Perretta, J.
Based upon his interpretation of the collective bargaining agreement between the city and the police unions, the arbitrator found that the city had violated the parties’ agreement by deducting ten percent of the cost of premiums for health maintenance organization (HMO) insurance from the pay of those officers insured under such plans and ordered the city to reimburse the officers for the deductions made during the fiscal year in dispute, 1991. A Superior Court judge determined that any error in the arbitrator’s decision was beyond the scope of judicial review and dismissed the city’s motion to vacate the award.1 The city argues on its appeal that, because the arbitrator’s award is based upon an error of law which taints his [672]*672decision and requires enforcement of an illegal parity clause, we should decide the controversy de novo rather than under the well-settled principle that an arbitrator’s errors of law are binding absent the existence of one of the grounds enumerated in G. L. c. 150C, § 11(a). We affirm the judgment. •
1. The police officers’ collective bargaining agreement. Paragraph 15.1(a) of Article 15 of the collective bargaining agreement between the parties, in effect from July 1, 1988, through June 30, 1991, provides, in pertinent part:
“The City agrees to maintain in effect for the duration of this Agreement the following programs of insurance: (a) Blue Cross-Blue Shield benefits as set forth in the Employee Booklet dated May 9, 1967 (effective January 1, 1967) which is hereby incorporated by reference. If greater benefits are adopted, for other city employees, such increased benefits shall be granted to employees under this agreement’2 (emphasis in original).
Because the city paid one hundred percent of the cost of the premium for its firefighters insured under HMO plans for fiscal year 1991, the police claimed that, based upon paragraph 15.1(a) of Article 15 of their bargaining agreement, they were entitled to reimbursement for their contributions to HMO premiums during the same fiscal year, July 1, 1990, through June 30, 1991.
2. The firefighters’ greater health benefits. To put the present dispute in context, it is necessary to explain why the firefighters insured under HMO plans contributed nothing toward the premiums during fiscal year 1991. The city’s agreement with its firefighters provided that the city agreed to maintain for the duration of the agreement, July 1, 1988, through June 30, 1991 (the same period as the police officers’ agreement), Blue Cross/ Blue Shield Municipal Master Medical Plan (Blue Cross/Blue Shield) insurance in effect on July 1, 1974, “or its equivalent” (emphasis supplied). Everett v. Labor Relations Commn., 416 [673]*673Mass. 620, 621 (1993) (Everett II). The agreement also provided that the amount of employee premium contributions to the offered insurance programs was fixed as of July 1, 1974, and that increases after that date would be borne by the city. Ibid. Because the cost of HMO coverage was less than the city’s contribution for the Blue Cross/Blue Shield plan, firefighters who elected HMO coverage contributed nothing toward the cost of the premiums for their coverage. Ibid.
General Laws c. 32B, § 16, was amended by St. 1989, c. 653, § 37, during the term of the firefighters’ agreement. As amended, § 16 requires that a public employee choosing HMO coverage contribute a “minimum of ten per cent of the total monthly premium cost” for his or her coverage. The statute, however, also contains a “savings” or “grandfather” provision. Chapter 653, § 218, provides in relevant part:
“Notwithstanding the [pertinent] provisions ... of section sixteen of chapter thirty-two of the General Laws, the percent contribution to the total monthly premium cost or rate for coverage under said section sixteen for any employees of any governmental unit where such percent contribution is determined by a collective bargaining agreement as of the effective date of this act shall not be altered until the expiration date of said collective bargaining agreement, unless the parties to said agreement agree otherwise.”
