These are eight petitions for writs of mandamus brought against the board of special commissioners appointed under the provisions of St. 1939, c. 467, § 2, to divide Suffolk County into representative districts, and to assign representatives thereto. In each case the respondent commissioners filed an answer and the petitioner filed a replication thereto. The Secretary of the Commonwealth is referred to in each of the petitions as a respondent. And he has answered admitting the facts alleged in the petitions, alleging that his duty in the premises is purely administrative, and submitting himself to the jurisdiction of the court. An agreed statement of facts was filed to which the Secretary assented. From that statement it appears that the respondent commissioners have acted to divide the county into'representative districts and to assign representatives thereto, and, under date of December 20, 1939, filed a report of their action with the Secretary and with the registrars of voters, or other body having similar powers ór duties, in each city or town in said county.
The petitioner in. each case is a legal voter in a ward of the city of Boston in said county. Three of these petitioners are legal voters in ward ten, two of them are legal voters in ward eleven, and one each is a legal voter in wards one, eight and nine, respectively. Each petition is based on the ground that the division of the county into *239representative districts and assignment of representatives thereto made by the respondent commissioners is invalid under the Constitution of the Commonwealth. The prayer of each petition is for a writ of mandamus commanding the respondent commissioners to make a new division and assignment, and commanding the Secretary to refrain from taking any action toward putting into effect the representative districts as set forth in said report.
The cases came on to be heard before a single justice of this court. He ordered them consolidated for the purpose of being heard together, found the facts to be as stated in the agreed statement of facts and reported the cases for the consideration of the full court upon the pleadings and the agreed statement of facts. On a report in this form no exercise of discretion is involved. The question for determination by the full court is whether the writs ought to issue as matter of law. Lowry v. Commissioner of Agriculture, 302 Mass. 111, 112. Attorney General v. Secretary of the Commonwealth, ante, 25, 27.
Article 21 of the Amendments to the Constitution of the Commonwealth in its present form (see art. 71) provides in part: "In the year nineteen hundred and thirty-five and every tenth year thereafter a census of the inhabitants of each city and town shall be taken and a special enumeration shall be made of the legal voters therein. . . . The house of representatives shall consist of two hundred and forty members, which shall be apportioned by the general court, at its first regular session after the return of each special enumeration, to the several counties of the commonwealth, equally, as nearly as may be, according to their relative numbers of legal voters, as ascertained by said special enumeration .... The county commissioners or other body acting as such or, in lieu thereof, such board of special commissioners in each county as may for that purpose be provided by law, shall . . . assemble at a shire town of their respective counties, and proceed, as soon as may be, to divide the same into representative districts of contiguous territory and assign representatives thereto, so that each representative in such county will represent an *240equal number of legal voters, as nearly as may be; and such districts shall be so formed that no town containing less than twelve thousand inhabitants according to said census, no precinct of any other town and no ward of a city shall be divided therefor, nor shall any district be made which shall be entitled to elect more than three representatives.”
By St. 1939, c. 467, § 1, substituting a new section for G. L. (Ter. Ed.) c. 57, § 4, the number of representatives apportioned to Suffolk County was forty-six. Suffolk County consists of the city of Boston divided into twenty-two wards, the city of Chelsea divided into five wards, the city of Revere and the town of Winthrop. It appears from the agreed statement of facts that the number of legal voters in Suffolk County at the time of the special enumeration of legal voters in the year 1935 was 358,083, and that the county was divided by the commissioners into twenty-six representative districts. The number of legal voters for each representative if apportioned with exact equality would be 7,784. The manner in which such districts are constituted, according to the report of the commissioners, the number of legal voters in each of these districts and the number of representatives assigned to each district by the commissioners are set out in a footnote.1
*241A petition for a writ of mandamus against the commissioners is a proper - method of attacking the validity of the division of the county into representative districts and the assignment of representatives thereto. Donovan v. Suffolk County Apportionment Commissioners, 225 Mass. 55. McGlue v. County Commissioners, 225 Mass. 59. Brophy v. Suffolk County Apportionment Commissioners, 225 Mass. 124. Merrill v. County Commissioners, 257 Mass. 184. See also Attorney General v. Suffolk County Apportionment Commissioners, 224 Mass. 598, 610-611. No question is raised as to the propriety of treating the Secretary of the Commonwealth as a party respondent. Compare Faulkner v. Lowell Trust Co. 285 Mass. 375, 377; Attorney General v. Secretary of the Commonwealth, ante, 25, 30. A legal voter in a representative district is a proper party to bring such a petition if he is aggrieved by the division and assignment, but he can be aggrieved only by reason of the effect of the division and assignment upon the representative district in which he is a voter and then only if in that district the ratio between voters and representatives is higher than the right ratio. McGlue v. County Commissioners, 225 Mass. 59, 61-62. The respondents make no contention that the petitioners are not proper parties to bring the several petitions. But no one of the petitions can be maintained unless there is invalidity in the action of the commissioners respecting the representative district in which the petitioner is a legal voter.
