. 148, § 9; St. 1896, c. 438, § 9, amended by Spec. St. 1917, c. 195; St. 1897, c. 239, § 10. Compare Johnson v. New York, 274 N. Y. 411, 423; Commonwealth v. Reeder, 171 Penn. St. 505, 517. See Attorney General v. Pelletier, 240 Mass. 264, 299. Nothing said in Opinion of the Justices, 229 Mass. 601, relied on by the petitioner, is adverse to the validity of the principle of limited voting as applied to cities. That opinion dealt with a proposed statute relating to a town, and referred to the “vital feature of the right of each qualified citizen to vote upon every question coming before the town meeting.” Page 608. But it was pointed out that the “fundamental and real distinction between the town and the city organization is that in the former all the qualified inhabitants meet together to deliberate and vote as individuals, each in his own right, while in the latter all municipal functions are performed by deputies.” Page 609. See art. 2 of the Amendments. The statute now in question relates merely to the manner in which such “deputies” are to be elected. In other jurisdictions statutes providing for limited voting in municipal elections have been held constitutional. Johnson v. New York, 274 N. Y. 411. Reutener v. Cleveland, 107 *324Ohio St. 117. See also Commonwealth v. Reeder, 171 Penn. St. 505. Where in some jurisdictions a provision for proportional representation involving limited voting has been regarded as unconstitutional, the conclusion to this effect has been based upon specific constitutional limitations. See People v. Elkus, 59 Cal. App. 396, 398; Wattles v. Upjohn, 211 Mich. 514, 530; Opinion to the Governor, 62 R I. 316, 321-322.
It cannot rightly be said that the method by which the minority groups to be represented in the municipal council under Plan E are selected is necessarily unreasonable. Such representation is limited in Cambridge to the nine largest groups of duly qualified voters as disclosed by the ballots —• the same number of groups as of members of the council to be elected. The selection of the groups to be represented is not based upon unreasonable distinctions. The groups are self-selected. Each duly qualified voter expresses by his ballot his choice of the group with which he wishes to be associated for the purpose of being represented in the municipal council. All such voters have an equal right to make such a choice. Such choice by a voter resembles somewhat the choice of a voter of the group with which he wishes to be associated in nominating candidates at the primary by enrolling with such group or party. See G. L. (Ter. Ed.) c. 53, §§ 37-38, as amended. It also resembles somewhat the choice by a voter of a group with which he wishes to be associated in obtaining the printing of the name of a candidate on a ballot by the use of nomination papers. See G. L. (Ter. Ed.) c. 53, § 6, as amended by St. 1939, c. 191. These principles are incidents of the Australian ballot system, the constitutionality of which has been affirmed. Miner v. Olin, 159 Mass. 487. Cole v. Tucker, 164 Mass. 486. Graham v. Roberts, 200 Mass. 152, 156. We conclude that Plan E cannot be struck down by reason of the inclusion therein of a provision for limited voting on the ground that such a provision is in itself unreasonable.
Nor does the principle of limited voting embodied in Plan E conflict with any specific provision of the Consti*325tution. No specific provision requires that result unless it be art. 9 of the Declaration of Rights upon which the petitioner particularly relies. As already indicated, we assume, without deciding, that this constitutional provision applies to municipal elections to the extent of guaranteeing “an equal right to elect officers” to all qualified voters within the city of Cambridge voting as a single election district as under Plan E. It is obvious, however, that the primary, if not the exclusive, purpose of this provision is to guarantee equality among all such voters. Such equality is not interfered with by a provision for limited voting.
But the petitioner urges that this constitutional provision should be interpreted as guaranteeing to each such voter the right to vote “for all officers” to be elected in the city, at least when the city is treated as a single election district. The language, however, requires no such interpretation. It is unlike the language in the Constitution of Minnesota, considered in Brown v. Smallwood, 130 Minn. 492, 497, providing that each qualified voter “shall be entitled to vote at such election . . . for all officers that now are or hereafter may be, elective by the people,” where the court held that this provision precluded preferential voting for a State officer. And in Opinion to the Governor, 62 R. I. 316, a majority of the judges expressed the opinion that a constitutional provision providing that qualified voters “shall have a right to vote in the election of all civil officers” precluded proportional representation involving limited voting and preferential voting, although another judge expressed the opinion that the words “a right to vote in the election of all civil officers” were not the equivalent of the words “a right to vote for all civil officers,” and that proportional representation would be constitutional. In Johnson v. New York, 274 N. Y. 411, however, the court held that a provision in the charter of the city of New York providing for the election of councilmen on the basis of proportional representation involving limited voting and preferential voting did not conflict with a constitutional provision that an elector “shall be entitled to vote at such election ... for all officers that now are or hereafter may *326be elective by the people.” Pages 418-419, 424. The court did not rely upon a so called home rule amendment. Page 431.
