This is another dispute arising out of legislative redistricting for the 2002 general election. See Mayor of Cambridge v. Secretary of the Commonwealth, ante 476, 477 (2002). In addition to declaratory and injunctive relief, the plaintiffs, registered voters living in various precincts of the town of Chelmsford, seek relief in the nature of mandamus against the defendant, Secretary of the Commonwealth, that would invalidate the 2001 redistricting plan for the 160 representative districts of the House of Representatives. The plaintiffs maintain that St. 2001, c. 125, § 1 (the redistricting statute), which establishes the new districts, is unconstitutional under art. 101, as amended by arts. 109, 117, and 119 of the Amendments to the Constitution of the Commonwealth, because it places portions of Chelmsford in four representative districts when art. 101’s requirements could have been satisfied by dividing it into fewer districts.2 The plaintiffs also claim that the redistricting constitutes unconstitutional partisan gerrymandering in violation of the equal protection clause of the Fourteenth Amendment to the United States Constitution.3 We conclude that the plaintiffs have failed to demonstrate that the redistricting statute violates *616either the Massachusetts or the United States Constitution. Accordingly, the defendant is entitled to judgment.
1. Procedural background. Section 2 of the redistricting statute vests jurisdiction in the Supreme Judicial Court for “any petition for a writ of mandamus relative to the establishment of 160 representative districts under section 1 [of this act].” See also art. 101, §§ 1 and 3. Accordingly, the plaintiffs filed their complaint in this court. The case was referred to the county court to be prepared for disposition “as promptly as possible.” The parties filed a statement of agreed facts. A single justice then ordered that the case proceed in this court on an expedited basis.
2. Constitutional and statutory requirements. Article 101, adopted in 1974, reduced the House of Representatives from 240 to 160 members, eliminated the last vestiges of territorial representation, and firmly established population equality as the main organizing principle for legislative districts.4 As we stated in Brookline v. Secretary of the Commonwealth, 417 Mass. 406, 423-424 (1994), “art. 101 directs that each representative ‘represent an equal number of inhabitants,’ not cities and towns, thereby requiring equal representation, in the sense that persons are placed in a district that has the same number of inhabitants as every other district, ‘as nearly as may be.’ ” As subsequently amended, art. 101 also requires the Legislature to redivide the Commonwealth into new representative, senatorial, and council-lor districts, in the year following each Federal census. The purpose for this mandatory decennial redivision is to ensure that districts are appropriately adjusted to meet population changes occurring in the ten-year period between each Federal census.
In dividing the Commonwealth into 160 representative *617districts, the Legislature must conform to State and Federal constitutional and statutory requirements, some of which are inherently contradictory. See Mayor of Cambridge v. Secretary of the Commonwealth, supra at 478-479. Article 101 mandates that the Legislature’s division of the Commonwealth results in districts “[1] of contiguous territory [2] so that each representative will represent an equal number of inhabitants, as nearly as may be; [3] and such districts shall be formed, as nearly as may be, without uniting two counties or parts of two or more counties, two towns or parts of two or more towns, two cities or parts of two or more cities, or a city and a town, or parts of cities and towns, into one district[; and 4 such] districts shall also be formed that no town containing less than twenty-five hundred inhabitants . . . shall be divided.” Merriam v. Secretary of the Commonwealth, 375 Mass. 246, 248 (1978). See Brookline v. Secretary of the Commonwealth, 417 Mass. 406, 413-414 (1994).
