DYK, Circuit Judge.

Harold D. Vicente Colon , with whom Harold D. Vicente-González and Vicente & Cuebas were on brief, for appellants.

Luis A. Oliver , with whom Melissa Hernández-Carrasquillo and Fiddler González & Rodríguez, PSC were on brief, for appellees.

Mark C. Fleming , Ari J. Savitzky , Peter J. Macdonald , Ross E. Firsenbaum , Adriel I. Cepeda Derieux , Michael J. Morillo , and Wilmer Cutler Pickering Hale and Dorr LLP on brief for UBS Financial Services Inc. and UBS Financial Services Incorporated of Puerto Rico, amici curiae.

Before Howard, Chief Judge, Dyk and Thompson, Circuit Judges.

DYK, Circuit Judge.

This case requires us to determine the test for district court federal question jurisdiction in the context of motions to vacate or modify an arbitration award. This turns on whether the court may look through the motion to the underlying dispute to determine whether the court would have federal question jurisdiction. Here, the district court applied the look-through test, finding that jurisdiction existed and that there was no basis for setting aside the award. We affirm, holding that the look-through approach is the correct test, that federal jurisdiction existed, and that the district court did not err in refusing to vacate the award and in confirming it.

I.

In 2006, appellants Dr. Luis Ortiz-Espinosa and his wife, Maritza Soto-Garcia; the conjugal partnership formed by them (Espinosa-Soto); and Luis Ortiz-Espinosa, as trustee of Centro Dermatológico San Pablo PSC Retirement Plan, opened two sets of brokerage investment accounts with BBVA Securities of Puerto Rico, Inc. ("BBVA"). The accounts included personal accounts for the married couple and accounts for a retirement plan. Rafael Rodríguez-Abella, a securities broker employed at BBVA, managed the accounts. The married couple deposited $2,113,154 into the personal accounts and $491,054 into the retirement plan accounts. By September 2009, the accounts had collectively suffered large losses in the amount of $2,049,340. The married couple believed that BBVA and Rodríguez-Abella were responsible for the losses. The brokerage agreements provided for arbitration of disputes before the Federal Industry Regulatory Authority ("FINRA").

On March 25, 2010, the married couple and representatives of the retirement plans (hereinafter, "claimants") sought arbitration with BBVA and Rodríguez-Abella in the FINRA forum. We refer to BBVA and Rodríguez-Abella as "defendants." In their statement of claim requesting arbitration, claimants alleged that between 2006 and 2009, defendants

in total disregard and open violation of the instructions received from [c]laimants and of [c]laimants' investment objectives, engaged in a pattern of unsuitable investments in high risk securities, with the sole objective of maximizing commissions or trading profits for [defendants], while deceiving [c]laimants about the true nature of the investments made by [defendants] in the Accounts. Said investments were made by [defendants] without consulting [c]laimants, and [defendants] exercised unauthorized discretion in the handling of the Accounts.

Appellants' Appx. 23–24.

Claimants asserted several claims under both federal and Puerto Rico law, alleging, inter alia , violations of Section 10(b) of the Securities Exchange Act, Rule 10b-5 of the Securities Exchange Commission, and also the securities laws of Puerto Rico. The statement of claim alleged claims under state tort and contract law as well. With respect to the retirement plan accounts, claimants also alleged that the investments and margin loans were violations of the Employee Retirement Income Security Act. Finally, in addition to compensatory damages in the amount of at least $2,102,976, claimants sought punitive damages, interest, attorney's fees, expenses, and disgorgement of defendants' commissions and service fees.

A FINRA arbitration panel comprised of three members conducted seventeen hearing sessions in Puerto Rico. On April 3, 2012, the arbitrators issued an award denying claimants' claims. The award stated in its entirety:

After considering the pleadings, the testimony and evidence presented at the hearing, and the post-hearing submissions, the Panel has decided in full and final resolution of the issues submitted for determination as follows:

The Panel finds for Respondents and Claimants' claims are denied in their entirety.

Any and all relief not specifically addressed herein, including Claimants' request for attorneys' fees and punitive damages, is denied.

Appellants' Appx. 38.

