POSNER, Chief Judge.

These consolidated appeals ask: When does a federal district court have the power to order the consolidation of arbitration proceedings before a single arbitral panel? The question grows out of a reinsurance contract between two (overlapping) sets of insurance companies. One set, the three "retrocessionaires" (Sun, Phoenix, and Cologne), agreed to reinsure workers' compensation reinsurance policies issued by the other set, the seven "retrocedents." (Two of the retrocessionaires, Phoenix and Cologne, are also retrocedents.) For clarity we'll call the retrocessionaires the "reinsurers," and the retrocedents the "insurers," though in fact both sets of companies are reinsurers, there being many layers of reinsurance in the workers' compensation insurance market.

The contract was negotiated on behalf of the insurers by Unicover Managers, Inc., described in the contract as their "manager." Unicover is a middleman in the workers' compensation reinsurance market. Although not technically an insurance company, it issues reinsurance contracts to insurance companies (the retrocedents in this case) and then in effect assigns these contracts to other insurance companies (the retrocessionaires), who then bear the risk created by the contracts and reap the premiums that the contracts specify.

The contract contains an arbitration provision pursuant to which Sun and Phoenix served a demand for arbitration on Unicover and its insurers. Four of the latter responded by filing their own demands, each seeking a separate arbitration between itself, on the one hand, and Sun and Phoenix, on the other. Each of the six companies filed a motion in the federal district court in Chicago (the venue prescribed by the arbitration provision of the contract) pursuant to section 4 of the Federal Arbitration Act, 9 U.S.C. § 4, to compel arbitration. The district court denied the reinsurers' motion for a single arbitration and granted the insurers' motions for separate arbitrations; its order, which wound up the proceedings in the district court, is appealable under 9 U.S.C. § 16(a)(3). See Iowa Grain Co. v. Brown, 171 F.3d 504, 507-08 (7th Cir. 1999); Napleton v. General Motors Corp., 138 F.3d 1209, 1212 (7th Cir. 1998); Augustea Impb Et Salvataggi v. Mitsubishi Corp., 126 F.3d 95, 99 (2d Cir. 1997). (Whether our test for the appealability of such orders is too demanding is at present before the Supreme Court. See Randolph v. Green Tree Financial Corp.-Alabama, 178 F.3d 1149, 1152-57 (11th Cir. 1999), cert. granted, 2000 WL 122150 (U.S. Apr. 3, 2000); Napleton v. General Motors Corp., supra, 138 F.3d at 1216-18 (dissenting opinion).) Two of the other insurers settled, and the position of the remaining two (which includes one of the companies that is both a retrocessionaire and a retrocedent, Cologne Life Reinsurance Company) is unclear. Sun and Phoenix stated in their demand for arbitration that they were seeking rescission of the reinsurance contract, plus damages, on the ground of fraud by Unicover (for which, they contend, the insurers, as Unicover's principals, are liable) in both the inducement and the performance of the contract. The potential damages could, we are told, exceed $2 billion.

None of the parties contends that the issue of one versus many arbitrations is for the arbitrators rather than the court to decide. The arbitration provision in the contract does not address the question of who decides, cf. First Options of Chicago, Inc. v. Kaplan, 514 U.S. 938, 945 (1995), and there are compelling practical objections to remitting the question to the arbitrators. See Thomas J. Stipanowich, "Arbitration and the Multiparty Dispute: The Search for Workable Solutions," 72 Iowa L. Rev. 473, 513 (1987). Arbitral panels are ad hoc, making it difficult to coordinate their decisions on such a question. And there are no contractual or statutory provisions for transferring cases between panels, should multiple arbitrations be commenced when the contract envisaged a single consolidated one.

