OPINION OF THE COURT
In this appeal we are asked whether an arbitrator acted properly when she determined that respondent Board of Education of the City of New York (the Board) arbitrarily selected teachers for an after-school reading program, and ordered the Board to provide a position to a qualified applicant whom the principal had passed over. We conclude that the award did not violate public policy and the arbitrator did not exceed her authority under the collective bargaining agreement.
I.
In September 1998 New York City School District 26 posted an announcement for anticipated vacancies in the position of “Per Session Teacher—Project Read After-School Program” in its elementary schools. The announcement set forth selection criteria, including a preference for teachers holding “Early Childhood/Reading License[s].”
Linda Feil applied for this position. While she did not hold either of the preferred licenses, she did have a “common branch” license and 26 years of primary school teaching experience, most recently as a third-grade teacher at PS 173. In addition, she had taught as a substitute teacher in Project Read and another reading program at PS 173.
The principal of PS 173 filled six openings in Project Read from the pool of applicants who responded to the posting. He did not select Feil, instead offering her work as a “primary *76substitute.” He also advised her that other district schools had inquired “if any of our excellent teachers would be available to teach Project Read in those schools.” He asked her to let him know right away if she was interested in this possibility. Of the six teachers whom the principal selected for a position in Project Read, two had the preferred licenses and less seniority than Feil. The remaining four did not have the preferred licenses; two had more seniority than Feil, two had less. The parties do not dispute that the six selected teachers are qualified; the parties do not dispute that Feil is qualified.
Feil’s union, appellant United Federation of Teachers (UFT), filed a grievance in Feil’s behalf under articles fifteen and twenty of the collective bargaining agreement (CBA). Article twenty-two of the CBA prescribes a four-stage grievance process, culminating in arbitration if the grievance is not otherwise resolved.
During a Step 2 grievance conference, UFT argued that Feil had been improperly denied a position in Project Read because she was qualified and more senior than two of the successful applicants. The principal replied that while he believed that Feil was a satisfactory teacher, the teachers he selected had, in his judgment and based on their applications, a greater level of specific teaching experience, which he detailed. He acknowledged that he took into consideration his personal observations of the various applicants in the classroom during his 15 years as principal. The deputy superintendent denied the grievance. He found that while satisfactory teaching and seniority were compelling selection criteria, they were not required by the posting and did not control the selection process for Project Read, a specialized program.
After a Step 3 hearing, the Chancellor’s representative found that the applicants were not equally qualified for the positions, and denied the grievance. UFT filed a demand for arbitration. The Board did not move to stay the arbitration, and so the grievance was submitted to an arbitrator jointly selected by UFT and the Board pursuant to the CBA.
The arbitrator accepted UFT’s formulation of the issue:
“Did the Board violate Articles Fifteen and Twenty of the 1995-2000 collective bargaining agreement when it denied Grievant Linda Feil, a teacher at PS. 173, the per session position of After-School Project Teacher at PS. 173? If so, what shall be the remedy?”
*77The arbitrator rejected UFT’s argument that the Project Read selection process was governed by the seniority provisions in article fifteen of the CBA entitled “Rates of Pay and Working Conditions of Per Session Teachers.” Instead, she found that the matter involved the application of article twenty of the CBA, entitled “Matters Not Covered.”1
The arbitrator also found that while the CBA contained no selection criteria for Project Read, “[t]he selection of teachers for positions in programs which are not covered by the Agreement [is] governed by managerial discretion.” The arbitrator determined that her power to decide whether the Board’s exercise of this discretion was arbitrary or capricious derived from article twenty-two (C) of the CBA.2
The arbitrator emphasized that Feil was well qualified for the position, and had more seniority than two of the teachers who were selected for the program. She recited testimony from another teacher who had been rejected for a position in Project Read the previous year because she was the most junior applicant. She discredited the principal’s testimony that the *78preferred license was a governing factor because four of the successful applicants did not hold this license. She found that there was no documentary evidence supporting the principal’s position that the successful applicants were better qualified for the positions than Feil, and concluded that the “selection process was arbitrary in nature.”