The equal protection provision of the Fourteenth Amendment independently imposes an equal representation requirement on electoral districting. Reynolds v. Sims, 377 U.S. 533, 577 (1964). The United States Supreme Court has stated that an apportionment plan with a maximum population deviation of under 10% is a deviation that the Legislature need not justify. Voinovich v. Quilter, 507 U.S. 146, 161 (1993), quoting Brown v. Thomson, 462 U.S. 835, 842-843 (1983). See Brookline v. Secretary of the Commonwealth, supra at 414, and cases cited. The maximum population deviation is calculated by determining the range of population deviation between the largest and smallest districts from the “ideal population” of a district.5 Mayor of Cambridge v. Secretary of the Commonwealth, supra at 478. See also Black Political Task Force v. Connolly, 679 F. Supp. 109, 114 (D. Mass. 1988). Thus, where a plan includes no district with a population more than 5% under or 5% over the “ideal district population,” the plan is within the 10% range and thus meets *618Federal population equality requirements (±5% standard).6 The Federal Voting Rights Act of 1965 must also be considered by the Legislature when implementing a redistricting plan. Brookline v. Secretary of the Commonwealth, supra at 414-415. See Mayor of Cambridge v. Secretary of the Commonwealth, supra at 479.
3. The 2001 redistricting plan. The 2001 redistricting statute and the legislative deliberation that led to its enactment cannot be adequately understood or evaluated without examining the progression and evolution of its predecessors. Between the adoption of art. 101 in 1974 and the enactment of the redistricting statute, the Legislature passed four successive redistricting plans. Each successive plan contained more districts that united parts of or whole cities, towns, or counties than the preceding plan, and each moved closer to population equality between districts, with only the last plan meeting the Federal ±5% standard.
The first plan (St. 1977, c. 277) was based on the 1975 State census.7 It included ninety-two (out of 160) districts that did not meet the art. 101 goal of avoiding combinations of political subdivisions. Even with all of these combinations the plan included districts that deviated from the ideal population by more than ±5%. Brookline v. Secretary of the Commonwealth, supra at 415-416 n.10.
The second plan (St. 1987, c. 341, as amended by St. 1987, c. 715) was based on the 1985 State census. It included ninety-five districts that did not meet the art. 101 goal of avoiding combinations of political subdivisions. But, like the 1977 plan, it also included districts that deviated from the ideal population by more than ±5%. Id. The plan was challenged in Federal court on equal protection (“one person one vote”) grounds in Black Political Task Force v. Connolly, supra. The population deviations between districts (including a maximum deviation of *61921.9%, id. at 124) were unsuccessfully justified in that case by the Secretary of the Commonwealth, who relied on art. 101’s instruction to minimize the creation of districts that combined political subdivisions. The court concluded that art. 101’s stated policy of minimizing the division and unification of cities and towns did not provide sufficient justification for the deviations from population equality and, accordingly, struck down the 1987 plan. Id. at 130-131.
In response to the decision in the Black Political Task Force case, the Legislature enacted a third plan (St. 1988, c. 11) that included one hundred districts that did not meet the art. 101 goal of avoiding combinations of political subdivisions. Yet the plan still contained some districts that deviated from the ideal population by the ±5% standard. Brookline v. Secretary of the Commonwealth, supra. Only two years later, when the 1990 Federal census was completed, ninety of the 160 districts were of questionable validity under Federal population equality standards. Id. at 411.
The fourth plan (St. 1993, c. 273, § 1) included 114 districts that did not meet the art. 101 goal of avoiding combinations of political subdivisions. However, unlike prior plans, this plan did not contain any districts that deviated from the ideal population by more than ±5%. Id. at 415. It was challenged by the town of Brookline for excessively dividing certain municipalities to further the goal of population equality and' minority representation. In denying the challenge we stated:
“We reject the contention that, in enacting [the plan], the Legislature erred by giving undue emphasis to population equality among districts. . . . The principle of electoral equality has long been recognized as one of the fundamental rights protected by our Constitution. In 1916, Chief Justice Rugg, speaking of art. 21 of the Amendments to our Constitution, observed: ‘The great principle established by this amendment is equality of representation among all the [citizens] of the Commonwealth. That is a fundamental principle of representative government. . . . There can be no equality among citizens if the vote of one counts for considerably more than that of another in electing public officials.’ ... In art. 101, the *620people placed population equality on at least the same footing with the respect expressed for the cohesiveness of political subdivisions.”