On July 29, 2012, claimants filed a complaint (hereinafter, "petition to vacate") in the Puerto Rico Court of First Instance requesting that the court vacate or modify the arbitration award. Claimants, in their petition to vacate, did not invoke the Federal Arbitration Act ("FAA"); instead, claimants sought relief under the Puerto Rico Arbitration Act ("PRAA"), 32 L.P.R.A. §§ 3201 et seq. The petition alleged various errors of the arbitrators, including the fact that they denied claimants' claims despite an alleged admission of responsibility by defendants and "clear evidence" supporting claimants' claims on the merits. Appellants' Appx. 15. The petition to vacate also alleged that the arbitrators were biased against claimants and had refused to hear relevant evidence.

On July 30, 2012, defendants removed the case to the United States District Court for the District of Puerto Rico asserting that the district court had federal question jurisdiction. There was no basis for diversity jurisdiction because all of the parties in this case are residents of Puerto Rico or are entities created or organized under the laws of Puerto Rico. Defendants based their claims of federal subject matter jurisdiction on a look-through approach, asserting that the underlying claims were based on federal securities laws, and that the district court would have had jurisdiction if the claims had been filed in district court. Defendants urged that the court also had supplemental jurisdiction over the state law claims.

On August 17, 2012, claimants moved to remand the case to Puerto Rico state court for lack of jurisdiction. The district court denied the motion for remand, holding that the court had federal question jurisdiction. It applied the look-through approach, determining that the underlying statement of claim alleged federal claims. Claimants filed an interlocutory appeal of the order denying their motion to remand, but on May 28, 2013, this Court dismissed the appeal because the order was not a final decision under 28 U.S.C. § 1291.

On December 17, 2015, the district court denied claimants' petition to vacate or modify the arbitration award and entered a judgment confirming the award, holding that claimants "did not demonstrate any plausible ground to vacate or modify the award." Appellants' Br. Add. 28. The court did not decide whether the FAA or PRAA standards for vacating or modifying an arbitration award applied. Instead, the court held that "given the similarities between the FAA and PRAA with respect to the grounds for vacating or modifying" an arbitration award, disturbing the award "is not warranted under FAA or PRAA." Appellants' Br. Add. 24 n.9. Claimants appeal both the district court's denial of their motion to remand and the judgment confirming the arbitration award. We have jurisdiction pursuant to 28 U.S.C. § 1291.

II.

We first consider the issue of federal question jurisdiction. Where pertinent facts are not in dispute, we review the district court's determination of subject matter jurisdiction de novo. Samaan v. St. Joseph Hosp. , 670 F.3d 21, 27 (1st Cir. 2012).

Defendants argue that the FAA applies here and that this circuit should adopt the look-through doctrine to determine whether the district court has subject matter jurisdiction over a motion to vacate an arbitration award. Claimants argue that they sued under the PRAA, and alleged only state law causes of action in their petition to vacate, so the district court did not have subject matter jurisdiction. Furthermore, they claim that the text of the FAA prohibits the extension of the look-through doctrine beyond § 4. For the reasons explained below, we agree with defendants on both points.

Although claimants brought their petition to vacate under 32 L.P.R.A. § 3222, the FAA applies to arbitration agreements "in any maritime transaction or a contract evidencing a transaction involving commerce." 9 U.S.C. § 2 ; see also Bernhardt v. Polygraphic Co. of Am. , 350 U.S. 198, 200–02, 76 S.Ct. 273, 100 L.Ed. 199 (1956). The Supreme Court has suggested that the parties may agree to review of arbitration awards under state law, explaining that "[t]he FAA is not the only way into court for parties wanting review of arbitration awards: they may contemplate enforcement under state statutory or common law, for example, where judicial review of different scope is arguable." Hall St. Assocs. v. Mattel, Inc. , 552 U.S. 576, 590, 128 S.Ct. 1396, 170 L.Ed.2d 254 (2008). But we read Hall Street as holding that where the FAA applies, it may be displaced by state law (if at all) only if the parties have so agreed explicitly. See id. Here, claimants have made no showing that the parties "contemplate[d] enforcement under" the PRAA, id. rather than the FAA. Claimants have not pointed to any language in their arbitration agreement indicating that the parties intended that state law would govern vacatur of the arbitration award. Accordingly, we will apply the FAA.