The award, issued on August 9, 1999, found that the Board violated article twenty of the CBA by acting in an arbitrary manner when selecting teachers for positions in Project Read. The arbitrator directed the Board to place Feil in Project Read at PS 173 for the 1999-2000 school year, and to award her back pay.
The Board appointed Feil to the position, but resisted the back pay award. Pursuant to CPLR article 75, UFT moved in Supreme Court to confirm the award. The Board cross-moved to vacate under CPLR 7511 (b) (1) (iii), arguing that the arbitrator exceeded her authority. Supreme Court confirmed the award and denied the Board’s cross motion. The Appellate Division unanimously reversed, vacating the award and holding that “this award violates public policy by impermissibly infringing on the nondelegable responsibility of the public school system to maintain educational standards” (298 AD2d 60, 61-62 [1st Dept 2002]). As an alternative basis for reversal, the Appellate Division found that the award “exceeded the arbitrator’s power” under the CBA (id. at 62).
II.
We begin our analysis by determining which of the parties’ arguments are subject to our review. We conclude, as the Appellate Division did, that by failing to move to stay and participating in the arbitration, the Board waived its right to seek vacatur of the award on the basis that the parties did not agree to arbitrate disputes arising out of Project Read. We further conclude that the Board’s actions did not forfeit its right to seek vacatur of the award on public policy grounds.
The role of public policy in restricting an arbitrator’s power to resolve disputes arises at two distinct points on the arbitration continuum. It first appears as a ground for obtaining a stay of arbitration when a party challenges the arbitrability of a dispute. It reappears as a ground for vacating the award as being made in excess of the arbitrator’s powers.
In Matter of City of Johnstown (Johnstown Police Benevolent Assn.) (99 NY2d 273 [2002]), we stated a two-part test for *79determining the arbitrability of a dispute: the “did-they-agree-to-arbitrate” prong, which requires that we examine the agreement to determine what issues the parties agreed to submit to arbitration; and the “may-they-arbitrate” prong, which asks “whether there is any statutory, constitutional or public policy prohibition against arbitration of the grievance” (99 NY2d at 278 [citations omitted]).
Because arbitrability is a threshold question going to the arbitrator’s power to resolve the dispute, a party can seek judicial intervention to determine whether the dispute is arbitrable before consenting to arbitration. Moreover, the CPLR requires that in order to raise the “did-they-agree-to-arbitrate” prong of arbitrability in a motion to vacate, a party must move to stay before participating in arbitration (compare CPLR 7511 [b] [1] with CPLR 7511 [b] [2]). Of course, a party may choose not to move to stay arbitration for a variety of legitimate economic or tactical reasons. But with forbearance comes risk: a party that participates in the arbitration may not later seek to vacate the award by claiming it never agreed to arbitrate the dispute in the first place (see Rochester City School Dist. v Rochester Teachers Assn., 41 NY2d 578, 583 [1977]).
By contrast, a party is not required to raise the “may-they-arbitrate” prong on a motion to stay, and may later seek to vacate an award as violative of public policy. Indeed, while public policy may be raised on a motion to stay, it can also be raised for the first time on a motion to vacate (see Hirsch v Hirsch, 37 NY2d 312, 315 [1975] [“(A) challenge to the arbitrability of an issue on public policy grounds may be made either on an application for a stay of arbitration . . . (or) on a motion to vacate the award” (citations omitted)]; see also Matter of Professional, Clerical, Tech. Empls. Assn. [Buffalo Bd. of Educ.], 90 NY2d 364, 373 [1997]).
We next consider whether the award violates public policy and whether the arbitrator exceeded her powers under the CBA.
III.
An arbitration award may be vacated on three narrow grounds: “it violates a strong public policy, is irrational, or clearly exceeds a specifically enumerated limitation on the arbitrator’s power” (Matter of Board of Educ. of Arlington Cent. School Dist. v Arlington Teachers Assn., 78 NY2d 33, 37 [1991] [citations omitted]). Only the public policy and enumerated powers grounds are disputed here.