Id. at 418, quoting Attorney Gen. v. Suffolk County Apportionment Comm’rs, 224 Mass. 598, 604 (1916).
The 2000 Federal census results revealed that, as a result of population growth and shifts, the representative districts established in 1993 once again no longer met Federal population equality standards and had to be significantly altered. The census showed that Commonwealth’s population had grown to 6,349,097 inhabitants, yielding a new ideal representative district population of 39,682 persons. This meant that, for Federal constitutional purposes, the presumptively permissible range for a district was now 39,682 ±5%, i.e., between 37,698 and 41,666 persons. The ideal population under the 1993 plan had been 37,603 persons, which now fell outside of the presumptively permissible range. Due to uneven population growth in different communities, the districts established in 1993 now deviated from the new ideal population by from -15.24% to +28.33% for a maximum deviation of 43.57%.8
The Legislature established a Joint Special Committee to recommend redistricting plans for House, Senate, Executive Council, and Congressional districts. After holding public hearings, the Committee issued a report and recommended a redistricting plan on October 18, 2001. The report noted the many constraints under which the committee operated, including population equality requirements, respecting racial minority representation, and the goal of keeping communities united. 2001 House Doc. No. 4700 at 4-6. Certain cities and towns could each naturally comprise a single district, and they were kept “united whenever possible.” Id. at 5. “The process, however, [was] not an exact science. One community with a precinct or two too many [did] not necessarily abut another *621community in need of a precinct or two.” Id. All of the recommended districts in the report were within the ±5% standard, and the committee recognized that this standard allowed some latitude to keep certain communities united. Id. The committee recommended that Chelmsford be divided among four representative districts.8 9
On October 22, 2001, the committee’s plan was debated by the full House, which adopted twenty-eight separate sets of amendments to the recomihended districts, including eight sets of amendments proposed by Republicans. These amendments substantively changed a total of seventy-four districts — nearly one-half of the 160 districts in the plan. Chelmsford remained divided among four representative districts, although one of the districts was slightly modified by amendment. The House then adopted the amended plan by a roll call vote, with 128 representative voting in favor of the amendments and twenty-three voting against them. A substantial number of Republicans (eight of twenty-one) voted “Yea” and ten Democrats voted “Nay.” The bill was passed by both the House and Senate and then signed by the Governor on November 8, 2001. St. 2001, c. 125.
The redistricting statute includes 116 districts that do not meet the art. 101 goal of avoiding combinations of political subdivisions. It divides Chelmsford among the following four districts: Second Middlesex district, with a population of 39,881; Fourteenth Middlesex district, with a population of 39,509; Sixteenth Middlesex district, with a population of 41,023; and Seventeenth Middlesex district, with a population of 41,363.10
4. The plaintiffs’ alternative plan. The plaintiffs have proffered to the court an alternative plan that would divide Chelms-ford between two of the four representative districts contem*622plated by the redistricting statute. The proposed redivision affects the population of each district, and creates a different level of deviation among all four. The maximum population deviation, computed by calculating the percentage deviation from the ideal district population figure of the largest and smallest of the four districts, is 5.04% under the alternative plan, as compared to 4.68% under the redistricting statute. The average population deviation of the four districts, computed by averaging the percentage that each district deviates from the ideal district population, is 2.81% in the alternative plan, as compared to 2.14% under the redistricting statute and 2.45% for the State as a whole.
5. Discussion.
a. Art. 101. The plaintiffs first argue that the redistricting plan embodied in St. 2001, c. 125, is unconstitutional because it violates art. 101’s directive that the Legislature keep intact cities, towns, and counties “as nearly as may be.” Although the plaintiffs have offered an alternative plan that more closely meets the territorial integrity requirement of art. 101, they “cannot prevail in this proceeding unless they establish beyond a reasonable doubt that it is impossible by any reasonable construction to interpret the [redistricting] statute in harmony with art. 101.” Merriam v. Secretary of the Commonwealth, 375 Mass. 246, 263 (1978). In this regard, the plaintiff bears a heavy burden of proof and “every reasonable presumption must be made in favor of the constitutionality of the statute.” Id.