The FAA provides several mechanisms for enforcing arbitration agreements and awards. Sections 3 and 4 provide that a court may, upon application, stay litigation pending arbitration and compel arbitration pursuant to an arbitration agreement. 9 U.S.C. §§ 3, 4. Once an arbitration award has issued, FAA sections 9 through 11 supply means for acquiring "a judicial decree confirming an award, an order vacating it, or an order modifying or correcting it." Hall St. , 552 U.S. at 582, 128 S.Ct. 1396. Upon an application to the court under § 9, the court " ‘must’ confirm an arbitration award ‘unless' it is vacated, modified, or corrected ‘as prescribed’ in §§ 10 and 11." Id. (quoting 9 U.S.C. § 9 ). Sections "10 and 11 respectively provide the FAA's exclusive grounds for expedited vacatur and modification." Id. at 584, 128 S.Ct. 1396.

An important goal of the FAA was to make arbitration agreements enforceable in the first instance. But the post-arbitration remedies were also a central component of the FAA structure, which sought to combat delays and expenses normally associated with litigation to enforce awards.

Before the FAA, "the only recourse of the successful party was to sue in a court of law upon the award," where the party was "subject to the delay always incident in any action at law and to defeat upon technicalities or otherwise in proving the award itself." Arbitration of Interstate Commercial Disputes, Joint Hearings before the Subcomms. of the Comms. on the Judiciary on S. 1005 and H.R. 646, 68th Cong., 1st Sess., 36 (1924). The FAA was viewed as solving these problems: "[u]nder the statute, if the award is not voluntarily performed, it must be entered as a judgment of the court, as a matter of course, unless grounds exist for its vacation, correction, or modification." Id. ; see also id. ("In all these proceedings there is no material expense or delay and no opportunity for technical procedure.").

The very existence of sections 9, 10, and 11 demonstrates the importance of post-award federal court review. Those provisions show that Congress contemplated that the federal courts would have a central role and broad authority to enforce arbitration agreements (including confirming, vacating, or modifying an arbitration award). Sections 9, 10, and 11 provide that proceedings may be brought in "the United States court in and for the district wherein the award was made." 9 U.S.C. § 10(a) ; accord §§ 9, 11. While these provisions do not themselves confer jurisdiction, they evidently contemplate that award enforcement will occur in federal courts as a matter of course. In fact, there is no explicit provision for post-award enforcement in state courts.

The Supreme Court has determined that the FAA adopted the look-through approach with respect to petitions to compel arbitration under 9 U.S.C § 4. In Vaden v. Discover Bank , 556 U.S. 49, 62, 129 S.Ct. 1262, 173 L.Ed.2d 206 (2009), the Court held that a "court may ‘look through’ a § 4 petition to determine whether it is predicated on an action that ‘arises under’ federal law." The proper jurisdictional inquiry for a motion to compel arbitration is whether, "save for [the arbitration] agreement," the court would have jurisdiction "over ‘a suit arising out of the controversy between the parties.’ " Id. at 70, 129 S.Ct. 1262 (alteration in original) (quoting 9 U.S.C. § 4 ). In so holding, the Court rejected a test that would require the court to look to the issues presented in the petition alone, which might include, for example, the parties' dispute over the arbitrability of the claims. Id. at 63, 129 S.Ct. 1262.

The Vaden Court relied on the text of § 4, which provides in relevant part that a party seeking to compel arbitration "may petition any United States district court which, save for such agreement, would have jurisdiction under Title 28, in a civil action or in admiralty of the subject matter of a suit arising out of the controversy between the parties." 9 U.S.C. § 4. The Court reasoned that "[t]he phrase ‘save for [the arbitration] agreement’ indicates that the district court should assume the absence of the arbitration agreement and determine whether it ‘would have jurisdiction under title 28’ without it." Vaden , 556 U.S. at 62, 129 S.Ct. 1262 (alteration in original). The phrase, "the controversy between the parties," the Court explained, "is most straightforwardly read to mean the ‘substantive conflict between the parties.’ " Id. at 62–63, 129 S.Ct. 1262 (quoting Discover Bank v. Vaden , 396 F.3d 366, 370 (4th Cir. 2005) ).

The Court noted that rejecting the look-through approach would lead to "curious practical consequences." Id. at 65, 129 S.Ct. 1262. The Court explained that if a federal court were permitted "to entertain a § 4 petition only when a federal-question suit is already before the court, when the parties satisfy the requirements for diversity-of-citizenship jurisdiction, or when the dispute over arbitrability involves a maritime contract," such an "approach would not accommodate a § 4 petitioner who could file a federal-question suit in (or remove such a suit to) federal court, but who has not done so." Id. By contrast, the look-through approach avoids this situation because it allows a party to request an order compelling arbitration without first "seeking federal adjudication of the very questions it wants to arbitrate rather than litigate." Id.

