Pursuant to a collective bargaining agreement, Boston police Officer John Bergquist grieved, then demanded arbitration regarding, a three-day suspension. An arbitrator upheld the charge of the city of Boston (city) that Bergquist had engaged in conduct unbecoming an officer, but found in favor of Bergquist on the charges of neglect of duty and failure to obey the orders and directives of a superior. The arbitrator then concluded that, given proof of only the single charge and Bergquist’s prior clean disciplinary record, a three-day suspension was excessive, and ordered that the penalty be reduced to a written reprimand.

*673The city commenced an action to vacate the arbitrator’s award, see G. L. c. 150C, § 11, on the ground that the arbitrator, having found that one of the charges had been proved, exceeded her authority by substituting her judgment for that of the city regarding the penalty to be imposed. A judge of the Superior Court agreed and entered a judgment that vacated the portion of the arbitrator’s award reducing the penalty and that affirmed the three-day suspension.1 The Boston Police Patrolmen’s Association, Bergquist’s union, appealed on his behalf. We reverse and reinstate the arbitrator’s award.

1. Background. The case arises out of a dispute between Bergquist and his patrol supervisor, Sergeant David Allen, regarding Bergquist’s alleged failure to write parking tickets. The facts pertaining to the confrontation are disputed, but a decision in this appeal does not turn on resolving the factual disagreements. The case was precipitated by a written notice served on Bergquist by Captain Frederick Daniels that set forth that Bergquist would be suspended for three days for violating department rules governing conduct unbecoming an officer, neglect of duty, and failure to obey orders and directives. Bergquist made a timely request for a departmental hearing; the hearing was conducted; and the suspension was upheld by the police commissioner. The union, in accordance with an applicable collective bargaining agreement, filed a grievance on Bergquist’s behalf; the grievance was denied after a hearing; and the union demanded arbitration.

The single arbitrator formulated the issues as follows:2 “Is the grievance arbitrable?[3] Was there just cause to discipline Officer John Bergquist for his conduct on December 5, 1998? If not, what shall be the remedy?” Following the arbitrator’s conclusion that the city had failed to prove two of the three charges and her reduction of the discipline from a three-day suspension to a letter of reprimand, the city filed a complaint in *674the Superior Court praying that the award be vacated. By means of a counterclaim, the union sought confirmation of the award. The union’s appeal from the judgment vacating the arbitrator’s award brings the case to this court.

2. Discussion. “Unlike our review of factual findings and legal rulings made by a trial judge, we are strictly bound by an arbitrator’s findings and legal conclusions, even if they appear erroneous, inconsistent, or unsupported by the record at the arbitration hearing.” Lynn v. Thompson, 435 Mass. 54, 61, cert, denied, 534 U.S. 1131 (2001). We do not mean thus to suggest any view of the merits of the arbitrator’s decision here. We mean only to emphasize that the parties, having contractually agreed to abide by the determination of a third party, cannot ordinarily obtain judicial relief if they disagree with the decision rendered by the individual whom they have empowered to adjudicate the controversy. Exceptions to this principle are limited. See G. L. c. 150C, § 11. Fraud or other impropriety may furnish a basis for setting aside an arbitration award. See Plymouth-Carver Regional Sch. Dist. v. J. Farmer & Co., 407 Mass. 1006, 1007 (1990). Likewise, confirmation shall be denied where the relief awarded offends public policy. See Bureau of Special Investigations v. Coalition of Pub. Safety, 430 Mass. 601, 603 (2000). Such allegations are not present here. However, arbitration being the product of an agreement, the arbitrator is without authority to decide matters outside the scope of what the parties have agreed shall be arbitrated. This is reflected in G. L. c. 150C, § 11(a), which provides in relevant part that “[ujpon application of a party, the superior court shall vacate an award if . . . (3) the arbitrators exceeded their powers.”

Here, the union argues that the arbitrator acted within her authority because, under Article V A, § 1, of the collective bargaining agreement, Bergquist was entitled not to be “disciplined or discharged without just cause.” In this regard, the union asserts that the concept of “just cause” requires consideration of the severity of the penalty that has been imposed in relationship to the offense. On its part, the city contends that the arbitrator was authorized to consider only whether the facts justified the imposition of discipline at all, and, if so, that the discipline imposed was beyond the scope of the parties’ referral.

*675The dispute is exacerbated at the outset by the lack of agreement regarding the source of the three issues formulated by the arbitrator. The union denies that the parties “agreed to” the formulation of the issues as set forth in the arbitrator’s decision. The city states that the parties “asked the arbitrator to answer only a limited question,” which the city expresses as “whether there was just cause to discipline the Officer for his conduct on the day in question.” The judge appears to have adopted the city’s position, stating that the parties agreed to the question, “Was there just cause to discipline Officer John Bergquist for conduct on December 5, 1998,” and remarking that the arbitrator “added” the question, “If not, what shall be the remedy?”

