
512 F.3d 716 (2008)
HOWARD UNIVERSITY, Appellant
v.
METROPOLITAN CAMPUS POLICE OFFICER'S UNION, Appellee.
No. 07-7055.
United States Court of Appeals, District of Columbia Circuit.
Argued December 13, 2007.
Decided January 18, 2008.
*717 *718 Keith J. Harrison argued the cause for appellant. With him on the briefs were Trina L. Fairley and Daniel M. Creekman.
William G. Jepsen, Jr. argued the cause and filed the brief for appellee.
Before: GINSBURG, Chief Judge, and SENTELLE and GARLAND, Circuit Judges.
Opinion for the Court filed by Chief Judge GINSBURG.
GINSBURG, Chief Judge:
Howard University appeals from the judgment of the district court affirming an arbitration award in favor of the union that represents the campus police. Howard claims the arbitrator did not have jurisdiction to resolve the dispute and, by excluding certain evidence relevant to the merits, made an error so egregious as to constitute "misconduct." We affirm the judgment of the district court.

I. Background
The Metropolitan Campus Police Officer's Union is the exclusive representative of "officers, sergeants, and other security personnel" employed by the Howard University Campus. Police Department. In December 2003, H. Patrick Swygert and Carla McCormick, respectively the presidents of the University and of the Union, signed a collective bargaining agreement (CBA), Appendix C of which was styled "Wage Compensation Package" and contained a list of planned salary increases for covered employees. The CBA included this arbitration clause: "[A]n allegation that there has been a violation, misapplication, or misinterpretation of the terms of this Agreement shall [be subject to arbitration]."
In May 2004, the Union filed a grievance claiming Howard had not increased salaries in accordance with Appendix C. Howard, which did not object to resolving the grievance through arbitration, argued before the arbitrator that inclusion of Appendix C in the contract was a mutual mistake. According to Howard, the parties had not reached an agreement on the wage compensation package when they signed the contract; they had intended to table negotiations until after the Christmas holiday, and unintentionally included Appendix C in the executed agreement. The arbitrator framed the dispute as follows: *719 "Whether or not the Parties had a meeting of the minds on Appendix C, the Wage Compensation package."
The arbitrator conducted an evidentiary hearing in which she heard testimony from, among others, Howard's chief negotiator, Leroy Jenkins, and the Union president, Carla McCormick. President Swygert, who had signed the CBA on Howard's behalf, did not testify. In order to show the Union had not intended to include Appendix C in the agreement, Howard proffered the testimony of Kimberly Kline, the Union's chief negotiator. The Union objected that Kline's testimony violated its attorney-client privilege and the arbitrator excluded it. In a declaration filed in the district court, Kline said she would have testified as follows:
During open negotiations, the parties agreed to continue negotiating over the Wage Compensation Package after the Agreement was signed. Specifically, the parties agreed to continue negotiating certain pay increases that the union members would receive on the basis of seniority over the term of CBA.
Following execution of the Agreement, the parties did, in fact, continue to negotiate over the specified pay increases. Attached hereto as Exhibit I is an email that I forwarded to Leroy T. Jenkins, counsel for Howard University, dated February 9, 2004, which was almost two months after the Agreement was executed. The purpose of this email was to continue negotiating the pay increases.
Howard also proffered, and the arbitrator received into evidence, the February 9 email mentioned in the declaration. It reads:
LeroyCould you fax me the Performance Appraisal that is being used for the guards. I assume the drug testing facilities appendix that was being used in the last contract is still okay. Also, do you have comments/suggestions regarding the salary bands that were submitted?
The arbitrator sustained the Union's grievance. Finding the February 9 email ambiguous and noting that President Swygert did not testify for Howard, she concluded there was no "clear and concrete evidence" to support the University's contention that Appendix C was included in the CBA by mutual mistake. She therefore held the University was required to abide by the wage terms in the Appendix.
