EASTERBROOK, Chief Judge.

Two insurance companies agreed in 1997 that Trustmark would reinsure some risks underwritten by John Hancock. The details of the parties' multiple contracts are unimportant for our purposes. It is enough to say that the insurers disagree about the meaning of "London Market Retrocessional Excess of Loss business", which Trustmark need not reinsure. The parties submitted their dispute to arbitration under the contracts' broad arbitration clauses. In March 2004 a tripartite panel (one arbitrator selected by each side, and these two selecting a third, called the umpire) made its award, supporting Hancock's view of Trustmark's obligations. The award was confirmed by a district court. 2004 WL 1376409, 2004 U.S. Dist. LEXIS 11370 (N.D.Ill June 17, 2004).

Trustmark was dissatisfied and refused to pay the bills that Hancock sent on the view that the confirmed award governed all of the parties' dealings. This led Hancock to commence a new arbitration in October 2004. Trustmark responded by arguing (among other things) that Hancock had secured the March 2004 award by failing to disclose four documents during arbitral discovery, an omission that Trust-mark labeled "fraud." Hancock named as its arbitrator Mark S. Gurevitz, who had participated in the first arbitration as well. Trustmark picked a person who had not participated in the earlier proceeding. The two party-chosen arbitrators selected a neutral umpire. One of the first issues the three-person panel had to tackle was what weight to give the 2004 decision. Hancock contended that it was largely dispositive; Trustmark contended that it should be ignored and the proceedings restarted from scratch. Consideration of this point was complicated by a confidentiality agreement that the parties had reached during the first proceeding. This agreement — which did not include its own arbitration clause — prevented Trustmark and Hancock from disclosing the evidence, proceedings, and award. The parties debated whether this agreement covered all disclosures, even to lawyers and successor arbitrators, or only disclosures to the out-side world (such as the firms' business rivals and the press). Gurevitz and the umpire concluded that the arbitrators themselves (and the parties' lawyers) are entitled to know and consider the evidence presented, and the results reached, in the first arbitration.

Before the panel commenced its hearing on the merits, Trustmark launched this suit under the diversity jurisdiction. The suit, filed in 2009, initially asked the court to vacate the decision that had confirmed the 2004 award. That request is so obviously untimely — the time to appeal the district judge's decision had expired five years earlier, and Fed.R.Civ.P. 60(b) does not allow that decision to be reopened — that Trustmark soon reformulated its principal contention, asking the court to enjoin further arbitration as long as Gurevitz remains a member of the new panel. The contracts require all three arbitrators to be "disinterested". Trustmark contended that Gurevitz is not, because he knows what happened in the first arbitration. It also insisted that the new arbitral panel is not entitled to form or act on any view about the meaning of the confidentiality agreement, because that agreement does not include an arbitration clause. Only a judge, Trustmark insisted, can determine what the confidentiality agreement requires.

The district court agreed with Trust-mark and issued an injunction. 680 F.Supp.2d 944 (N.D.Ill. 2010). The judge wrote that Gurevitz is not "disinterested" because he knows what happened during the first arbitration and could be called as a fact witness about those proceedings. The judge also ruled that the second panel is not entitled to consider the decision made by the first panel. The injunction stopped the arbitration in its tracks. Hancock has appealed.

Equitable relief depends on irreparable injury, and the first question we must address is whether Trustmark showed any. Here is the district court's entire discussion of that subject:

Trustmark cannot be forced to arbitrate issues that it did not agree to arbitrate. See AT T Technologies v. Communications Workers of America, 475 U.S. 643, 648 [ 106 S.Ct. 1415, 89 L.Ed.2d 648] (1986). "Forcing a party to arbitrate a matter that the party never agreed to arbitrate, regardless of the final result through arbitration or judicial review, unalterably deprives the party of its right to select the forum in which it wishes to resolve disputes[,]" causing irreparable harm. Chicago School Reform Bd. of Trustees v. Diversified Pharmaceutical Services, Inc., 40 F.Supp.2d 987, 996 (N.D.IU. 1999). This is a harm faced uniquely by Trustmark if it is denied relief and such harm tips the scale in favor of granting injunction. This irreparable harm, coupled with Trustmark's success on the merits, militates in favor of granting an injunction in this case.

680 F.Supp.2d at 949. There are two principal problems with this understanding.

First, Trustmark did agree to arbitrate the question whether the contracts provide reinsurance for certain risks. Yet the district court blocked rather than enforced that contractual undertaking.