The Supreme Court has not decided whether the same jurisdictional look-through approach also applies to petitions to confirm, vacate, or modify an arbitration award under §§ 9–11. To be sure, there is a difference in statutory language between § 4 and the latter sections. In particular, the latter sections do not include the "save for [the arbitration] agreement" and "arising out of the controversy between the parties" language relied upon by the Supreme Court in Vaden . The question is whether this difference in language between the pre-award enforcement provision of § 4 and the post-award enforcement provisions of §§ 9–11 warrants a different test for federal question jurisdiction.

Following Vaden , there exists a split among our sister circuits on this question. The Second Circuit has held that the look-through approach applies at least to § 10 petitions to vacate. Doscher , 832 F.3d at 388. By contrast, the Seventh and Third Circuits have held the opposite: that Vaden is distinguishable (primarily based on the difference in statutory language) and that "a federal issue resolved by the arbitrator does not supply subject-matter jurisdiction for review or enforcement of the award." Magruder v. Fid. Brokerage Servs. LLC , 818 F.3d 285, 288 (7th Cir. 2016) ; see also Goldman v. Citigroup Glob. Mkts. Inc. , 834 F.3d 242, 255 (3d Cir. 2016) (look-through does not apply to § 10 motions to vacate).

As we now explain, we agree with the Second Circuit that the look-through approach cannot be limited to § 4 petitions to compel. Initially, we note that the mere difference in statutory text between the sections does not itself compel a holding that the sections are to be interpreted differently. See Clay v. United States , 537 U.S. 522, 529–30, 123 S.Ct. 1072, 155 L.Ed.2d 88 (2003) ; City of Columbus v. Ours Garage & Wrecker Serv., Inc. , 536 U.S. 424, 435–36, 122 S.Ct. 2226, 153 L.Ed.2d 430 (2002) ; Martin v. Hadix , 527 U.S. 343, 355–57, 119 S.Ct. 1998, 144 L.Ed.2d 347 (1999) ; see also Merrill Lynch, Pierce, Fenner & Smith Inc. v. Manning , ––– U.S. ––––, 136 S.Ct. 1562, 1570–71, 194 L.Ed.2d 671 (2016) (construing "completely different language"—the phrase "brought to enforce" in § 27 of the Securities Exchange Act of 1934 and the phrase "arising under" in 28 U.S.C. § 1331 —to have the same meaning for determining federal jurisdiction).

There are, moreover, several important policy reasons supporting applying the look-through approach to the award enforcement provisions. In light of the important role intended for the federal courts in enforcing arbitration agreements post-award, it would make no sense to effectively exclude federal question jurisdiction over those cases. And, the look-through approach is the only possible approach that would provide such federal jurisdiction.

There would seem to be only three possible tests for "arising under" jurisdiction under 28 U.S.C. § 1331. First, FAA §§ 9–11 could be viewed as each creating a federal cause of action because section 10 on its face provides substantive rules of decision for vacating an arbitration award. See Doscher , 832 F.3d at 387 ; Kasap , 166 F.3d at 1247. Such a reading would appear to be consistent with the general rule that a court has federal question jurisdiction where federal law creates the cause of action and provides the rules of decision.

However, the Supreme Court has foreclosed this first possibility, holding that federal question jurisdiction over controversies involving arbitration cannot be based on the fact that the FAA establishes the relevant substantive law. See Hall St. , 552 U.S. at 581–82, 128 S.Ct. 1396 ; Moses H. Cone Mem'l Hosp. v. Mercury Constr. Corp. , 460 U.S. 1, 25 n.32, 103 S.Ct. 927, 74 L.Ed.2d 765 (1983).