The constitutional provisions considered in other cases in substance provide that all qualified voters shall be entitled to vote “in all elections,” not in terms “for all officers” — language that also is more specific than the language of said art. 9. In Wattles v. Upjohn, 211 Mich. 514, 532, the court said that a guaranty in the Constitution of Michigan of a right to vote meant in substance the same as the guaranty of a right to vote “at such elections . . . for all officers” elective by the people in the Constitution of Minnesota, as construed in the case of Brown v. Smallwood, and held that proportional representation involving limited and preferential voting was unconstitutional under this provision of the Michigan Constitution. In People v. Elkus, 59 Cal. App. 396, the court reached a like conclusion, saying that the “right to vote ‘at all elections’ includes the right to vote for a candidate for every office to be filled.” Pages 398-399. And in State v. Constantine, 42 Ohio St. 437, it was held that a constitutional provision that an elector “shall be entitled to vote at all elections” precluded limited voting on the ground that under such a provision “each elector is entitled to vote for each officer, whose election is submitted to the electors.” Page 442. But in the later case of Reutener v. Cleveland, 107 Ohio St. 117, the court said that the Constantine case “extended the plain language of the constitution far beyond the word-meaning” of this constitutional provision (page 138), and held that a charter of a city providing for proportional representation including limited voting and preferential voting was constitutional. In so doing, however, the court relied upon a so called home rule amendment to the Constitution. And in Commonwealth v. Reeder, 171 Penn. St. 505, the court held that a constitutional provision that a qualified voter “shall be entitled to vote at all elections” did not preclude limited voting. The court refused to enlarge the scope of the words of the Constitution by adding “also for every candidate of a group of candidates for the same office” in accordance *327with a contention made before it. Pages 514, 516. Whatever might be our opinion under different constitutional provisions, we think that the guaranty of “an equal right to elect officers”'by art. 9 of the Declaration of Rights is not to be construed as granting a right to vote “for all officers” to be elected in a city, and that it goes no farther than to guarantee equality among all duly qualified voters of the “right to elect officers.”
The absence from our Constitution of a so called home rule amendment, such as was relied on in Reutener v. Cleveland, 107 Ohio St. 117 (compare Johnson v. New York, 274 N. Y. 411), in our opinion is not particularly significant with respect to the matter of limited voting in view of the broad power conferred upon the General Court by art. 2 of the Amendments. Neither by art. 9 of the Declaration of Rights nor by any other provision of the Constitution is Plan E rendered unconstitutional by reason of the incorporation therein of the principle of limited voting.
C. Plan E as applied to the city of Cambridge is not unconstitutional by reason of the provision therein for preferential voting.
The essential feature of preferential voting is that a voter, though permitted to cast only one effective vote for an officer, is permitted to express not only a first choice for one candidate but also one or more other choices, in the order of his preference, for other candidates for the same office. Under Plan E a voter is permitted to express as many such choices as he sees fit indicating his relative preferences among the candidates, and the manner in which his vote is to be counted with respect to the several choices is determined in accordance with the statutes already set forth in this opinion.
The cases already cited in which proportional representation involving both limited voting and preferential voting has been held unconstitutional under the governing State Constitution have been decided upon the ground that the principle of limited voting involved therein was in conflict with such Constitution — contrary to the conclusion reached by us in the present case under the Constitution of this *328Commonwealth. This was true of People v. Elkus, 59 Cal. App. 396, and of Wattles v. Upjohn, 211 Mich. 514 — although in the latter case there are statements adverse to the principle of preferential voting as embodied in a statute somewhat similar to the statute now under consideration. And the conclusion stated in Opinion to the Governor, 62 R. I. 316, was based on a like ground. In Brown v. Smallwood, 130 Minn. 492, the principle of limited voting was not involved, but the principle of preferential voting was held to be in conflict with a constitutional provision that every qualified voter “shall be entitled” to “vote” “for all officers” elective by the people, on the ground that the “word ‘vote’ meant a choice for a candidate by one constitutionally qualified to exercise a choice” and “nothing else,” and that the “preferential system directly diminishes the right of an elector to give an effective vote for the candidate of his choice.” Page 498. But, on the other hand, in Orpen v. Watson, 87 N. J. L. 69, affirmed 88 N. J. L. 379, preferential voting, where the voting was not limited, was held not to be in conflict with a constitution containing a like provision on the ground that “as it is only the choice votes which go to make a majority that are counted as effective votes, and as no voter can vote for the same person but once in expressing his different choices, he can in no way cast more than one vote which can be counted for each office to be filled, because none of his other choice votes enter into or influence the result.” Page 73. It may well be that in Reutener v. Cleveland, 107 Ohio St. 117, where both limited voting and preferential voting were involved, the principle of preferential voting was sustained by reason of a so called home rule amendment, but in Johnson v. New York, 274 N. Y. 411, the court, without relying upon such an amendment, held constitutional a provision for preferential voting, combined with limited voting, resembling that here in question, in spite of a constitutional provision that a qualified voter shall be “entitled to vote . . . for all officers” elective by the people. See pages 418-419, 424, 429-430. The case of Commonwealth v. Reeder, 171 Penn. St. 505, did not involve the principle of *329preferential voting. These cases as a whole furnish no persuasive authority that the principle of preferential voting is in conflict with any provisions of the Constitution of this Commonwealth, including art. 9 of the Declaration of Rights.