When, after the enactment of Chapter 653, the city announced that employees covered by an HMO would be required to contribute a minimum of ten percent toward the monthly premium cost, the firefighters’ union filed a charge with the Labor Relations Commission (commission) alleging that the city had engaged in a prohibited practice by unilaterally deducting ten percent of the HMO premium costs, thereby directly violating its duty to bargain under G. L. c. 150E, § 10(a)(5).3 Based upon the language of the firefighters’ agreement, that the city would provide the “Blue Cross/Blue Shield Municipal Master Medical Plan in effect on July 1, 1974,” or “its [674]*674equivalent,” Everett II, 416 Mass. at 625, and the testimony of the union’s president, that the parties to the agreement intended to treat HMO coverage the same as Blue Cross/Blue Shield, the commission found that the city had agreed to contribute the same amount for Blue Cross/Blue Shield or its equivalent, and that the city knew at the time it entered into the agreement that its terms would result in its payment of one hundred percent of the premiums for HMO coverage. Id. at 626. Because the city, under the bargaining agreement, had agreed to contribute the same dollar amount toward both types of coverage, the agreement determined the percentage contribution rate toward HMO coverage which was, therefore, entitled to the grandfather protection provided by St. 1989, c. 653, § 218. Id. at 626-627.
Based upon this reasoning, the commission ordered the city to reimburse the firefighters their ten percent contributions, with interest, which had been deducted from their pay from July 1, 1990, through June 30, 1991, the expiration date of the collective bargaining agreement. On the city’s appeal, the court found and concluded that the commission’s decision was based upon substantial evidence and “accepted] ” its determinations. Id. at 627.
3. The police unions’ first arbitration grievance. In 1992, while the dispute between the city and the firefighters was ongoing, the police officers’ unions filed a grievance against the city and proceeded to arbitration on the issue of whether the city violated its bargaining agreement with them by requiring that police officers who had elected HMO coverage contribute ten percent of the cost of HMO premiums. The decision of this arbitrator was issued subsequent to the commission’s decision on the firefighters’ complaint but prior to its affirmance in Everett II, 416 Mass. 620. He found that paragraph 15.1(a) of Article 15 of the police officers’ agreement did not refer to any insurance plan other than Blue Cross/Blue Shield, nor did it require the city to maintain “its equivalent,” as with the firefighters. He construed the “greater benefits” language of paragraph 15.1(a) to mean that “[a]ny qualitative or quantitative improvement in the health insurance benefit offered to other City employees would have to be given to . . . [police officers].” Based upon his interpretation of paragraph 15.1(a), this arbitrator determined [675]*675that the city had not violated the collective bargaining agreement and denied the unions’ grievance.4
4. The present grievance.
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Perretta, J.
Based upon his interpretation of the collective bargaining agreement between the city and the police unions, the arbitrator found that the city had violated the parties’ agreement by deducting ten percent of the cost of premiums for health maintenance organization (HMO) insurance from the pay of those officers insured under such plans and ordered the city to reimburse the officers for the deductions made during the fiscal year in dispute, 1991. A Superior Court judge determined that any error in the arbitrator’s decision was beyond the scope of judicial review and dismissed the city’s motion to vacate the award.1 The city argues on its appeal that, because the arbitrator’s award is based upon an error of law which taints his [672]*672decision and requires enforcement of an illegal parity clause, we should decide the controversy de novo rather than under the well-settled principle that an arbitrator’s errors of law are binding absent the existence of one of the grounds enumerated in G. L. c. 150C, § 11(a). We affirm the judgment. •
1. The police officers’ collective bargaining agreement. Paragraph 15.1(a) of Article 15 of the collective bargaining agreement between the parties, in effect from July 1, 1988, through June 30, 1991, provides, in pertinent part:
“The City agrees to maintain in effect for the duration of this Agreement the following programs of insurance: (a) Blue Cross-Blue Shield benefits as set forth in the Employee Booklet dated May 9, 1967 (effective January 1, 1967) which is hereby incorporated by reference. If greater benefits are adopted, for other city employees, such increased benefits shall be granted to employees under this agreement’2 (emphasis in original).
Because the city paid one hundred percent of the cost of the premium for its firefighters insured under HMO plans for fiscal year 1991, the police claimed that, based upon paragraph 15.1(a) of Article 15 of their bargaining agreement, they were entitled to reimbursement for their contributions to HMO premiums during the same fiscal year, July 1, 1990, through June 30, 1991.
