This court’s order of July 14, 1998, affirmed the ruling of the State Ballot Law Commission (commission) that the plaintiffs did not comply with the commission’s discovery rule, 801 Code Mass. Regs. § 1.01(8)(f), as modified by 950 Code Mass. Regs. § 59.03(18) (1993), and thus failed to challenge *117with sufficient particularity signatures from Barnstable and Berkshire counties. This opinion states the reasons for that order.
I
The plaintiffs originally challenged a decision of the commission to include on the November, 1998, Statewide ballot a referendum to repeal Chapter 164 of the Acts of 1997.3 They argued that the petition forms used to collect signatures in support of the referendum suffered from several constitutional or statutory defects: (1) that all the petition forms used to collect signatures violated the requirement of art. 48 of the Amendments of the Massachusetts Constitution that a summary of the law in question be “at the top” of the form; (2) that some signatures were on forms that violated art. 48 and G. L. c. 53, § 22A, because the referendum’s proponents added a preprinted box containing the name of their organization and a return address on the forms; (3) that some signatures were on forms that improperly contained a hand stamp in blue or red ink with similar information; and (4) that some signatures were on forms on which the referendum’s proponents had highlighted certain sentences in the official summary.4 In Hurst v. State Ballot Law Comm’n, 427 Mass. 825, 830-831 (1998) (Hurst I), we held that some, but not all, of the petition forms were improper. We rejected the challenge to all of the petition forms made on the ground that the required summary was not at the top of the form, but we agreed with the objectors that the petition forms containing hand stamping, shaded boxes, and highlighting were defective because they were not exact copies of the official form, as required by law. Our decision served to invalidate all properly objected-to signatures on petition forms bearing these defects, except those with hand stamping. Our ruling as to the effect of hand stamping was made prospective only and did not serve to invalidate any signatures in this referendum petition.
The parties disagreed as to whether the elimination of the *118petition forms thus invalidated reduced the number of valid signatures below the minimum required to place the question on the November ballot. The dispute turned on the admissibility of several hundred signatures from Barnstable and Berkshire counties that were collected on forms that are defective according to our ruling in Hurst I. When signatures are drawn into question in a petition challenge, the commission’s regulations require that:
“Not later than the third weekday before the date of the hearing contained in the Secretary’s notice, the objector shall file and cause to be delivered to the respondent a list of all signatures on the respondent’s nomination paper or petition which are drawn in question by the objection, showing the page and line where each is located, and the reason why each is alleged to be improper.”
801 Code Mass. Regs. § 1.01(8)(f), as modified by 950 Code Mass. Regs. § 59.03(18). On April 1, 1998, when the plaintiffs originally lodged their challenge to the signatures contained in defective petition forms, they filed their “List of Contested Petitions and Signatures,” setting out, by petition numbers, though not by petition line, the signatures which they challenged, designating the number of signatures on each challenged petition form, and setting out with some particularity why each was alleged to be improper. The commission found this challenge sufficient; it identified the petitions objected to and challenged globally all signatures on those challenged petition forms. The list submitted, however, did not include any signatures or petitions from Barnstable and Berkshire counties. On April 6, 1998, the first day of the hearing, the defendants objected to the introduction of challenges to signatures from Barnstable and Berkshire counties because a challenge to those signatures had not been timely filed in compliance with § 1.01(8)(f). On April 8, 1998, two days after the commencement of the hearing, the plaintiffs filed a “Supplemental Identification of Challenged Signatures” containing signatures from Barnstable and Berkshire counties alleged to be improper.
In its original decision, the commission did not reach the validity of the plaintiffs’ challenge to the signatures from Barn-stable and Berkshire counties because, under its ruling, the sufficiency of the number of signatures did not depend on the signatures from these two counties. Our decision in Hurst I *119entailed that the sufficiency of the number of valid signatures depends on this very issue.5 By our order of June 24, 1998, we remanded the case to the commission to consider whether the plaintiffs properly raised a challenge to signatures from these two counties and the effect of the commission’s conclusion on that question on the status of the referendum.6 In its decision on remand, the commission found that the plaintiffs did not properly raise their challenge, and that accordingly there was a sufficient number of certified signatures to place the referendum on the ballot.
n
The plaintiffs argue that their noncompliance with § 1.01(8)(f) does not render their challenge to the signatures from Barnstable and Berkshire counties improper. They assert that the purpose of the discovery rule of § 1.01(8)(f) is to identify specific signatures said to be invalid because of some defect relating to individual signers or their signatures, and that therefore the rule is inapplicable when a challenge is to defects in petition forms that invalidate all signatures contained in forms with that defect. They rely on two past decisions of the commission, Jay Donovan vs. Richard Brenton, SBLC 90-2, and Thomas Hamill vs. William C. Sawyer, SBLC 90-14, to support their position. In those cases, both involving nomination of political candidates, the commission drew a distinction *120between challenges to nomination forms and challenges to the signatures on those forms. The plaintiffs argue that their objections too related to defects in the form of some of the petitions rather than to the invalidity of individual signatures.