Second, the proposition that going forward with an arbitration "unalterably deprives the party of its right to select the forum" — a proposition for which the court did not cite any statute or appellate decision — is false. Once the arbitration ends, a party that believes the proceeding flawed because the arbitrators exceeded their remit has a simple remedy: a proceeding under the Federal Arbitration Act to deny enforcement to the award. See 9 U.S.C. § 10(a)(4) (award may be set aside "where the arbitrators exceeded their powers"). If the award should be set aside, litigation in the proper forum would ensue.

The only potential injury from waiting until the arbitrators have made their award is delay and the out-of-pocket costs of paying the arbitrators and legal counsel. Long ago the Supreme Court held that the delay and expense of adjudication are not "irreparable injury" — if they were, every discovery order would cause irreparable injury. See, e.g., Petroleum Exploration, Inc. v. Public Service Commission, 304 U.S. 209, 222, 58 S.Ct. 834, 82 L.Ed. 1294 (1938); Renegotiation Board v. Bannercraft Clothing Co., 415 U.S. 1, 24, 94 S.Ct. 1028, 39 L.Ed.2d 123 (1974); FTC v. Standard Oil Co., 449 U.S. 232, 244, 101 S.Ct. 488, 66 L.Ed.2d 416 (1980). We held in PaineWebber Inc. v. Farnam, 843 F.2d 1050 (7th Cir. 1988), and Graphic Communications Union v. Chicago Tribune Co., 779 F.2d 13 (7th Cir. 1985), that the sort of argument Trustmark advances in its effort to establish "irreparable injury" is frivolous.

We could stop here, but the district court's decision leaves a cloud over this arbitration and the reputation of arbitrator Gurevitz, a reputation that Trustmark seems determined to tarnish. We therefore add that the district court erred on the merits in addition to mistakenly believing that Trustmark has established irreparable injury.

The contracts require all three arbitrators to be "disinterested." When used with respect to adjudication, this word means lacking a financial or other personal stake in the outcome. See generally Caperton v. A.T. Massey Coal Co., ___ U.S. ___, 129 S.Ct. 2252, 173 L.Ed.2d 1208 (2009). Norms of insurance-industry arbitration track this understanding. ARIAS U.S., Practical Guide to Reinsurance Arbitration Procedure § 2.3 (rev. ed. 2004) ("disinterest" means no financial stake in the outcome and not being under a party's direct control).

Gurevitz does not have any stake in the outcome of this arbitration. Like any other privately appointed arbitrator, he does have a reputational interest: if his decision disappoints the person who put him on the panel, he is less likely to be selected as an arbitrator in the future. Federal judges, by contrast, serve during good behavior and need not worry about how their decisions may affect their careers. But the interest in potential future employment is endemic to arbitration that permits parties to choose who will decide. See Sphere Drake Insurance Ltd. v. All American Life Insurance Co., 307 F.3d 617, 622 (7th Cir. 2002) ("evident partiality" for arbitrators means acts that simultaneously show support for one side and disregard the rules; party-appointed arbitrators can't be dismissed on the ground that they are inclined to support the party who named them). Sometimes parties agree that arbitrators will be named by independent entities, such as the American Arbitration Association, but Trustmark and Hancock reserved the power of appointment. A court cannot properly deem the interest in reemployment created by this arrangement a disqualifying event.

Instead of asking whether Gurevitz had a financial or other personal stake in the outcome, the district judge asked whether he had knowledge about the dispute. Answering yes, the judge deemed the knowledge a form of prohibited "interest." As we observed in Sphere Drake, however, private parties often select arbitrators precisely because they know something about the controversy. 307 F.3d at. 620. Arbitration need not follow the pattern of jury trials, in which a factfinder's ignorance is a prime desideratum. Nothing in the parties' contract requires arbitrators to arrive with empty heads. Federal judges, of all people, should not confuse knowledge with a disqualifying "interest." For judges regularly hear multiple suits arising from the same controversy. The district judge who resolved this very dispute also entered the order enforcing the 2004 award. If knowing about what happened in 2004 is an impermissible "interest," or makes the person a "fact witness" about what had occurred in 2004, then the district judge should have stepped aside from the current suit. Yet that was not required. Knowledge acquired in a judicial capacity does not require disqualification. See Liteky v. United States, 510 U.S. 540, 114 S.Ct. 1147, 127 L.Ed.2d 474 (1994). Likewise with knowledge acquired in arbitration.