2. The firefighters’ greater health benefits. To put the present dispute in context, it is necessary to explain why the firefighters insured under HMO plans contributed nothing toward the premiums during fiscal year 1991. The city’s agreement with its firefighters provided that the city agreed to maintain for the duration of the agreement, July 1, 1988, through June 30, 1991 (the same period as the police officers’ agreement), Blue Cross/ Blue Shield Municipal Master Medical Plan (Blue Cross/Blue Shield) insurance in effect on July 1, 1974, “or its equivalent” (emphasis supplied). Everett v. Labor Relations Commn., 416 [673]*673Mass. 620, 621 (1993) (Everett II). The agreement also provided that the amount of employee premium contributions to the offered insurance programs was fixed as of July 1, 1974, and that increases after that date would be borne by the city. Ibid. Because the cost of HMO coverage was less than the city’s contribution for the Blue Cross/Blue Shield plan, firefighters who elected HMO coverage contributed nothing toward the cost of the premiums for their coverage. Ibid.
General Laws c. 32B, § 16, was amended by St. 1989, c. 653, § 37, during the term of the firefighters’ agreement. As amended, § 16 requires that a public employee choosing HMO coverage contribute a “minimum of ten per cent of the total monthly premium cost” for his or her coverage. The statute, however, also contains a “savings” or “grandfather” provision. Chapter 653, § 218, provides in relevant part:
“Notwithstanding the [pertinent] provisions ... of section sixteen of chapter thirty-two of the General Laws, the percent contribution to the total monthly premium cost or rate for coverage under said section sixteen for any employees of any governmental unit where such percent contribution is determined by a collective bargaining agreement as of the effective date of this act shall not be altered until the expiration date of said collective bargaining agreement, unless the parties to said agreement agree otherwise.”
When, after the enactment of Chapter 653, the city announced that employees covered by an HMO would be required to contribute a minimum of ten percent toward the monthly premium cost, the firefighters’ union filed a charge with the Labor Relations Commission (commission) alleging that the city had engaged in a prohibited practice by unilaterally deducting ten percent of the HMO premium costs, thereby directly violating its duty to bargain under G. L. c. 150E, § 10(a)(5).3 Based upon the language of the firefighters’ agreement, that the city would provide the “Blue Cross/Blue Shield Municipal Master Medical Plan in effect on July 1, 1974,” or “its [674]*674equivalent,” Everett II, 416 Mass. at 625, and the testimony of the union’s president, that the parties to the agreement intended to treat HMO coverage the same as Blue Cross/Blue Shield, the commission found that the city had agreed to contribute the same amount for Blue Cross/Blue Shield or its equivalent, and that the city knew at the time it entered into the agreement that its terms would result in its payment of one hundred percent of the premiums for HMO coverage. Id. at 626. Because the city, under the bargaining agreement, had agreed to contribute the same dollar amount toward both types of coverage, the agreement determined the percentage contribution rate toward HMO coverage which was, therefore, entitled to the grandfather protection provided by St. 1989, c. 653, § 218. Id. at 626-627.
Based upon this reasoning, the commission ordered the city to reimburse the firefighters their ten percent contributions, with interest, which had been deducted from their pay from July 1, 1990, through June 30, 1991, the expiration date of the collective bargaining agreement. On the city’s appeal, the court found and concluded that the commission’s decision was based upon substantial evidence and “accepted] ” its determinations. Id. at 627.