As discussed in Mayor of Cambridge v. Secretary of the Commonwealth, ante 476, 484 (2002), we have adopted a two-step inquiry to determine whether a redistricting plan meets the territorial requirements of art. 101. The plaintiff must first demonstrate that “the constitutional requirement of equal representation ‘can be achieved . . . without dividing a municipality and [that] an entire municipality can be kept in one district without a “ripple effect” on other defined districts.’ ” Id., quoting Merriam v. Secretary of the Commonwealth, supra at 264 (Wilkins, L, dissenting). A “ripple effect” is created when fewer divisions of the town in question result in the increased division of neighboring towns and communities. Id., citing Brookline v. Secretary of the Commonwealth, 417 Mass. 406, 422 (1994) (alternative plan *623created “ripple effect” where it resulted in additional division of neighboring towns). If this burden is met, the plaintiff must next establish that the Legislature’s plan is without justification. Id. The Legislature’s proffered justification is entitled to a “high degree of deference.” However, the Legislature’s discretion is not without limit; the Massachusetts Constitution “prohibits] any departure from either [the territorial integrity or population equality requirement] that is unreasonable in the light of all the limitations imposed upon legislative action.” Merriam v. Secretary of the Commonwealth, supra at 260, quoting Attorney Gen. v. Secretary of the Commonwealth, 306 Mass. 25, 31-34 (1940).
We assume, without deciding, as the Secretary has, that the plaintiffs have met the first prong by proffering a satisfactory alternative plan. Under that plan, Chelmsford would be divided between only two districts; the population of the reconfigured Second, Fourteenth, Sixteenth, and Seventeenth Middlesex districts proposed by the plaintiffs would each be well within the Federal population equality ±5% standard; and there would be no identifiable adverse impact on other municipalities.
We therefore turn to the justification, that is, a closer degree of population equality. The plaintiffs’ plan creates higher maximum and average deviations in population equality for the four districts in question. As described above, population equality, or the “one person one vote” construct, has been the driving force behind court and constitutional reform of the electoral districting process. Although the plaintiffs’ alternative plan meets Federal equal protection requirements, Brown v. Thomson, 462 U.S. 835, 842 (1983) (less than 10% maximum deviation), art. 101’s requirement that the Legislature achieve population equality “as nearly as may be” leaves the Legislature with considerable discretion to seek closer approximation to population equality than is required by the Federal equal protection clause. Certainly, our Constitution does not require that once the Federal equality of population requirement is met, the Legislature must maximize territorial integrity rather than seek to achieve closer population equality among the districts. As stated in Mayor of Cambridge v. Secretary of the Commonwealth, supra at 482, the two requirements of art. 101 are inherently contradictory.
*624While it is the responsibility of the Legislature to draw the redistricting plan, there is no definitive way to find the “best” such plan, because there is no single “best” way for the Legislature, let alone the courts, to determine which trade-offs between population equality, minority vote dilution,11 and territorial cohesion are most appropriate. The interaction of these factors is extraordinarily complex in the development of the Statewide plan, requiring an accumulation of difficult, interlocking judgments. In simplest terms, and as evident from the history of redistricting statutes enacted since the adoption of art. 101, if the Legislature wishes to more closely achieve the ideal of districts with equal populations, it must often create more districts that cross city, town, or county lines.