In rejecting this argument below, the commission relied on the fact that the plaintiffs themselves had couched their challenge as a challenge to signatures. The plaintiffs concede as much, but point out that their challenge to the signatures was premised on the defects of the petition forms. Their claim was that the signatures were fraudulently obtained in the sense that they were obtained on forms with alterations that tended to mislead. It follows, according to the plaintiffs, that their challenge was primarily one to the petition forms, and only derivatively to the signatures.
Section 1.01(8)(f), the discovery rule, is a regulation that the commission has promulgated in accordance with G. L. c. 55B, § 4. An agency’s interpretation of its own regulation is entitled to “substantial deference.” See Torres v. Commissioner of Correction, 427 Mass. 611, 617 n.10 (1998). See also Boston Police Superior Officers Fed’n v. Boston, 414 Mass. 458, 462 (1993). As long as the agency’s interpretation is not arbitrary, capricious, or contrary to law, it should be respected. Cf. Gloucester v. Civil Serv. Comm’n, 408 Mass. 292, 297 (1990) (“We need only inquire whether the commission’s decision was ‘legally tenable and supported by substantial evidence on the record as a whole’ ”), quoting Commissioner of Health & Hosps. of Boston v. Civil Serv. Comm’n, 23 Mass. App. Ct. 410, 411 (1987). In concluding that the plaintiffs’ challenge to signatures from Barn-stable and Berkshire counties was improperly raised, the commission stated:
“It has long been held by the Commission that when a challenge to signatures is raised before the Commission, the objector is required to comply with 801 [Code Mass. Regs. §] 1.01(8)(f) as modified by 950 [Code Mass. Regs. §] 59.03(18) and timely file a list of challenged signatures. Our cases require automatic dismissal, or in this case, exclusion of signatures not supplied in a timely fashion, since the failure to supply such information ‘affects’ the respondent’s ‘substantial rights’ to prepare the case. . . . The Commission requires strict adherence to this rule given the unusually brief procedural schedule under G. L. *121c. 55B. . . . Strict adherence is even more evident in the instant matter given the large number of signatures and petitions challenged, and to be considered in such a condensed time frame.”
Because this interpretation of § 1.01(8)(f) is not arbitrary, capricious, or contrary to law, we affirm the commission’s decision.
The distinction crucial to the commission’s decision is not the distinction between challenges to petition forms and challenges to signatures, but rather between challenges that identify the allegedly invalid signatures and make evident their exact number, and challenges that do not. Given the tight procedural schedule required under G. L. c. 55B, §§ 8-10, both the commission and the defendants have an interest in identifying the allegedly invalid signatures and determining their exact number. If this requires sifting through many hundreds, perhaps thousands, of petition forms, then the commission’s present application of its discovery rule obliges objectors to identify at the time of their objection tifie particular petitions objected to. From this the scope of the objection and its potential effect on the validity of the referendum may be calculated. We note again that as to the objections relating to other counties, which the commission was willing to consider, it did not insist that the objectors identify the signatures objected to line-by-line but was satisfied by a designation of the petition number objected to and the number of signatures on each challenged form. What § 1.01(8)(f), under the commission’s interpretation, therefore requires is the timely disclosure of each petition being challenged, the number of signatures affected by the challenge, and the nature of the challenge.7 Our conclusion that the commission’s interpretation of § 1.01(8)(f) is a reasonable one is *122confirmed by the fact that the plaintiffs themselves so understood it and complied with it in respect to all counties except Barnstable and Berkshire.
m
Our analysis in the preceding section is premised on this court’s jurisdiction to review decisions of the commission pursuant to the Administrative Procedure Act, G. L. c. 30A, § 14. See G. L. c. 55B, § 4. The plaintiffs argue, however, that our jurisdiction to judge the validity of signatures gathered from Barnstable and Berkshire counties is not limited to judicial review of the commission’s decisions with the attendant deference to decisions of agencies interpreting their own regulations. Instead, they claim, according to G. L. c. 56, § 59,8 we have independent jurisdiction to enforce the requirement of use of “exact copies” of petition forms pursuant to G. L. c. 53, § 22A. The plaintiffs rightly point out that this court has affirmed this independent concurrent jurisdiction to enforce the ballot laws. See McCarthy v. Secretary of the Commonwealth, 371 Mass. 667, 676-677 & n.11 (1977).