The second possible test for federal question jurisdiction invokes the theory that federal jurisdiction exists where non-FAA federal law provides grounds for vacating the award. See Goldman , 834 F.3d at 255 ; Carter v. Health Net of Cal., Inc. , 374 F.3d 830, 836–37 & n.4 (9th Cir. 2004) ; Greenberg v. Bear, Stearns & Co. , 220 F.3d 22, 27 (2d Cir. 2000)overruled on other grounds by Doscher , 832 F.3d 372. However, this theory largely depends on the continued vitality of the "manifest disregard" doctrine (allowing an award to be set aside if it was made in manifest disregard of federal law), which "has been thrown into doubt by [Hall Street ], where the Supreme Court ‘h[e]ld that [9 U.S.C. § 10 ] ... provide[s] the FAA's exclusive grounds for expedited vacatur.’ " Bangor Gas Co. v. H.Q. Energy Servs. (U.S.) Inc. , 695 F.3d 181, 187 (1st Cir. 2012) (alteration in original) (quoting Hall St. , 552 U.S. at 584, 128 S.Ct. 1396 ). This circuit has "not squarely determined whether our manifest disregard case law can be reconciled with Hall Street ." Raymond James Fin. Servs., Inc. v. Fenyk , 780 F.3d 59, 64–65 (1st Cir. 2015) (citation and quotation marks omitted).

We need not and do not decide now whether manifest disregard remains as an available basis for vacatur. However, if it does survive, we agree with the courts that have held that Hall Street compels the conclusion that it does so only as a judicial gloss on § 10. See Johnson v. Wells Fargo Home Mortg., Inc. , 635 F.3d 401, 414 (9th Cir. 2011) ; T.Co Metals, LLC v. Dempsey Pipe & Supply, Inc. , 592 F.3d 329, 340 (2d Cir. 2010). If this is so, however, a claim of manifest disregard cannot provide federal question jurisdiction since, as discussed above, the law is settled that the FAA, including § 10, does not create a basis for federal question jurisdiction. See Hall St. , 552 U.S. at 581–82, 128 S.Ct. 1396 ; Moses H. Cone , 460 U.S. at 25 n.32, 103 S.Ct. 927.

This leaves only a third, alternative approach: that the look-through test adopted in Vaden for § 4 petitions applies to sections 9, 10, and 11 of the FAA. It is the only approach available that provides broad federal court jurisdiction over proceedings to enforce awards, a clear objective of the FAA. Congress cannot have intended jurisdiction over §§ 9–11 petitions only to exist in diversity or perhaps in admiralty.

The look-through approach also provides a unitary jurisdictional approach to the FAA, an objective endorsed by various cases. See Harry Hoffman Printing , 912 F.2d at 611 n.1 ; Garrett , 7 F.3d at 884. Applying the look-through approach to post-award decisions avoids a "bizarre" distinction that would otherwise follow: "a petition to compel arbitration could be brought in federal court, but a petition under FAA §§ 9 or 10 to confirm or vacate the arbitration award in the same dispute could not." Westmoreland Capital Corp. v. Findlay , 100 F.3d 263, 268 (2d Cir. 1996)abrogated by Vaden , 556 U.S. 49, 129 S.Ct. 1262 ; see also Doscher , 832 F.3d at 383 ("[H]ow can a federal court's jurisdiction under the same jurisdictional statute differ between § 4 and all other remedies under the Act?"); id. at 387 (noting that excluding federal question jurisdiction here would result in a "totally artificial distinction" between cases stayed under § 3 and freestanding § 10 petitions filed in the same court) (quoting Vaden , 556 U.S. at 65, 129 S.Ct. 1262 ).

Applying the look-through approach to §§ 9–11 additionally avoids "curious practical consequences" similar to those that the Supreme Court recognized in Vaden as supporting § 4 jurisdiction. 556 U.S. at 65, 129 S.Ct. 1262. Allowing a federal court to compel arbitration in a federal question case but then later denying a federal forum for confirming, modifying, or vacating the award would lead to strange consequences. Remitting the litigants to state court for post-award enforcement proceedings would create potential inconsistency between the federal pre-award decision and the later state court decision involving the question of whether the arbitrators exceeded their powers by deciding issues that are not properly subject to arbitration. See Coady v. Ashcraft & Gerel , 223 F.3d 1, 9 (1st Cir. 2000). Doctrines of issue preclusion may not protect against this eventuality in part because some state courts do not regard the FAA as preempting state law.

Finally, apart from arbitration agreement interpretation, a reviewing court in post-arbitration proceedings may be called to answer questions that implicate federal law. For example, a reviewing court may be asked to determine whether the arbitrators "refus[ed] to hear evidence pertinent and material to the controversy," possibly requiring the court to consider questions of federal law in deciding whether the disregarded or excluded evidence was "material to the controversy." 9 U.S.C. § 10(a)(3). Regardless of the avenue by which federal law becomes relevant in reviewing an arbitration award, it would seem particularly strange to deny a federal forum where the underlying claim, as here, is based on the Securities Exchange Act of 1934, claims over which the federal district courts have exclusive jurisdiction. See Manning , 136 S.Ct. at 1566. This potential for conflict further counsels that the look-through approach should apply consistently under the FAA.