Howard moved for reconsideration, which the arbitrator denied. The Union then moved to confirm the arbitration award in the Superior Court of the District of Columbia, and Howard removed the case to district court pursuant to Section 301(a) of the Labor Management Relations Act, 29 U.S.C. § 185(a), which provides that "[s]uits for violation of contracts between an employer and a labor organization . . . may be brought in any district court of the United States having jurisdiction of the parties." Once in district court, Howard filed a motion to vacate the award, contending for the first time that the arbitrator "did not have substantive jurisdiction under the CBA to determine whether Howard University and the Union formed [a] `meeting of the minds'. . . ." Howard also argued the arbitrator had impermissibly excluded the testimony of Kimberly Kline.
The district court affirmed the award. Howard Univ. v. Metro. Campus Police Officer's Union, 519 F.Supp.2d 27 (D.D.C. 2007). The court agreed with Howard that whether there was a "meeting of the minds" on Appendix C did not fall within the scope of the arbitration clause in the CBA, but held Howard had forfeited that point because it did not make the argument during the arbitration. Id. at 31-35, *720 The district court then held that, assuming the arbitrator had erred in excluding Kline's testimony, the error did not constitute gross misconduct or deprive Howard of a fundamentally fair hearing and therefore did not provide a reason to vacate the award. Id. at 35-39.
Howard appealed to this court.

II. Analysis
We review the district court's decision de novo. Teamsters Local Union No. 61 v. UPS, Inc., 272 F.3d 600, 603 (D.C.Cir.2001). Under long-standing precedent, we may vacate a labor arbitration award only if it does not "draw[] its essence" from the terms of the collective bargaining agreement. United Steelworkers of Am. v. Enter. Wheel & Car Corp., 363 U.S. 593, 597, 80 S.Ct. 1358, 4 L.Ed.2d 1424 (1960). This leaves us very little scope for review:
While courts . . . may review the sub stance of an arbitration award, only the narrowest circumstances will justify setting the award aside. An arbitrator cannot, for instance, . . . ignore the contract and dispense his own brand of industrial justice. But if an arbitrator was arguably construing or applying the contract, a court must defer to the arbitrator's judgment.
Madison Hotel v. Hotel & Restaurant Employees, Local 25, 144 F.3d 855, 858-59 (D.C.Cir.1998) (en banc) (citations and internal quotation marks omitted).
That the arbitrator may have made a "mistake of law" does not affect the standard of review: The parties "have agreed to be bound by the arbitrator's interpretation without regard to whether a judge would reach the same result. . . ." Am. Postal Workers Union v. USPS (APWU), 789 F.2d 1, 6-7 (D.C.Cir.1986); see also Cole v. Burns Int'l Sec. Servs., 105 F.3d 1465, 1475 (D.C.Cir.1997) ("The deference due to arbitrators in the collective bargaining context may be justified even when arbitrators rely on `external' or `public' law in interpreting a collective bargaining agreement").
A. Arbitrability
Howard contends the arbitrator lacked jurisdiction to hear the grievance, but it did not raise this objection until it moved in the district court to vacate the award. As a result, the Union argues, the objection was forfeit.
We agree with the Union, as does every other circuit to have considered the issue: Absent excusable ignorance of a predicate fact, a party that does not object to the arbitrator's jurisdiction during the arbitration may not later do so in court. See United Indus. Workers v. Gov't of the V.I., 987 F.2d 162; 167-68 (3d Cir.1993); United Food and Commercial Workers, Local 400 v. Marval Poultry Co., Inc., 876 F.2d 346, 353 (4th Cir.1989); Jones Dairy Farm v. Local No. P-1236, United Food and Commercial Workers Int'l Union, 760 F.2d 173, 175-76 (7th Cir.1985); George Day Constr. Co. v. United Bhd. of Carpenters & Joiners of Am., Local 354, 722 F.2d 1471, 1475-76 (9th Cir.1984); Piggly Wiggly Operators' Warehouse, Inc. v. Piggly Wiggly Operators' Warehouse Indep. Truck Drivers Union, Local No. 1, 611 F.2d 580, 584 (5th Cir.1980); cf. Madison Hotel, 144 F.3d at 859-60 (Henderson, J., concurring in the judgment) We so hold for two reasons.