In defending the district court's refusal to order the single arbitration sought by their opponents, the insurers press upon us a series of cases in this and other courts that, they say, hold that a federal district court cannot grant a motion to consolidate separate arbitration proceedings unless the contract on which the arbitration is founded expressly authorizes consolidation. Champ v. Siegel Trading Co., 55 F.3d 269, 275-77 (7th Cir. 1995); Glencore, Ltd. v. Schnitzer Steel Products Co., 189 F.3d 264 (2d Cir. 1999); Government of United Kingdom v. Boeing Co., 998 F.2d 68, 71-74 (2d Cir. 1993); American Centennial Ins. Co. v. National Casualty Co., 951 F.2d 107 (6th Cir. 1991); Baesler v. Continental Grain Co., 900 F.2d 1193 (8th Cir. 1990); Protective Life Ins. Corp. v. Lincoln Nat'l Life Ins. Corp., 873 F.2d 281 (11th Cir. 1989) (per curiam); Del E. Webb Construction v. Richardson Hospital Authority, 823 F.2d 145, 150 (5th Cir. 1987); Weyerhaeuser Co. v. Western Seas Shipping Co., 743 F.2d 635 (9th Cir. 1984). All that these cases actually hold, however, is that unless the contract provides for consolidated arbitration, the court cannot order it. E.g., Government of United Kingdom v. Boeing Co., supra, 998 F.2d at 72 ("Each of our sister circuit courts that has considered the question since these Supreme Court decisions has held that district courts do not have the authority under the FAA to consolidate arbitrations absent the parties' consent") (emphasis added); American Centennial Ins. Co. v. National Casualty Co., supra, 951 F.2d at 108 ("we align ourselves with the view taken by the Fifth, Eighth, Ninth, and Eleventh Circuits, and hold that a district court is without power to consolidate arbitration proceedings, over the objection of a party to the arbitration agreement, when the agreement is silent regarding consolidation") (emphasis added).

A court can in appropriate circumstances consolidate cases before it (just as we have consolidated the three separate appeals taken from the district court's order), whether or not the parties want the cases consolidated, e.g., Fed.R.Civ.P. 42(a), or stay or transfer a case in order to enable the consolidated or otherwise orderly disposition of multiple proceedings. E.g., 28 U.S.C. § 1404; Finova Capital Corp. v. Ryan Helicopters U.S.A., Inc., 180 F.3d 896 (7th Cir. 1999); Evans Transportation Co. v. Scullin Steel Co., 693 F.2d 715 (7th Cir. 1982). But it cannot consolidate, transfer, etc. arbitration proceedings in defiance of the parties' wishes or contractual undertakings. The arbitration of contractual disputes pursuant to an arbitration clause in the contract is not a stage in a judicial proceeding but an alternative to such a proceeding, and the court cannot mess in the arbitrators' procedures beyond the very limited extent permitted by sections 9 and 10 of the Federal Arbitration Act (the provisions governing judicial review of arbitration awards). E.g., Baravati v. Josephthal, Lyon Ross, Inc., 28 F.3d 704, 709 (7th Cir. 1994); UHC Management Co. v. Computer Sciences Corp., 148 F.3d 992, 997 (8th Cir. 1998). But we cannot see any reason why, in interpreting the arbitration clause for purposes of deciding whether to order consolidation, the court should (as the language we quoted from the American Centennial case might, if read literally, be thought to suggest) place its thumb on the scale, insisting that it be "clear," rather than merely more likely than not, that the parties intended consolidation. It is not as if consolidation of arbitration proceedings were somehow disfavored; quite the contrary — the same considerations of adjudicative economy that argue in favor of consolidating closely related court cases argue for consolidating closely related arbitrations. To repeat, the court has no power to order such consolidation if the parties' contract does not authorize it. But in deciding whether the contract does authorize it the court may resort to the usual methods of contract interpretation, just as courts do in interpreting other provisions in an arbitration clause. See, e.g., First Options of Chicago, Inc. v. Kaplan, supra, 514 U.S. at 944; Mastrobuono v. Shearson Lehman Hutton, Inc., 514 U.S. 52, 62-63 (1995); Volt Information Sciences, Inc. v. Board of Trustees, 489 U.S. 468, 475 (1989); Perry v. Thomas, 482 U.S. 483, 492 n. 9 (1987); Brennan v. King, 139 F.3d 258, 264 (1st Cir. 1998).