For all of these reasons, we conclude that the look-through approach applies to sections 9, 10, and 11 of the FAA. Applying the look-through approach here, upon review of claimants' statement of claim, there is no question that claimants' claims involving federal securities laws arise under federal law. Indeed, at oral argument, claimants conceded that if we were to adopt the look-through approach, claimants lose on this issue. Accordingly, the district court properly exercised jurisdiction over claimants' petition to vacate.

III.

We review the district court's decision to confirm or vacate an arbitration award de novo. Cytyc Corp. v. DEKA Prods. Ltd. P'ship , 439 F.3d 27, 32 (1st Cir. 2006). As a threshold matter, the parties dispute whether the court should apply the FAA or the state PRAA grounds for vacatur in reviewing the award. The district court did not resolve this question, holding that the statutory grounds are essentially the same. Because we have already held that the FAA governs in this case, we need not decide whether the PRAA confers different grounds for vacatur.

Turning to the merits, we see no error in the district court's decision here refusing to vacate (and confirming) the award under the FAA. The court's review of an arbitration award "is extremely narrow and exceedingly deferential." Raymond James , 780 F.3d at 63 (citation and quotation marks omitted); see also Cytyc Corp. , 439 F.3d at 32 ; Teamsters Local Union No. 42 v. Supervalu, Inc. , 212 F.3d 59, 61 (1st Cir. 2000) ("Arbitral awards are nearly impervious to judicial oversight."). In reviewing an arbitration award under the FAA, "courts ‘do not sit to hear claims of factual or legal error by an arbitrator as an appellate court does in reviewing decisions of lower courts.’ " Advest, Inc. v. McCarthy , 914 F.2d 6, 8 (1st Cir. 1990) (quoting United Paperworkers Int'l Union v. Misco, Inc. , 484 U.S. 29, 38, 108 S.Ct. 364, 98 L.Ed.2d 286 (1987) ). This limited review applies "[e]ven where such error is painfully clear, [because] courts are not authorized to reconsider the merits of arbitration awards." Id. (internal quotation marks omitted); see also Stolt-Nielsen , 559 U.S. at 671, 130 S.Ct. 1758 ("It is not enough for petitioners to show that the panel committed an error—or even a serious error."); McCarthy v. Citigroup Glob. Mkts. Inc. , 463 F.3d 87, 93–94 (1st Cir. 2006). The burden is on the claimants to establish that the award should be set aside. See JCI Commc'ns, Inc. v. Int'l Bhd. of Elec. Workers, Local 103 , 324 F.3d 42, 51 (1st Cir. 2003). The grounds are set forth in Section 10 and include only the following:

(1) where the award was procured by corruption, fraud, or undue means;

(2) where there was evident partiality or corruption in the arbitrators, or either of them;

(3) where the arbitrators were guilty of misconduct in refusing to postpone the hearing, upon sufficient cause shown, or in refusing to hear evidence pertinent and material to the controversy; or of any other misbehavior by which the rights of any party have been prejudiced; or

(4) where the arbitrators exceeded their powers, or so imperfectly executed them that a mutual, final, and definite award upon the subject matter submitted was not made.

9 U.S.C. § 10(a).

Claimants did not expressly invoke FAA § 10. Instead, claimants' petition to vacate and subsequent briefing cite vacatur provisions of the PRAA, 32 L.P.R.A. § 3222(b) and (c), which are analogous to FAA § 10(a)(2) and (a)(3), respectively. Accordingly, we address claimants' claims under the PRAA as though they had been brought under the analogous provisions of the FAA.

Claimants have put forth essentially three theories as to why vacatur or modification of the arbitration award is warranted. Claimants argue that these errors collectively show evident partiality of the arbitrators (§ 10(a)(2) ) and that the arbitrators engaged in misconduct or misbehavior that prejudiced claimants' rights (§ 10(a)(3) ).

Claimants' first and primary theory is that the arbitrators were obligated to impose liability on defendants—but did not—after they were presented with "overwhelming" evidence supporting their case and after defendants' counsel made an alleged admission of "shared responsibility" during closing arguments at the hearing. Appellants' Br. 11, 14.