Arbitrator Gurevitz is as "disinterested" as the district judge himself and just as entitled to participate. That Gurevitz signed the confidentiality agreement does not affect this conclusion; he signed as an adjudicator. The district judge himself implemented the confidentiality agreement, in a similar adjudicatory capacity, when confirming the first panel's award. 2004 WL 1376409 at *1-2, 2004 U.S. Dist. LEXIS 11370 at *4-5. If there is any difference between the two adjudicators, Gurevitz has the stronger entitlement to participate in this second round, because as we stressed in Sphere Drake it takes more to disqualify an arbitrator than to disqualify a judge. 307 F.3d at 621. See also Merit Insurance Co. v. Leatherby Insurance Co., 714 F.2d 673 (7th Cir. 1983). No party in federal court is entitled to pick his judge, but contracts allowing parties to choose their arbitrators are common; these parties' arrangement instantiates the practice. When one party is entitled to choose its own arbitrator, and in doing so follows all contractual requirements, a court ought not abet the other side's strategy to eject its opponent's choice.

The district judge also erred in concluding that the arbitrators are powerless to construe the confidentiality agreement. True, that agreement lacks its own arbitration clause, but the parties did agree to arbitrate their disputes about reinsurance. Arbitrators who have been appointed to resolve a commercial dispute are entitled to resolve ancillary questions that affect their task. See Howsam v. Dean Witter Reynolds, Inc., 537 U.S. 79, 84, 123 S.Ct. 588, 154 L.Ed.2d 491 (2002). What's more, the confidentiality agreement — a standard form in insurance arbitration, signed while the arbitration was under way — is closely related to the substance of the first arbitration and presumptively within the scope of the reinsurance contracts' comprehensive arbitration clauses, which cover all disputes arising out of the original dispute. Cf. Sweet Dreams Unlimited, Inc. v. Dial-A-Mattress International, Ltd., 1 F.3d 639, 642 (7th Cir. 1993).

Suppose that Trustmark and Hancock had agreed to use the procedural rules of the American Arbitration Association, but had not included a separate arbitration clause in that contract. The panel could interpret and apply the AAA's rules; a party dissatisfied by a procedural ruling could not run to a federal district court and get review in mid-arbitration, one ruling at a time, just because neither the AAA's rulebook nor the contract adopting them had a freestanding arbitration clause. So, too, with the terms of the Federal Arbitration Act. Several parts of this statute govern the management of arbitration. For example, § 7 says that arbitrators may summon witnesses and require them to bring documents. 9 U.S.C. § 7. The Act is a statute; naturally it does not contain an arbitration clause; yet no one supposes (at least, no one should suppose) that every time an arbitrator summons (or doesn't summon) a witness, or decides which documents the parties must produce, one or both of the contestants can get immediate review in a federal district court. That would be the end of arbitration as a speedy and (relatively) low-cost alternative to litigation.

Arbitrators are entitled to decide for themselves those procedural questions that arise on the way to a final disposition, including the preclusive effect (if any) of an earlier award. Consolidation Coal Co. v. United Mine Workers, 213 F.3d 404, 407 (7th Cir. 2000); Chicago Typographical Union v. Chicago Sun-Times, Inc., 860 F.2d 1420, 1424 (7th Cir. 1988). If in doing so the arbitrators exceed their powers, the court may vacate the award at the end of the proceeding. 9 U.S.C. § 10(a)(4). But among the powers of an arbitrator is the power to interpret the written word, and this implies the power to err; an award need not be correct to be enforceable. See, e.g., Major League Baseball Players Ass'n v. Garvey, 532 U.S. 504, 121 S.Ct. 1724, 149 L.Ed.2d 740 (2001). It is enough if the arbitrators honestly try to carry out the governing agreements. "[T]he question for decision by a federal court asked to set aside an arbitration award . . . is not whether the arbitrator or arbitrators erred in interpreting the contract; it is not whether they clearly erred in interpreting the contract; it is not whether they grossly erred in interpreting the contract; it is whether they interpreted the contract." Hill v. Norfolk Western Ry., 814 F.2d 1192, 1194-95 (7th Cir. 1987). See also, e.g., Operating Engineers Local 139 v. J.H. Findorff Son, Inc., 393 F.3d 742 (7th Cir. 2004). When this arbitration resumes, the panel is entitled to follow its own view about the meaning of the confidentiality agreement; it need not knuckle under to the district judge's prematurely announced understanding.

REVERSED