The inquiry in these cases, therefore, is limited to the first, eighth, ninth, tenth and eleventh districts, except as, in determining whether there is discrimination against any of these districts, other districts are to be considered.
The constitutional provision under which the present controversy arises is the requirement that the commissioners shall proceed “to divide the . . . [county] into representative districts of contiguous territory and assign representatives thereto, so that each representative in such county will represent an equal number of legal voters, as nearly as may be.” The requirement that each district shall consist *242of “contiguous territory” was complied with. And there was no violation of the provisions that “no town containing less than twelve thousand inhabitants . . . [according to the special enumeration] and no ward of a city shall be divided therefor, nor shall any district be made which shall be entitled to elect more than three representatives.” The sole contention of the petitioners is that the commissioners failed to comply with the requirement of equality of representation.
In assigning the forty-six representatives apportioned to Suffolk County to the twenty-six districts, three representatives were assigned to one district, two representatives to each of eighteen districts, including the first district, and one representative to each of the seven remaining districts, including the eighth, ninth, tenth and eleventh districts. No two wards of the city of Boston were combined in a single district. In each of the five districts in controversy the number of voters for each representative exceeds the unit of representation for the county of 7,784 voters: in the first district by 21% of the representative unit, in the eighth district by 39% of such unit, in the ninth district by 49% of such unit, in the tenth district by 59% of such unit, and in the eleventh district by 57% of such unit. In no other district does the number of legal voters exceed the representative unit by more than 20% thereof or fall below it by more than 21% thereof. In six districts the divergence from such unit is less than 5% and in two others less than 10%. The average divergence in the districts, other than those in controversy, from the representative unit is 11.88% of such unit. The average divergence in all districts in the county is 18.25%.
The limitations upon the power of the court to review a division of the county into representative districts and assignment of representatives thereto have been stated in earlier cases and need not be restated in detail. See, especially, Attorney General v. Suffolk County Apportionment Commissioners, 224 Mass. 598, 607-608; Brophy v. Suffolk County Apportionment Commissioners, 225 Mass. 124, 126, 128-129. See also Attorney General v. Secretary *243of the Commonwealth, ante, 25, 31-32, 34. It is the function of the commissioners, and not of the court, to make the „ division and assignment. And the constitutional requirement of equality of representation “as nearly as may be” imports that the problem to be solved by the commissioners is not purely mathematical, but rather that it involves the exercise of their judgment and discretion. The court cannot substitute its judgment and discretion for that of the commissioners. It cannot strike down a division and assignment made by them merely because it is not literally the nearest approximation to equality of representation among the districts that an ingenious- mind can devise. Every reasonable presumption must be made in favor of the action of the commissioners. The division and assignment cannot be struck down on the ground of inequality of representation unless the “inequalities . . . are ... so great and the means for avoiding them ... so clear as to leave fair-minded men in no reasonable doubt that there is a grave and unnecessary inequality between the different districts,” and that the “division . . . [and assignment is] so vicious in its nature as to transcend the constitutional power of the commissioners.” Brophy v. Suffolk County Apportionment Commissioners, 225 Mass. 124, 128-129.
The petitioners, in support of their contentions, have submitted for consideration of the court a plan of division of the county into representative districts and the assignment of representatives thereto that avoids some of the inequalities in the division and assignment made by the commissioners. For reasons already stated, the possibility of such a division and assignment is not in itself fatal to the division and assignment actually made. The suggested plan has weight only so far as it tends to show that the division and assignment actually made is unreasonable. See Attorney General v. Secretary of the Commonwealth, ante, 25, 35.
In the light of these governing principles, and of the facts previously stated, we proceed to a consideration of the districts involved in the petitions.