*80As we recently stated, the scope of the public policy exception to an arbitrator’s power to resolve disputes is extremely narrow (see Matter of New York City Tr. Auth. v Transport Workers Union of Am., Local 100, AFL-CIO, 99 NY2d 1, 6-7 [2002] [“(J)udicial intervention on public policy grounds constitutes a narrow exception to the otherwise broad power of parties to agree to arbitrate all of the disputes arising out of their juridical relationships, and the correlative, expansive power of arbitrators to fashion fair determinations of the parties’ rights and remedies”]).3 Moreover, “judicial restraint under the public policy exception is particularly appropriate in arbitrations pursuant to public employment collective bargaining agreements” (id. at 7).
In Transport Workers, we established a two-prong test for determining whether an arbitration award violates public policy. First, where a court can conclude “without engaging in any extended factfinding or legal analysis” that a law “prohibit[s], in an absolute sense, [the] particular matters [to be] decided ... by [arbitration]” (99 NY2d at 8, 9 [citations and emphasis omitted]), an arbitrator cannot act. Second, an arbitrator cannot issue an award where “the award itself ‘violate [s] a well-defined constitutional, statutory or common law of this State’ ” (id. at 11 [citation omitted]).
Transport Workers spoke to whether two awards should be vacated on public policy grounds because they improperly infringed on the employer’s statutory duty “[t]o exercise all requisite and necessary authority to manage, control and direct the maintenance and operation of transit facilities . . . for the convenience and safety of the public” (99 NY2d at 8, quoting Public Authorities Law § 1204 [15]). We upheld the awards, finding that Public Authorities Law § 1204 (15) contained only a general responsibility that did not prohibit delegation of the duty “in an absolute sense” (99 NY2d at 9), and that no other well-defined law or policy barred the awards.
Citing Matter of Cohoes City School Dist. v Cohoes Teachers Assn. (40 NY2d 774 [1976]), Matter of Candor Cent. School Dist. (Candor Teachers Assn.) (42 NY2d 266 [1977]) and Honeoye Falls-Lima Cent. School Dist. v Honeoye Falls-Lima Educ. Assn. (49 NY2d 732 [1980]), the Board argues that this award should be vacated because public policy prohibits it from bargaining *81away its vested responsibility to determine if a candidate is qualified for a teaching position. We have never held, however, that an award violates public policy if it affects teacher qualifications (see Matter of Enlarged City School Dist. of Troy [Troy Teachers Assn.], 69 NY2d 905, 907 [1987] [“Even assuming that the School District must remain the ultimate judge of an applicant’s qualifications . . .” (emphasis added)]). Moreover, even if we had, this “policy” is not triggered by the facts here, as the award did not force the Board to hire or select a nonqualified candidate for a teaching position. Rather, the award overruled the Board’s decision not to select a particular qualified candidate where the arbitrator found the selection process arbitrary and capricious (see Matter of Middle Country Teachers Assn. v Middle Country Cent. School Dist., 231 AD2d 570, 572 [2d Dept 1996], Iv denied 89 NY2d 806 [1997] [declining to vacate award in favor of grievant as against public policy where grievant, the “weakest qualified applicant,” was nonetheless qualified]).
The Board further relies on Honeoye for the principle that public policy prohibits a school board from “surrender [ing] through collective bargaining a responsibility vested in the board in the interest of maintaining adequate standards in the classrooms” (49 NY2d at 734 [emphasis added]). We have never held, however, that the interest of “maintaining adequate standards” is, standing alone, sufficient to vacate an award as violative of public policy (see Cohoes City School Dist., 40 NY2d at 775-778 [public policy bars delegation of tenure decisions]; Candor Cent. School Dist., 42 NY2d at 271 [public policy bars delegation of right to terminate a probationary appointment at the close of the probationary period]; Honeoye, 49 NY2d at 733 [public policy bars delegation of responsibility for implementing layoffs]). This maintenance-of-adequate-standards principle is akin to the statute we reviewed in Transport Workers. It is a general responsibility and does not “prohibit, in an absolute sense,” an arbitrator from reviewing a school’s selection from among qualified candidates for an after-school position. It is only when the interest in maintaining adequate standards is attached to a well-defined law that public policy is implicated. The Board points to no such law applicable to the decision made here, and so cannot meet the second prong of the Transport Workers test.