First, arbitration is a matter of consent; if a party submits to arbitration without objecting to the arbitrator's jurisdiction, then it may fairly be said to have consented to the arbitration, and the other party, having gone forward with the proceeding, may fairly be said to have relied upon that consent. See United Indus. *721 Workers, 987 F.2d at 168 ("Once the parties have mutually agreed to refer a matter to an arbitrator, they are bound by his decision and may not later challenge his authority to resolve the claim").
Second, requiring a party to object to the arbitrator's jurisdiction during the arbitration conserves resources. If a party objects to the arbitrator's jurisdiction and the arbitrator sustains the objection, then the, parties can go directly to court and, if the court affirms, avoid an unnecessary arbitration proceeding.
Howard invokes International Brotherhood of Electrical Workers, Local Union No. 545 v. Hope Electrical Corp., 380 F.3d 1084 (8th Cir.2004), but that case is not to the contrary. There, the court did permit an employer to object to an arbitrator's jurisdiction after the arbitration had concluded, but the employer had not participated in the arbitration, id. at 1101, and therefore could not be said to have consented to the arbitration. In this case Howard slept through its opportunity to object to the arbitrator's jurisdiction and may not avoid the consequence now that it has awakened.[*]
B. Exclusion of evidence
Howard contends the award should be vacated because the arbitrator excluded Kline's testimony, and points us to the Supreme Court's instruction to "look[ ] to the [Federal Arbitration Act] for guidance in labor arbitration cases." United Paperworkers Int'l Union v. Misco, Inc., 484 U.S. 29, 41 n. 9, 108 S.Ct. 364, 98 L.Ed.2d 286 (1987). The FAA provides a federal court may set aside an arbitration award when "the arbitrators were guilty of misconduct . . . in refusing to hear evidence pertinent and material to the controversy." 9 U.S.C. § 10(a)(3). The scope of review under this provision is narrow, however, because, as we have said before:
[I]n making evidentiary determinations, an arbitrator need not follow all the niceties observed by the federal courts. The arbitrator need only grant the parties a fundamentally fair hearing. . . .
[A] federal court may vacate an award only if the panel's refusal to hear pertinent and material evidence prejudices the rights of the parties to the arbitration proceedings.
Lessin v. Merrill Lynch, Pierce, Fenner & Smith, Inc., 481 F.3d 813, 816, 818 (D.C.Cir.2007) (citations, internal quotation marks, and alteration omitted).
Howard argues the arbitrator erred in excluding Kline's testimony based upon the attorney-client privilege because her testimony contained no privileged statements; it referred only to communications made in open negotiations with Howard. Moreover, Howard submits, her testimony spoke directly to the central issue at the hearing, that is, whether the parties had made a mutual mistake in including Appendix C in the CBA. It therefore contends this error was so prejudicial that it amounted to the type of "misconduct . . in refusing to hear evidence pertinent and *722 material to the controversy," 9 U.S.C. § 10(a)(3), that justifies vacating an arbitration award.
There was no misconduct in the exclusion of Kline's testimony. Although Howard is correct that testimony by an attorney describing statements made in open negotiations would not be subject to the attorney-client privilege in a federal court, see In re Sealed Case, 877 F.2d 976, 980 (D.C.Cir.1989), the arbitrator was not bound by the particulars of federal law governing the attorney-client privilege. See CBA § 30.3.4.2 ("[T]he conduct of the arbitration hearing shall be in accordance with the rules of the American Arbitration Association"); Labor Arbitration Rules of the American Arbitration Association, Rule 28 ("The arbitrator shall be the judge of the relevance and materiality of the evidence offered and conformity to legal rules of evidence shall not be necessary"); see also APWU, 789 F.2d at 6 ("When construction of the contract implicitly or directly requires an application of . . . statutory or decisional law, the parties have necessarily bargained for the arbitrator's interpretation of the law and are bound by it"). Accordingly, the question is not whether the arbitrator correctly applied federal law; the question is whether her decision to exclude the evidence out of a concern for a client's asserted interest in confidentiality amounted to "misconduct." Plainly it did not.