There is no presumptive number of districts into which a city or town of a given size may be divided to which the Legislature must adhere.12 Nor has this court ever established a guideline above which efforts to achieve greater population equality may not intrude. It is the Legislature that has the authority and the discretion to determine “the extent to which either of these requirements shall yield to the other.” Merriam v. Secretary of the Commonwealth, supra at 260, quoting Attorney Gen. v. Secretary of the Commonwealth, supra at 31-34.13
It is in this context that the plaintiffs must carry their burden *625of demonstrating beyond a reasonable doubt that the departures they complain of are “unreasonable.” We recognize that the plaintiffs’ plan and the Legislature’s plan differ only in relatively small degrees. However, the Legislature reasonably could have concluded that it was preferable to seek a closer approximation of population equality in the districts in the Chelmsford area, as part of a Statewide plan that sought to balance these conflicting objectives throughout, at the expense of dividing the town among four districts. This choice is related to the permissible, well-understood, legislative objective of achieving greater equality of population.14 That Chelmsford was consequently divided among four rather than two districts does not constitute a “substantial derogation” from the art. 101 requirement that territorial integrity be honored “as nearly as may be.” If it did, any number of similar divisions made throughout the State (see note 12, supra) would be subject to the same criticism. Because the statute is entitled to “every reasonable presumption in favor of [its] constitutionality,” id. at 263, we will not disturb the Legislature’s determination.
b. Political gerrymandering. The plaintiffs next argue that St. 2001, C..125, constitutes a partisan political gerrymander in violation of the Federal equal protection clause. They assert that Chelmsford has been and is currently represented in the House of Representatives by a Republican, and that the Legislature’s plan will destroy Chelmsford’s Republican influence by dividing Chelmsford among districts that are currently represented by Democrats. We reject the plaintiffs’ claim, as they have not proved that the Legislature’s plan will lead to the disproportionately low representation of Republicans in the House of Representatives as a whole.
The United States Supreme Court, in Davis v. Bandemer, 478 U.S. 109, 127 (1986) (plurality opinion), held that to establish an equal protection violation based on partisan political gerrymandering, a plaintiff must demonstrate that the redistricting *626scheme has both a discriminatory intent and a discriminatory effect.15 See Terrazas v. Slagle, 821 F. Supp. 1162, 1172 (W.D. Tex. 1993). As to discriminatory effect, the Court noted that “the mere fact that a particular apportionment scheme makes it more difficult for a particular group in a particular district to elect the representatives of its choice does not render that scheme constitutionally infirm.” Davis v. Bandemer, supra at 131. To find an equal protection violation, we must find “a history (actual or projected) of disproportionate results” and indications that a party has been denied fair representation. Id. at 139. “[A]n equal protection violation may be found only where the electoral system substantially disadvantages certain voters in their opportunity to influence the political process effectively.” Id. at 133. The claim must be supported by evidence of “continued frustration of the will of a majority of the voters or effective denial to a minority of voters of a fair chance to influence the political process.” Id.
The plaintiffs have not shown that the Legislature’s redistricting plan has a discriminatory effect. Although they assert that Chelmsford voters have, in the past, played a part in electing a Republican to the House of Representatives, they have not demonstrated that the division of Chelmsford will result in a diminished Republican influence in either the relevant districts or the House of Representatives as a whole. Nor have the plaintiffs shown discriminatory intent on the part of the Legislature. To succeed on a political gerrymandering claim, a plaintiff must show that the Legislature has made a purposeful, concerted effort to disfavor a political party through the redistricting process. The plaintiffs have offered no evidence *627indicating that the Legislature’s redistricting statute was the result of such efforts.
6. Conclusion. Judgment is to be entered for the Secretary of the Commonwealth declaring that the redistricting plan in St. 2001, c. 125, § 1, does not violate art. 101, and otherwise denying the relief requested by the plaintiffs.
So ordered.
Article 101 of the Amendments to the Constitution of the Commonwealth, as amended, states, in part, that the Legislature shall “divide the Commonwealth into one hundred and sixty representative districts of contiguous territory so that each representative will represent an equal number of inhabitants, as nearly as may be; and such districts shall be formed, as nearly as may be, without uniting two counties or parts of two or more counties, two towns or parts of two or more towns, two cities or parts of two or more cities, or a city and a town, or parts of cities and towns, into one district. Such districts shall also be so formed that no town containing less than twenty-five hundred inhabitants . . . shall be divided.”