The provision embodied in Plan E for preferential voting in city elections cannot be declared unconstitutional on the ground that it is in conflict with ordinary principles of plurality voting. Plurality voting is not required in such elections by any express provision of the Constitution of the Commonwealth. The specific provision in the Constitution requiring such voting applies only to the election of “civil officers . . . whose election is provided for by the constitution.” Art. 14 of the Amendments, adopted to do away with majority voting for such officers. But undoubtedly plurality voting for municipal officers has largely prevailed in city elections and is permissible, though not required by art. 2 of the Amendments. However, city elections under Plan E are in accordance with the principle of plurality voting, subject to the provision for limited voting, if the choices of the voters, other than their first choices, as well as their first choices, are considered in the manner provided in the plan. The nine candidates receiving the largest numbers of effective votes counted in accordance with the plan are elected, as would be true in ordinary plurality voting. Moreover, each candidate receiving a number of votes representing first choices equal to the prescribed “quota” would inevitably be elected since no more than nine candidates could each receive more than that number of effective votes, and first choices could in no event be disregarded so as to produce a different result. It is only with respect to candidates that receive votes representing first choices less in number than the “quota” that the result could possibly be affected by votes representing second or successive choices. The question of the constitutionality of preferential voting as embodied in Plan E arises particularly by reason of this possibility and by reason of the manner in which choices of voters other than their first choices are given effect.
*330There is no provision in the Constitution of this Commonwealth granting to each qualified voter the right to vote “for all officers” elective by the people that would warrant the implication drawn from such a constitutional provision in Brown v. Smallwood, 130 Minn. 492, that preferential voting diminishes the right of a voter “to give an effective vote for the candidate of his choice,” even if we thought this implication required by such a constitutional provision. But in Orpen v. Watson, 87 N. J. L. 69, affirmed 88 N. J. L. 379, in sustaining the validity of preferential voting, no such implication was drawn from a like constitutional provision, and it was said that, though a voter could express different choices, “he can in no way cast more than one vote which can be counted for each office to be filled.” Page 73. We think that under Plan E no voter can cast more than one effective vote, even though he has the privilege of expressing preferences as to the candidate for whom his 'vote shall be effective when it is demonstrated that it will not be effective for a candidate for whom he has expressed a greater preference, and that the provision for preferential voting violates no provision of the Constitution of this Commonwealth on the ground that it permits a voter to cast more than one vote for the office to be filled. Indeed, we do not intimate that the provision for preferential voting •would violate any provision of the Constitution even if it 'did permit a voter to cast more than one such vote. Moreover, while in one aspect the existence of the privilege of expressing preferences in all duly qualified voters in the city of Cambridge may diminish the right of a voter to secure the election of a particular candidate (see Brown v Smallwood, 130 Minn. 492), as compared with such right under principles of plurality voting, in another aspect the existence of the privilege may reasonably be thought to enlarge the right of such voter to secure representation in the municipal council. And we find nothing in the Constitution that on this ground precludes preferential voting in view of the broad scope of art. 2 of the Amendments with respect to providing for different ways of electing municipal officers. See Graham v. Roberts, 200 Mass. 152, 154.
*331In view of the broad scope of this Amendment, the test of the constitutional validity of the provision for preferential voting embodied in Plan E, as applied to the election of members of the municipal council in the city of Cambridge, is its reasonableness and its effect upon the equal right of all duly qualified voters of said city — where, as here, the city is treated as a single election district — to elect officers of such city. We perceive no constitutional objection to the provision on the ground that it is unreasonable, if equality among duly qualified voters to elect members of the municipal council is not impaired thereby. And even with respect to such equality, if the governing principle is reasonable and the same for all voters, the provision for preferential voting cannot be struck down on the ground that in some of its applications to particular situations exact mathematical equality may not result. Theoretical perfection is not essential to constitutional validity. Compare Attorney General v. Secretary of the Commonwealth, 306 Mass. 25, 31-35; Graham v. Special Commissioners of Suffolk County, 306 Mass. 237, 242-243.