3. The police unions’ first arbitration grievance. In 1992, while the dispute between the city and the firefighters was ongoing, the police officers’ unions filed a grievance against the city and proceeded to arbitration on the issue of whether the city violated its bargaining agreement with them by requiring that police officers who had elected HMO coverage contribute ten percent of the cost of HMO premiums. The decision of this arbitrator was issued subsequent to the commission’s decision on the firefighters’ complaint but prior to its affirmance in Everett II, 416 Mass. 620. He found that paragraph 15.1(a) of Article 15 of the police officers’ agreement did not refer to any insurance plan other than Blue Cross/Blue Shield, nor did it require the city to maintain “its equivalent,” as with the firefighters. He construed the “greater benefits” language of paragraph 15.1(a) to mean that “[a]ny qualitative or quantitative improvement in the health insurance benefit offered to other City employees would have to be given to . . . [police officers].” Based upon his interpretation of paragraph 15.1(a), this arbitrator determined [675]*675that the city had not violated the collective bargaining agreement and denied the unions’ grievance.4
4. The present grievance. Neither the city nor the police unions moved to confirm or vacate the decision of the arbitrator on the first grievance filed by the police officers’ unions. Instead, on March 31, 1994, three months after the court’s decision in Everett II, supra, the police officers filed the grievance now in issue. This arbitrator ruled that he was not bound by the decision of the first arbitrator because that decision “addressed a different article” of the bargaining agreement and because the police unions had “no actionable claim under Article 15” until the firefighters’ case before the commission was concluded.
Turning to the merits of the grievance, the arbitrator found that clauses similar to Article 15 “generally require an employer to give to one group of employees that which it gave to another group”; that the word “adopt,” as used in paragraph 15.1(a), was intended by the parties to be broader in meaning than “negotiate”; and that, had the city intended the word “adopt” to mean negotiated greater benefits, the city should have said so at the time the parties were negotiating the language of the agreement. The arbitrator ordered the city to reimburse police union members for the money deducted from their pay for contributions to the cost of HMO premiums for fiscal year 1991, and refused to consider whether his award violated G. L. c. 32B, § 16, as amended, and whether paragraph 15.1(a) of the bargaining agreement was an illegal parity contract. The arbitrator based his refusal on, inter alia, the fact that the parties had not authorized him to consider the effect of “external law” in construing their agreement.
5. Discussion. We will assume without deciding that the arbitrator committed an error of law in not binding the parties to the first arbitrator’s decision. See Bailey v. Metropolitan Property & Liab. Ins. Co., 24 Mass. App. Ct. 34, 35-37 (1987).5 The error, if any, is based upon the arbitrator’s reading of that decision and not a flagrant or arbitrary disregard for correct principles of law. See Marino v. Tagaris, 395 Mass. 397, 400 (1985). We will further assume without deciding that, as the city claims, the arbitrator’s award is based upon an erroneous [676]*676interpretation of the word “adopt” in paragraph 15.1(a). See Swampscott Educ. Assn. v. Swampscott, 391 Mass. 864, 866-868 (1984).
Neither of these assumed errors would provide us with a basis for setting aside the award. “A matter submitted to arbitration is subject to a very narrow scope of review. Absent fraud, errors of law or fact are not sufficient grounds to set aside an award. See Trustees of Boston & Me. Corp. v. Massachusetts Bay Transp. Authy., 363 Mass. 386, 390 (1973). ‘Even a grossly erroneous decision is binding . . . .’Id. Courts inquire into an arbitration award only to determine if the arbitrator has exceeded the scope of his authority, or decided the matter based on ‘fraud, arbitrary conduct, or procedural irregularity in the hearings.’ Marino v. Tagaris, 395 Mass. 397, 400 (1985), quoting Greene v. Mari & Sons Flooring Co., 362 Mass. 560, 563 (1972).” Plymouth-Carver Regional Sch. Dist. v. J. Farmer & Co., 407 Mass. 1006, 1007 (1990).
We next take up the question whether the arbitrator’s award requires the city to violate G. L. c. 32B, § 16, and the public policy of the Commonwealth. “Arbitration, it is clear, may not ‘award relief of a nature which offends public policy or which directs or requires a result contrary to express statutory provision,’ S.E. Eager, The Arbitration Contract and Proceedings § 121.6 (1971), or otherwise transcends the limits of the contract of which the agreement to arbitrate is but a part.” Lawrence v. Falzarano, 380 Mass. 18, 28 (1980). Because we are required to determine whether the award must be set aside on either of these bases, we need not separately consider the arbitrator’s refusal to look to external law on these issues. But see Billerica v. International Assn. of Firefighters, Local 1495, 415 Mass. 692, 693 n.1 (1993), where an arbitrator’s refusal to look to external law in ordering enforcement of a minimum-staffing requirement during the second year of a collective bargaining agreement in the absence of available appropriated funds was said “to be an unsatisfactory approach to dispute resolution, particularly because one of the issues stipulated to the arbitrator was what the remedy should be if the town violated the terms of the agreement.”