According to the declaration filed in the district court, Kline, speaking for the Union, made the statements at issue to Leroy Jenkins, Howard's chief negotiator, during the negotiations. At the arbitration hearing, Jenkins testified on Howard's behalf regarding these statements. Although Jenkins's testimony is not in the district court record, he could only have testified to the effect that the parties made a mutual mistakewhich means Kline's testimony would have been duplicative. The only value apparently to be added by Kline's testimony was that, as the attorney and chief negotiator for the Union, she could most credibly speak to the Union's intentions. Her credibility arose, however, from her direct knowledge of the Union's intentions during negotiations, and that knowledge derived at least in part from privileged communications and in whole from her representation of the Union, Therefore, the arbitrator's decision to bar Kline's testimony out of a concern for a client's interest in confidentiality, even if her testimony nominally contained only unprivileged statements, was certainly not misconduct.
Moreover, "a federal court may vacate an award only if the [arbitrator]'s refusal to hear pertinent and material evidence prejudices the rights of the parties to the arbitration proceedings." Lessin, 481 F.3d at 818 (internal quotation marks omitted). We see little if any prejudice to Howard from the exclusion of Kline's testimony. First, as noted, Jenkins could only have testified on Howard's behalf as to what was said during the negotiations, which was the sole topic of Kline's testimony. Second, the arbitrator based her decision in part upon the failure of Swygert, who signed the CBA for Howard, to testify as to the University's intentions; Kline's testimony would have done nothing to cure that defect in Howard's case.
But wait! Howard objects that Swygert had no knowledge of Howard's intentions and was merely "performing the ministerial act of signing the Agreement presented to him." Perhaps soHoward did not make that point when it moved for reconsideration, nor does it' claim in its brief to have made the point during the hearing but we cannot, consistent with the applicable standard of review, fault the arbitrator for drawing a negative inference from *723 Swygert's failure to testify. Cf. Hoxie v. DEA, 419 F.3d 477, 483 (6th Cir.2005) ("[A] negative inference can be drawn from a failure to testify in civil proceedings"); EZ Pawn Corp. v. Mancias, 934 S.W.2d 87, 90 (Tex.1996) ("We presume a party . . . who has the opportunity to read an arbitration agreement and signs it, knows its contents"). Nor does drawing such an inference approach in gravity the type of error that justifies vacating an arbitration award for misconduct.
Howard relies heavily upon three cases from other circuits, Tempo Shain Corp. v. Bertek, Inc., 120 F.3d 16 (2d Cir.1997); Gulf Coast Industrial Workers Union v. Exxon Co., 70 F.3d 847 (5th Cir.1995); and Hoteles Condado Beach v. Union De Tronquistas Local 901, 763 F.2d 34 (1 st Cir. 1985), in which the courts vacated arbitration awards on the ground of misconduct because the arbitrator failed to consider certain evidence. In each case, however, the court found the excluded evidence was critical to the proponent's case. In this case, as we have seen, the arbitrator acted reasonably in excluding the evidence based upon a concern for client confidentiality, and the exclusion of the evidence, far from being a serious blow to Howard's case, caused it little if any prejudice. In these circumstances, we have no reason to vacate the arbitration award for misconduct.

III. Conclusion
For the reasons set out above, the judgment of the district court is
Affirmed.
NOTES
[*]  In any event, the Union's allegation that Howard did not comply with Appendix C plainly fell within the parties' agreement to submit to arbitration any "allegation that there has been a violation . . . of the terms of this Agreement." The phrase "this Agreement" obviously refers to the contract duly executed by the parties. That an arbitrator may rule a rovision is unenforceable because the parties made a mutual mistake does not mean the provision is not part of the contract. See Buckeye Check Cashing, Inc. v. Cardegna, 546 U.S. 440, 448, 126 S.Ct. 1204, 163 L.Ed.2d 1038 (2006) (holding contracts that are voidable or void ab initio are still "contracts" within the meaning of the Federal Arbitration Act).