*244It may fairly be assumed that the plan of division and assignment proposed by the petitioners is as favorable to their contentions as any that can be devised. No suggestion is made therein that any change with relation to the districts in Chelsea, Revere and Winthrop would tend to avoid discrimination against the districts in controversy, and we do not discuss these districts outside the city of Boston. The wards of the city of Boston — which are indivisible units under the Constitution — are large, ranging from ward eight, with 10,787 legal voters, to ward twenty, with 19,254 legal voters: in each instance, therefore, considerably exceeding in size the unit of representation. This fact, even though under the constitutional provision one, two or three representatives may be assigned to a representative district, presents an inherent difficulty in attaining a close approximation to equality among the districts and may justify greater divergence from the unit of representation than would be permissible in other circumstances. Brophy v. Suffolk County Apportionment Commissioners, 225 Mass. 124, 126. See also Attorney General v. Secretary of the Commonwealth, ante, 25, 36.
In the first district — which is involved in one of the petitions — the number of legal voters for each representative, according to the division and assignment made by the commissioners, exceeds the 0unit of representation for the county by 21% of that unit. This divergence is smaller, measured in percentages, than the divergences in several of the districts under a previous apportionment of Suffolk County that was held valid in Brophy v. Suffolk County Apportionment Commissioners, 225 Mass. 124. See Attorney General v. Secretary of the Commonwealth, ante, 25, 38. The petitioners suggest no method by which this divergence could have been avoided. No such method is apparent. Without further discussion we conclude that no unreasonable and unavoidable discrimination against the petitioner living in the first district is shown, and that his petition cannot be maintained.
The other districts — the eighth, ninth, tenth and eleventh — involved in one or more of the petitions pre*245sent more serious questions. The divergence from the unit of representation in each of these districts in excess of such unit is large, being, as already stated, respectively, 39% of that unit in the eighth district, 49% thereof in the ninth district, 59% thereof in the tenth district and 57% thereof in the eleventh district. The largest divergence from the unit of representation below such unit is in the fifth district where such divergence is 21% of the representative unit. ■ And in some other districts the divergences below the representative unit are nearly as great. As a result of these divergences, the voting power of a legal voter in the eighth district is slightly under 57%, that of a voter in the ninth district slightly over 52%, that of a legal voter in the tenth district slightly over 49%, and that of a legal voter in the eleventh district slightly under 50% of the voting power of a legal voter in the fifth district. There are other substantial, though somewhat lesser, inequalities unfavorable to the legal voters in the districts in question between the voting power of such legal voters and that of legal voters in several districts other than the fifth district. The question for decision is whether, by reason of these divergences and inequalities, the division of the county into representative districts and assignment thereto of representatives made by the commissioners so unreasonably discriminates against any of the petitioners that the division and assignment must be declared invalid.
The cases relating to previous apportionments of Suffolk County naturally deal with situations closely similar to that here presented, and comparison of these cases with the present case is instructive. In Brophy v. Suffolk County Apportionment Commissioners, 225 Mass. 124, where the apportionment was held valid, the greatest divergence in any district in excess of the representative unit was 31.43% of the unit, and the greatest divergence in any district below the unit was 25.50% thereof. The voting power of a legal voter in the former district was slightly over 59% of the voting power of a legal voter in the latter district. And there were other substantial inequalities in voting power among the districts. On the other hand, in Donovan v. *246Suffolk County Apportionment Commissioners, 225 Mass. 55, where the apportionment was held invalid, the greatest divergence in any district in excess of the representative unit was 71.7%, and the greatest divergence in any district below the unit was 25.50% thereof. The voting power of a legal voter in the former district was slightly over 43% of the voting power of a legal voter in the latter district. And there were other substantial inequalities in voting power among these districts. In Attorney General v. Suffolk County Apportionment Commissioners, 224 Mass. 598, where the apportionment was held invalid, the divergences and inequalities were much greater than in the Donovan case. In Merrill v. County Commissioners, 257 Mass. 184, where an apportionment of Essex County was held invalid, the voting power of a legal voter in the district having the greatest divergence in excess of the representative unit was slightly over 50% of the voting power of a legal voter in the district having the greatest divergence below such unit, and there were other substantial inequalities in voting power among the districts. It was found, however, that it “is possible to divide and apportion Essex County so that the numerical excess and shortage of the several districts complained of . . . would be materially lessened.”
It is apparent from the above analysis that the present case falls between the Brophy case, where the apportionment was held valid, and the Donovan case, where the apportionment was held invalid. Doubtless such large divergences from the representative unit as exist in the districts involved in the petitions and such inequalities in voting power between the legal voters in these districts respectively and those in other districts cannot be justified if there was any reasonable method of avoiding them.