The arbitrator’s award is not contrary to G. L. c. 32B, § 16, as amended.
“In enacting St. 1989, c. 653, §§ 37 and 218, the [677]*677Legislature was undoubtedly aware of the following: (a) that there was no prior legislative authorization mandating contribution from employees for the cost of HMO premiums; (b) that existing collective bargaining agreements were likely to contain provisions which required governmental units to contribute on an equal dollars basis ... to the payment of premium costs for both group indemnity and HMO plans; (c) that some protection for these provisions was necessary to avoid a claim that the new assessment authorized by § 37 unlawfully impaired rights protected by existing collective bargaining agreements; and (d) that there could be myriad variations in existing collective bargaining agreements concerning employee health care benefits and payment of the premiums therefor which could require interpretation.”
Everett v. Local 1656, Intl. Assn. of Firefighters, 411 Mass. 361, 366 (1991) (Everett I).
Although the arbitrator’s interpretation of the word “adopt” may have erroneously swept the police officers into the grandfather provision of § 218, his award is not contrary to the language or the intent of G. L. c. 32B, § 16, as amended.
It is also the city’s position that the arbitrator’s award must be set aside because it is based upon a parity clause, paragraph 15.1(a) of Article 15 of the bargaining agreement, which violates public policy.
In Massachusetts Hy. Dept. v. American Fedn. of State, County & Mun. Employees, 420 Mass. 13, 16 (1995), the court stated: “To be vindicated, public policy ‘must be well defined and dominant, and is to be ascertained “by reference to the laws and legal precedents and not from general considerations of supposed public interests.” ’ W.R. Grace & Co. v. Local Union 759, Intl. Union of United Rubber, Cork, Linoleum & Plastic Workers, 461 U.S. 757, 766 (1983), quoting Muschany v. United States, 324 U.S. 49, 66 (1945).”
The commission has found that parity agreements “must be considered as unlawful, as they impair the ability of the exclusive representative to fulfill its obligations of bargaining on behalf of the employees it represents.” Medford Sch. Comm., 3 MLC 1413, 1414 (1977). See Town of Andover, 18 MLC 1311, 1313 (1992). Contrast City of Beverly, 19 MLC 1725, 1728-1730 (1993), where the disputed clause was held to be a valid “work-preservation” clause and not a parity provision.
[678]*678We are not prepared to hold that the clause in dispute is a parity clause which violates clearly defined and established public policy until the commission (see note 2, supra) at least has had the opportunity to consider the clause and determine whether it had any impact on the bargaining process between the city and the police officers’ unions in negotiating the agreement in issue. These very questions have been pending before the commission without decision for quite some time because of the parties’ failure, for whatever reason, to file a joint stipulation of facts.
At oral argument, the parties resisted our suggestion that this appeal be stayed pending completion of the proceedings before the commission. They argued that the public policy issue is a question of law and that because either party could appeal the commission’s decision, the issue should be resolved by us sooner rather than later. On the limited record before us and in light of the procedural posture created by the parties in presenting this appeal, we refuse to consider whether parity clauses are per se illegal and in violation of public policy. Instead, and based upon the fact that the unions understandably do not complain about the greater benefits their members received under the agreement, which was limited in time and which does not appear to have prevented the city from bargaining with its other employees, we conclude that enforcement of paragraph 15.1(a) of Article 15 of the agreement, as construed by the arbitrator, does not violate a well-defined and dominant public policy, ascertained from laws and legal precedents. Massachusetts Hy. Dept. v. American Fedn. of State, County & Mun. Employees, 420 Mass. at 16.
It follows from what we have said that the judgment of the Superior Court dismissing the city’s motion to vacate the arbitrator’s award is affirmed.
So ordered.