The jurisdiction the plaintiffs invoke under G. L. c. 56, § 59, is an equitable one and the balance of equity does not favor them. As pointed out in the preceding section, the plaintiffs initially did not question the applicability of the commission’s discovery rule set out in § 1.01(8)(f), and complied with it. Given this state of affairs, the plaintiffs cannot claim that they did not have sufficient warning or that their interests were unjustly harmed. Moreover, the commission’s rule is a reasonable one, designed to allow the expeditious resolution of challenges such as are brought here. Equity does not demand that this rule be overlooked. Finally, we note that the objections we upheld in Hurst I were quite formal and — as the dissenters in that case pointed out, Hurst I, supra at 832 (Greaney, J., dissenting in part) — risked frustrating the will of the voters for *123the sake of establishing and enforcing a clearly administrable bright-line rule. The plaintiffs, having taken their stand and prevailed on the strict observance of a formal rule, are hardly in a position to ask for an equitable dispensation from another formal rule that does not favor them.
Statute 1997, c. 164, is entitled: “An Act relative to restructuring the electric utility industry in the commonwealth, regulating the provision of electricity and other services, and promoting enhanced consumer protections therein.”
In their original objection, the plaintiffs also alleged that, aside from the signatures contained in the petition forms containing the aforementioned defects, some individual signatures were forged. Without conceding that these signatures were forged, the defendants stipulated with the plaintiffs not to submit 272 of these signatures to the commission.
The defendants were required to submit at least 32,464 valid signatures to place the referendum on the official ballot. If the plaintiffs’ challenge to the signatures from Barnstable and Berkshire counties was properly-raised, then only 32,178 valid signatures were submitted by the defendants. If the challenge was improper, then 32,925 valid signatures were submitted by the defendants.
The defendants originally filed 8,783 signatures from Middlesex County. However, only 8,116 were allowed pursuant to the county distribution rule of art. 48, General Provisions, II, of the Amendments to the Massachusetts Constitution. The defendants therefore had submitted 667 excess signatures. The parties agreed during the commission proceedings that the defendants may draw from these excess signatures should any signatures from Middlesex County turn out to be invalid. Our decision in Hurst v. State Ballot Law Comm’n, 427 Mass. 825 (1998), rendered invalid 2,385 signatures from Middlesex County. We ordered that the commission consider the bearing of these excess signatures. Id. at 831 n.10. The parties’ dispute, however, does not turn on these excess signatures from Middlesex County as their addition does not put the number above the required minimum without all of the signatures from Barnstable and Berkshire counties.
This interpretation of the discovery rule is consistent with Jay Donovan vs. Richard Brenton, SBLC 90-2, a case in which the commission did not require a submission of a list of signatures and on which the plaintiffs in the present case rely. In Donovan, a challenge was based on an incorrect designation of the relevant district number on all nomination papers on which voter signatures were gathered in the town of Burlington. Because the defective nomination papers were restricted to one town, the exact number of allegedly invalid signatures was immediately evident to the commission and the defendant in that case. The rule may not be consistent, however, with Thomas Hamill vs. William C. Sawyer, SBLC 90-14, another case in which the commission did not require a submission of a list of signatures and on which the plaintiffs in the present case rely. The defect challenged in Hamill, which preceded the 1990 amendment to G. L. c. 53, § 22A, St. 1990, c. 269, § 11, was the use of *122“copies” of nomination papers. Although the challenge was to forms rather than to signatures, it was not clear from the challenge exactly how many signatures were alleged to be invalid. It also does not appear from the statement of reasons of the case whether the objector had designated by petition number the petitions to which he objected as being copies.
General Laws c. 56, § 59, states, in part: “The supreme judicial court and the superior court department of the trial court shall have jurisdiction of civil actions to enforce the provisions of chapters fifty to fifty-six, inclusive, and may award relief formerly available in equity or by mandamus.”