The only method suggested by the petitioners of avoiding these divergences and inequalities to any substantial extent is the combination, in several instances, of two wards of the city of Boston in a single district. And no other possible method of such avoidance is apparent. Apart from the districts composed of parts of the county *247outside the city of Boston and apart from the twentieth district, consisting of ward twenty of that city, to which three representatives were assigned — districts as to which no contention is made — there are twenty-one districts, each composed of a single ward of the city of Boston, to which thirty-eight representatives were to be assigned. Necessarily at least four of these districts would have only one representative each. The four districts to each of which only one representative was assigned by the commissioners are the districts involved in these petitions. The petitioners suggest that two of these districts, consisting of wards eight and nine respectively, should have been combined in one district and three representatives should have been assigned thereto, and that in like manner two of these districts, consisting of wards ten and eleven respectively, should have been combined in one district and three representatives should have been assigned thereto. In order, however, to gain the two additional representatives required to carry out this arrangement the petitioners suggest two other double districts, one of them a combination of two districts consisting of wards four and five respectively, and the other a combination of two districts consisting of wards thirteen and fifteen respectively, and the assignment to each of the double districts so created of three representatives instead of two representatives each to the four districts as now constituted. In no one of the four proposed double districts would there be a divergence from the representative unit of more than 7.5% of such unit, and in no one of them would a legal voter have less than 76.9% of the voting power of any other legal voter in the city of Boston. Obviously the creation of four double districts, as suggested by the petitioners, would have avoided in a substantial degree the discrimination against the legal voters in the districts involved in these petitions.
It was said, however, in Brophy v. Suffolk County Apportionment Commissioners, 225 Mass. 124, 127, that there “are obvious objections which may be urged against combinations of wards into double or triple districts. The *248avoidance of them has something in its favor.” The respondent commissioners, in dividing Suffolk County into representative districts and assigning representatives thereto, have consistently avoided throughout the city of Boston the creation of double or triple districts. In the exercise of their judgment and discretion they were warranted in giving some weight to the objections to the creation of such districts. The question for our determination is whether the commissioners have given unreasonable weight to such objections in view of the resulting divergences from the representative unit and inequalities of voting power among the districts that affect the petitioners adversely. Considering the extent of the divergences and inequalities in the apportionment held valid in the Brophy case and recognizing that the duty of dividing Suffolk County into representative districts and assigning representatives thereto is imposed by the Constitution upon the commissioners, to be exercised in accordance with their judgment and discretion, and that every reasonable presumption of validity attaches to a division and assignment made in performance of this duty, we cannot rightly say that the failure of the commissioners to avoid divergences from the representative unit and inequalities in voting power by creating double districts was so unreasonable in its effect upon any of the petitioners that the division and assignment, for this reason, transcends the constitutional power of the commissioners and should be declared void. See Attorney General v. Secretary of the Commonwealth, ante, 25, 47. It follows that the petitions relating to the eighth, ninth and eleventh districts cannot be maintained.
What has previously been said disposes also of the petition relating to the tenth district, apart from one other consideration. Naturally the four districts to each of which only one representative should be assigned would be the four districts having the smallest number of legal voters. These districts are the eighth, ninth, fifth and eleventh. The tenth district — having 12,427 legal voters — to which one representative was assigned by the commissioners is slightly larger than the fifth district — having *24912,213 voters — to which two representatives were assigned by the commissioners. On a strictly mathematical basis two representatives, instead of one representative, should have been assigned to the tenth district, and one representative, instead of two representatives should have been assigned to the fifth district. The excess in number of legal voters in the tenth district over the number of such voters in the fifth district, however, is so slight — 214 voters — that an assignment of two representatives to the former district and one representative to the latter district would make no substantial change in the inequalities in voting power among the districts throughout the county. The effect would have been merely to substitute a district in which the voting power of a legal voter was 50.66%, for a district in which such power was 49.13% of the voting power of a voter in the district in which such voting power was the greatest. We cannot rightly say, according to the principles already stated, that the failure of the commissioners to make such a substitution was so unreasonable as to invalidate the division and assignment made by them. The petitions relating to the tenth district, therefore, cannot be maintained.
It follows that the petition in each case must be dismissed.
So ordered.
The districts numbered from one to twenty-two, inclusive, are located in the city of Boston.
District No. 23 consists of wards 1, 2 and 3 of Chelsea, with a population of 8,389 and 1 representative; district No. 24 consists of wards 4 and 5 of Chelsea, with a population of 6,283 and 1 representative; district No. 25 consists of the city of Revere, with a population of 15,028 and 2 representatives; district No. 26 consists of the town of Winthrop, with a population of 8,581 and 1 representative.