Because the scope of the arbitrator’s authority is central to a resolution of this dispute, indeed central to all arbitrations, it is with some bewilderment that we note that these parties, each experienced in the collective bargaining arena, appear to have arbitrated this case without sharing an understanding of what the arbitrator was being asked to decide. We turn to the pleadings to resolve the dilemma. In its complaint seeking to vacate the arbitration award, the city alleged as follows in paragraph 9: “The parties agreed to submit the following issues to an arbitrator for her determination: a. Is the grievance arbitrable? b. Was there just cause to discipline Officer John Bergquist for his conduct on December 5, 1998? c. If not, what shall be the remedy?” In its answer to the complaint, the union admitted the allegations of the said paragraph 9. “In any civil action pleadings shall not be evidence on the trial, but the allegations therein shall bind the party making them.” G. L. c. 231, § 87. Whether proceedings to confirm or vacate an arbitration award constitute a “civil action” need not consume our attention. At least in this case, where the proceedings were initiated by a complaint asserting factual propositions, followed by an answer responding to the factual allegations, the principle applies. Consequently, the portions of the pleadings referred to became the equivalent of a stipulation on the subject, and we govern ourselves accordingly in our analysis.4

Given the formulation of the questions, there is little doubt *676that the parties referred to the arbitrator the issue of the justice of the penalty. Otherwise, the third question, as to remedy, becomes meaningless. That question cannot be considered in a vacuum, but instead must be read with the second question. Thus, in the second question, the arbitrator was asked whether there was “just cause to discipline Officer John Bergquist for his conduct.” To this inquiry, there appear at first blush to be two possible responses: there was just cause or there was not just cause. The latter finding without more (i.e., that there was no just cause for discipline) would presumably end the case, the city would lose, and the officer would be restored to his position without any adverse consequences.

However, the third question demonstrates that the referral to the arbitrator was not intended to be so simple. That question (“If not, what shall be the remedy?”) presupposes that the arbitrator has answered the second question in the negative: in other words, that there has been a determination that the city did not have just cause to discipline Officer Bergquist. Nevertheless, the inquiry does not end at this point. Rather, the parties specifically requested that the arbitrator, having concluded that just cause was lacking, decide what would be an appropriate remedy.

The third question makes sense only on the view that a consideration of “just cause to discipline” includes whether the discipline was suitable in light of the offense. The city’s theory that the penalty was outside the arbitrator’s jurisdiction fails to account for the presence of a question that explicitly refers to “the remedy.” We conclude that the parties anticipated the possibility that the arbitrator would determine that the sanction visited on Officer Bergquist was too harsh (either because it was excessive in the light of fully proved charges, or because, as here, not all the charges were proved), and, should that occur, left to the arbitrator the task of fashioning a penalty that was suitable.5 Arbitration of the level of discipline is also consistent with the definition of the term “grievance” in Article VI, § 1, *677of the collective bargaining agreement, i.e., “any dispute concerning the interpretation, application, or enforcement of this Agreement.”

Given this “broad arbitration clause,” see Local No. 1710, Intl. Assn. of Firefighters, AFL-CIO v. Chicopee, 430 Mass. 417, 422 (1999), we are satisfied that the severity with which this municipal employer treats its police officers in disciplinary proceedings can be the subject of a grievance. Indeed, collective bargaining agreements “usually do not limit the arbitrator’s power to formulate remedies in discharge or discipline cases,” and arbitrators “have consistently held that an excessively harsh penalty for misconduct violates the requirement that discipline be imposed only for just cause.” American Bar Association, Discipline & Discharge in Arbitration, at 85-86 (Norman Brand ed., 1998). “Normally, an arbitrator is authorized to disagree with the sanction imposed for employee misconduct.” United Paperworkers Intl. Union, AFL-CIO v. Misco, Inc., 484 U.S. 29, 41 (1987) (case under Federal Arbitration Act). For the reasons stated above, we conclude that the parties, consistent with the collective bargaining agreement, included the level of discipline within the arbitral reference. The arbitrator’s resolution of issues within the scope of the parties’ reference is final. See Plymouth-Carver Regional Sch. Dist. v. J. Farmer & Co., 407 Mass. at 1007.

3. Conclusion. The judgment of the Superior Court is reversed. Judgment shall enter confirming the arbitrator’s award.

So ordered.