The plaintiffs also claim in a single sentence that the redistricting statute violates due process. Their claim does not rise to the level of acceptable appellate argument. See Adoption of Kimberly, 414 Mass. 526, 536-537 (1993).
The Constitution formerly provided for cities and towns themselves to be represented in the House of Representatives. PartH, c. 1, § 3, art. 2 of the Massachusetts Constitution. Arts. 12, 13 of the Amendments to the Massachusetts Constitution. Municipal representation ended, however, in 1857, with the adoption of art. 21 of the Amendments that required that representation be apportioned to and within counties, “equally, as nearly as may be,” based on the numbers of “legal voters.” In 1970, art. 92 of the Amendments was ratified, requiring that every representative district in the Commonwealth comprise “an equal number of inhabitants, as nearly as may be,” and ending apportionment by county except that Dukes and Nantucket counties were each made a separate district. In 1974, art. 101 eliminated those exceptions.
The “ideal population” of a district is the mathematical division of the number of districts into the total population.
A plan, of course, can still meet Federal population requirements even if it had a district that was 6% over the ideal population so long as no other district was more than 4%.
The use of the State census was abolished by art. 117 of the Amendments to the Massachusetts Constitution, which amended art. 101 in 1990 to require the Federal census be used as the basis for determining districts.
Based on the 2000 census results, nearly 200 cities and towns also redrew their ward or precinct lines. These new “building blocks” became the basis for the new districts to be drawn by the Legislature. They vary in size from many hundred to many thousand, are therefore not interchangeable in size and substantially complicate the task of building districts that are both compact and equal in population.
Prior to the present redistricting statute, the entirety of Chelmsford was combined with the town of Carlisle to comprise a single district. See St. 1993, c. 273, § 1. According to the 2000 census on which the challenged redistricting plan is based, the population of Chelmsford is 33,858. Because the ideal population size of each district is 39,682, the entire population of Chelmsford comprises more than 15% less than an ideal district.
Chelmsford residents will comprise 27% of the Second Middlesex district, 20% of the Fourteenth Middlesex district, 28% of the Sixteenth Middlesex district, and only 9% of the Seventeenth Middlesex district.
Minority vote dilution was not a factor directly implicated in creating the districts among which Chelmsford was divided, but was very much a factor in redistricting decisions Statewide.
To the extent Chelmsford’s complaint is premised on four being too many divisions for a town of 33,858, its plight is hardly unique. A cursory review of the redistricting statute reveals many others similarly situated including:
City or Town Population Number of Districts
Bourne 18,721 3
Easton 22,299 3
Freetown 8,472 3
Middleborough 19,941 3
Oxford 13,352 3
Randolph 30,963 3
Walpole 22,824 4
Westborough 17,997 3
Article 101 offers no guidance on whether the appropriate price to be paid for one less district that unites a city and a town is an additional one-half *625percent, or l%,or 2% average or maximum deviation from population equality. It is left to the Legislature to make judgments regarding these trade-offs.
It is not, as the dissent suggests, inconsistent with one of the Legislature’s stated objectives to use the flexibility of the Federal ±5% standard to try and keep some communities that were within that deviation range together. It is undisputed that Chelmsford’s population did not fall within that range.
Davis v. Bandemer, 478 U.S. 109, 127 (1986), was decided by a fragmented Court. A majority held that partisan political gerrymandering complaints were justiciable. However, the Court was divided as to the requirements for such a claim. Id. “When a fragmented Court decides a case and no single rationale explaining the result enjoys the assent of five Justices, ‘the holding of the Court may be viewed as that position taken by those Members who concurred in the judgments on the narrowest grounds ....’” Marks v. United States, 430 U.S. 188, 193 (1977), quoting Gregg v. Georgia, 428 U.S. 153, 169 n.15 (1976) (opinion of Stewart, Powell, & Stevens, JJ.). We apply the plurality opinion, which provides the narrowest grounds. Terrazas v. Slagle, 821 F. Supp. 1162, 1172 n.12 (W.D. Tex. 1993).