The available grounds of vacatur do not allow a federal court to revisit the arbitrators' ultimate determination of whether or not to impose liability. See Advest , 914 F.2d at 8. That the arbitrators apparently were unconvinced by claimants' evidence and denied their claims, without more, does not establish that the arbitrators were biased or guilty of misbehavior. To the extent that claimants suggest that defense counsel made an "admission" at closing argument, we do not read counsel's comments as a clear admission of liability. Read in context, counsel's statements are more reasonably interpreted as an argument that claimants should be held accountable for their role, if any, in their own losses. Counsel does not appear to have suggested that defendants admitted to any particular proportion of responsibility.

Second, claimants argue that one arbitrator was partial to defendants as evidenced by comments he made during one of the hearings. During claimants' questioning of a witness apparently related to claimants' allegations of defendants' prior bad acts, the arbitrator said "if I were [defendants' counsel], I would have a sore throat from objection for irrelevancies." Appellants' Appx. at 75. Read in context, however, the arbitrator's statements indicate that he was concerned with the number and length of the hearings, as well as the potential for scheduling issues if the hearings needed to be prolonged. He suggested to claimants that he believed the particular line of questioning was irrelevant and that claimants should move on to other questions. This hardly supports the existence of bias, and without more, claimants have not established "specific facts that indicate improper motives on the part of an arbitrator." JCI Commc'ns , 324 F.3d at 51 (quoting Al Harbi v. Citibank, N.A. , 85 F.3d 680, 683 (D.C. Cir. 1996) ). A reasonable person would not "have to conclude" from this exchange that the arbitrator was evidently partial to defendants. Id.

Third and finally, claimants argue that the arbitrators failed to admit relevant evidence relating to claims previously brought against defendant Rodríguez-Abella by unrelated parties. Claimants' third theory also fails. "Of course, § 10(a)(3) does not require arbitrators to consider every piece of relevant evidence presented to them." Doral Fin. Corp. v. Garcia-Velez , 725 F.3d 27, 31 (1st Cir. 2013). "An arbitration award must not be set aside for the arbitrator's refusal to hear evidence that is cumulative or irrelevant." Hoteles Condado Beach, La Concha & Convention Ctr. v. Union De Tronquistas Local 901 , 763 F.2d 34, 40 (1st Cir. 1985) (citations omitted). "Vacatur is appropriate only when the exclusion of relevant evidence so affects the rights of a party that it may be said that he was deprived of a fair hearing." Id. (internal quotation marks omitted).

Here, claimants have not established that they were deprived of a fair hearing. The record shows that claimants were permitted to ask some questions about Rodríguez-Abella's former clients' actions against him. The arbitrators sustained objections based on relevancy only because those prior actions had been settled. We need not decide whether under the Federal Rules of Evidence, such evidence would be admissible. See United States v. Bailey , 696 F.3d 794, 800 (9th Cir. 2012). Whether or not such evidence would be admissible in federal court, we will not disturb the arbitrators' decisions sustaining defendants' evidentiary objections. See Hoteles Condado Beach , 763 F.2d at 39–40 ("Absent exceptional circumstances, ... a reviewing court may not overturn an arbitration award based on the arbitrator's determination of the relevancy or persuasiveness of the evidence submitted by the parties.").

Apart from claimants' three theories of vacatur, claimants suggest in their petition to vacate that the same alleged errors resulted in an error in number calculation warranting modification of the award. See 9 U.S.C. § 11(a). However, § 11 plainly does not provide for modification where claimants' sole position is that the arbitrators erred in denying their claims. See Advest , 914 F.2d at 8 n.4 (noting that " § 11 provides for correction of ‘evident’ and ‘material’ arithmetic or descriptive errors").

Because we affirm the district court's determination that vacatur or modification of the arbitration award is not warranted, we also affirm the court's confirmation of the award. See 9 U.S.C. § 9 ("[T]he court must grant [an order confirming the award] unless the award is vacated, modified, or corrected as prescribed in sections 10 and 11 of this title.").

IV.

We conclude that the district court properly exercised jurisdiction over claimants' petition to vacate or modify the arbitration award. We also hold that the district court was correct in denying claimants' petition and confirming the award. Accordingly, we affirm.

AFFIRMED. Costs to appellees.