We cannot rightly say that it is so unreasonable as to be unconstitutional and beyond the power of the - General Court, in the exercise of its legislative judgment and discretion, to provide for the representation of minority groups in the municipal council or to enlarge the possibility of a voter’s being represented therein by giving him an opportunity to express more than one preference among candidates for election thereto, even though his right to representation therein by the candidate of his first choice is somewhat diminished, so long as all duly qualified voters are treated alike. In this respect the provision for preferential .voting and that for limited voting stand on the same footing.
Obviously, the provision for preferential voting does not impair the equal right of all duly qualified voters in the city to mark and to cast their ballots. In these respects all such voters are treated alike. And all of them are treated alike in that each voter is entitled to cast an effective vote for only one candidate for election to the *332municipal council. If any inequality results from the provision for preferential voting, it must result from the manner in which the votes of the several voters are counted for the several candidates and the effect of counting the votes in this manner upon the result of the election. But even in respect to the manner in which the votes are counted, the same governing principle applies to all duly qualified voters.
The expression of preferences made by the voters upon the ballots shows the relative order in which they wish their choices to be given effect. Obviously, it is reasonable to give effect where possible to the first choices of the voters. This, in substance, is what is done in plurality voting where only one choice can be expressed. In preferential voting no voter whose vote is counted for the candidate of his first choice is for that reason denied equality in the election. The vote is counted in accordance with the will of the- voter. Moreover, as already pointed out, all candidates receiving a number of such votes equal to the “quota" are elected irrespective of other choices expressed by voters. So far as this result is concerned, the provision for preferential voting is without effect. This is true even though, according to the prescribed manner of counting, some- of the votes actually counted for such candidates may represent second or successive:, choices. (G. L. [Ter. Eel.3. c. 54A, § 9 [e30
All other results, however, may be affected by the provision for preferential voting. They, may be affected by the manner of transferring to other candidates votes representing greater preferences for candidates elected or eliminated from the counting as defeated. § 9 (e), (g), (h), (i), (j), (1). These results may be affected, to some extent, by the order in which the ballots are counted, and this order depends in some degree on the element of chance. See G. L. (Ter. Ed.) c. 54A, §§ 8, 9 (d). Without attempting to analyze in detail all possible situations resulting from the multitude of possible combinations of votes representing different degrees of preference expressed by the voters, we consider the possible situations generally.
*333There is no such lack of reasonableness or of equality in the method of eliminating candidates from the counting as defeated — with the result that all undefeated candidates are elected — as to invalidate the method of counting. § 9 (g), (1). Each candidate who is eliminated upon the first count because "credited with fewer ballots than the number of signatures required for his nomination” — that is, fifty — based on "first available choices” — which may include choices other than "first choices” —would be eliminated if only actual "first choices” were counted. And the elimination from the counting of candidates receiving so few actual "first choices” could not be pronounced unreasonable. Later eliminations are of the "candidate who is then lowest.” § 9 (i), (j). It is apparent that the result as to which candidate is so eliminated may depend to some extent upon the order in which the ballots are counted. But a candidate cannot be so eliminated if he receives a number of votes representing "first choices” equal to the "quota” or even if he receives votes representing “first available choices,” as of the time of the counting, equal to that number. And, moreover, a voter whose preference was expressed for a candidate who is eliminated in this manner is not deprived, by the elimination of such candidate, of participation in the' election, though his vote as counted will represent a lesser preference. The elimination* of a candidate follows from'the application of uniform principles of counting to complicated situations arising out of an attempt to give to voters greater privileges of choice than they have under plurality voting. The statute contains careful provisions designed to exclude favoritism in counting or advantage to any voter on an arbitrary ground. See G. L. (Ter. Ed.) c. 54A, §§ 8, 9 (d). The relative weight to be given, in accordance with a uniform principle, to successive choices of a voter is a matter for the reasonable exercise of legislative judgment and discretion. The method of counting must be practicable. And a method of counting is not necessarily vitiated by the possibility of an element of chance in its application to some situations that may arise if, in general, equality among all qualified voters is *334maintained. See Johnston v. State, 128 Ind. 16. See also Grubb v. Turner, 259 Ill. 436, 446; Clarion Borough’s Election, 189 Penn. St. 79. Compare G. L. (Ter. Ed.) c. 43, § 44D; Walsh v. Boyle, 179 App. Div. (N. Y.) 582, 586. We think that the element of chance in the determination of the candidates that from time to time are to be eliminated under Plan E is not so great as necessarily to vitiate the method of counting embodied therein. See G. L. (Ter. Ed.) c. 43, § 115; c. 54A, § 9.