Next, Matter of Three Vil. Teachers’ Assn. v Three Vil. Cent. School Dist. (128 AD2d 626 [2d Dept 1987], Iv denied 70 NY2d 608 [1987]), relied on by the Appellate Division below, does not *82control the outcome here. In Three Village, the Court found that the “school district’s ultimate responsibility to determine the qualifications required and preferred for a particular teaching position . . . and to determine whether a prospective applicant is possessed of those qualifications is a responsibility of the type that may not be bargained away, as it is central to the maintenance of adequate standards in the classroom” (128 AD2d at 627 [citation omitted]).
Importantly, the Three Village court found that the award violated Education Law § 2573 (9), which provides that no teacher “shall be appointed to the teaching force of a city who does not possess qualifications required under this chapter and under the regulations prescribed by the commissioner of education.” Here, the award does not impinge on the school’s responsibility to appoint qualified teachers to positions in the public schools, nor is Education Law § 2573 (9) even applicable. Three Village also involved a “past practice” that “permitted the school district a degree of discretion” in determining teacher qualifications (128 AD2d at 627).4
Given the narrow scope of the public policy exception to an arbitrator’s powers, we decline to find that public policy has an interest in choosing from among qualified candidates for after-school teaching positions. The Board has provided no reason why public policy requires such a result. The question left open in Enlarged City School Dist. is not implicated on these facts, and so we leave its resolution for another day.
Finally, we also disagree with the Appellate Division’s alternative conclusion that the arbitrator exceeded the scope of her authority under the CBA. “[I]t is not for the courts to interpret the substantive conditions of the contract or to *83determine the merits of the dispute” (Board of Educ., Lakeland Cent. School Dist. of Shrub Oak v Barni, 51 NY2d 894, 895 [1980]). This is true “even where ‘the apparent, or even the plain, meaning of the words’ of the contract has been disregarded” (Maross Constr. v Central N.Y. Regional Transp. Auth., 66 NY2d 341, 346 [1985] [citation omitted]). In Matter of New York State Correctional Officers & Police Benevolent Assn. v State of New York (94 NY2d 321 [1999]), we refused to disturb an award, cognizant of the fact that “[a] court cannot examine the merits of an arbitration award and substitute its judgment for that of the arbitrator simply because it believes its interpretation would be the better one. Indeed, even in circumstances where an arbitrator makes errors of law or fact, courts will not assume the role of overseers to conform the award to their sense of justice” (id. at 326 [citations omitted and emphasis added]).
The arbitrator determined that the dispute fell within the scope of article twenty of the CBA. She found that the principal’s decisionmaking process was arbitrary and capricious. These interpretations and factual findings appear highly debatable on this record; however, whether we agree with the arbitrator is beside the point. Further, the Board may not revive what is, in actuality, a challenge to arbitrability in another guise. By submitting to arbitration, the Board ran the risk that the arbitrator would find Project Read covered under some provision of the CBA, as she did, notwithstanding the Board’s position that Project Read positions were outside the agreement’s scope.
Having determined that the selection process for Project Read was encompassed within article twenty, the arbitrator had the authority under article twenty-two to find that the Board’s exercise of its discretion under this provision was arbitrary and capricious, and to fashion an appropriate remedy. In finding that the arbitrator had “couched her analysis of the case in procedural terms” but that her decision was really “directed at the substantive grounds on which the selection was made” (298 AD2d at 66), the Appellate Division went beyond the face of the award and substituted its judgment for the arbitrator’s. This was error.
Accordingly, the order of the Appellate Division should be reversed, with costs, and the order and judgment of Supreme Court reinstated.
*84Chief Judge Kaye and Judges G.B. Smith, Ciparick, Rosenblatt and Gbaffeo concur.
Order reversed, etc.