There is also an element of chance involved in the method of counting votes representing first choices. I.t cannot rightly be said that, where there is an excess of votes representing first choices for a candidate above the “quota,” it is unreasonable or productive of inequality to . count such excess for candidates who represent second or successive choices of the voters in accordance' with a uniform principle. For example, if there are votes representing first choices of twice the number of the “quota,” it is not necessarily unreasonable or productive of inequality to allot two members of the municipal council to the voters casting such votes, in accordance with the principle of permitting representation in such council to each group of voters of a number at least equal to the “quota.” But an element of chance arises in determining which of the votes representing first choices shall be counted for the candidates of the voters’ first choices and which for candidates of their second or successive choices. However, a voter, whose vote has been counted as an effective vote for the candidate of his first choice who is elected, has exercised his full right to elect, and has no just grievance unless by reason of comparison with a like voter whose vote is not so counted but is counted for the candidate of his second or other successive choice. In this situation and like situations there is, doubtless, a serious question as to inequality among voters. However, for reasons similar to those stated with respect to the ehmination as defeated of candidates having the lowest numbers of votes, we conclude that this feature of the method of counting does not vitiate it. (Like principles govern where there would be an excess of “first *335available choices” properly counted.) There were somewhat similar provisions with respect to counting votes, involving elements of chance, in the statutes providing for proportional representation involving preferential voting, held valid in Johnson v. New York, 274 N. Y. 411, and Beutener v. Cleveland, 107 Ohio St. 117.
Second. Under the Constitution of the United States.
The petitioner contends that Plan E, in its provision for proportional representation, is in violation of art. 1, § 10, of the Constitution of the United States, in that it impairs the obligation of a contract, and in violation of the Fourteenth Amendment to that Constitution in that it “abridges the privileges or immunities of the petitioner . . . the property rights of the petitioner are lost without due process of the law, and . . . the petitioner is not afforded the equal protection of the laws of the Commonwealth,” on the ground that, as the petitioner contends, such provision “interferes with the petitioner’s right to vote and his right to have his vote counted.” The petitioner bases this contention in its several aspects upon the existence of a right in him, under the Constitution of the Commonwealth, particularly art. 9 of the Declaration of Rights thereof, to vote and to have his vote counted for all officers of the city of Cambridge that are elective — a right in the nature of a property right arising out of the Constitution of the Commonwealth considered as a contract — and upon his argument in support of his contention that he has such a right. What has been said here with respect to his contention under the Constitution of this Commonwealth in holding that he has no such right thereunder is sufficient to dispose of this contention .without further discussion. See also Hile v. Cleveland, 107 Ohio St. 144, 152-153; S. C. 266 U. S. 582. The case cited involved the validity, under both the Constitution of the State and that of the United States, of the city charter considered in Reutener v. Cleveland, 107 Ohio St. 117. Its validity was sustained by the State court. A writ of error was dismissed by the Supreme Court of the United States for “want of jurisdiction,” apparently on the *336ground that the case presented no substantial question under the Constitution of the United States.
The petitioner contends further that the provision for proportional representation embodied in Plan E is in violation of the provision of art. 4, § 4, of the Constitution of the United States, that the “United States shall guarantee to every state in this Union a republican form of government.” It is, however, well settled by decisions of the Supreme Court of the United States that questions arising under this provision “are political, not judicial, in character and thus are for the consideration of the Congress and not the courts.” Ohio v. Akron Metropolitan Park District, 281 U. S. 74, 80, and cases cited. Highland Farms Dairy, Inc. v. Agnew, 300 U. S. 608, 612. Compare Hile v. Cleveland, 107 Ohio St. 144; S. C. 266 U. S. 582. Obviously, the State courts cannot derive from this constitutional provision authority to adjudicate such a question. Attacks upon the constitutionality of Plan E to be effective must be based on other constitutional grounds.
None of the contentions of the petitioner that Plan E is in conflict with the Constitution of this Commonwealth or with the Constitution of the United States can be sustained. It follows that as matter of law the only conclusion that can be reached upon this record is that the petition cannot be maintained and should be dismissed.
Report discharged.
Case to stand for further hearing in the Superior Court in accordance with this opinion.