The arbitration provision in this case neither clearly permits nor clearly forbids consolidation. In fact, it's a muddle, suggesting that the parties did not think about the issue. So far as bears on the question of consolidation, the provision reads as follows:

Any dispute arising out of the interpretation, performance or breach of this Agreement, including the formation or validity thereof, will be submitted for decision to a panel of three arbitrators. . . . One arbitrator will be chosen by each party [and the party-designated arbitrators will then choose a third, a neutral to preside over the panel and presumably cast the deciding vote in a close case]. . . . Unless otherwise mutually agreed by the parties, arbitration will take place in Chicago. . . . If more than one Retrocessionaire is involved in arbitration where there are common questions of law or fact and a possibility of conflicting awards or inconsistent results, all such Retrocessionaires will constitute and act as one party for purposes of this Article [the arbitration provision]. . . .

The insurers argue that since each of them is a party to the contract, it is impossible that each could have a right to select one arbitrator if a panel of three arbitrators is to decide a dispute involving more than one party on the insurers' side. There is no problem if there is more than one party on the reinsurers' side, by virtue of the last sentence we quoted, whereby all the reinsurers are to constitute a single party. But that does not solve the problem of multiple parties on the insurers' side, because there is no corresponding clause authorizing them to be treated as one. The insurers argue that this asymmetry is powerful evidence against such treatment.

But this leaves out of account that any dispute is to be referred to a panel of three arbitrators, not just a dispute between the reinsurers and a single insurer. As normally understood, the word "dispute" (a word not defined in the contract) does not exclude a dispute involving multiple parties. So far as can be inferred from the parties' demands for arbitration — which are our only clue to the nature of the fight between the parties — there is indeed a single dispute between the reinsurers on the one hand and the insurers on the other, arising out of the conduct of Unicover in negotiating and administering the reinsurance contract.

If "dispute" is taken in its ordinary sense and "party" in the sense in which each of the insurers is a separate party to these appeals (the sense in which we used the word earlier in this opinion), then the first two sentences that we quoted from the arbitration provision are in hopeless conflict. What to do? As a semantic matter, it is easier to dissolve the conflict by reading "party" to mean "side," a common usage, than it is to read "dispute" to mean a dispute with only one party on each side, an uncommon usage. But what then of the fact that the arbitration provision expressly makes the reinsurers one party for purposes of arbitration yet is silent about the insurers? The sensible answer — which incidentally demonstrates the limited utility, see, e.g., In re Continental Casualty Co., 29 F.3d 292, 294 (7th Cir. 1994); In re American Reserve Corp., 840 F.2d 487, 492 (7th Cir. 1988); Illinois Dept. of Public Aid v. Schweiker, 707 F.2d 273, 277 (7th Cir. 1983); In re Sealed Case No. 97-3112, 181 F.3d 128, 132 (D.C. Cir. 1999) (en banc); William N. Eskridge, Jr., "Norms, Empiricism, and Canons in Statutory Interpretation," 66 U. Chi. L. Rev. 671, 676-77 (1999), of the rule of interpretation that goes by the impressive name of expressio unius est exclusio alterius — is that the contract itself makes the insurers one party but not the reinsurers, so that making the reinsurers a single party for purposes of arbitration suggests if anything an intent to have a single arbitration proceeding when there is a single dispute, even if it's a dispute with more than one of the insurers. The contract was negotiated on the insurers' side by Unicover as their agent, and Unicover is also the administrator of the contract. The parties could foresee that any dispute arising out of either the formation or the administration of the contract would be a dispute between the reinsurers and (or over the behavior of) Unicover. Unicover didn't want to be in the position of having to arbitrate separately with each reinsurer, so the arbitration provision specifies that the reinsurers shall constitute a single party. Presumably the reinsurers didn't want to arbitrate separately with each insurer, either, especially since the contract places no limit on the number of insurers that Unicover might bring into the pool of insurers to whom it would be issuing reinsurance policies and then laying off the risk created by those policies on the reinsurers. Another straw in the wind is the provision for arbitration in Chicago, which just happens to be Unicover's headquarters but not that of any of the other parties.

We cannot say that these textual inferences are conclusive in favor of consolidation, but they support it, as do practical considerations, which are relevant to disambiguating a contract, because parties to a contract generally aim at obtaining sensible results in a sensible way. See, e.g., Bratton v. Roadway Package System, Inc., 77 F.3d 168, 173 (7th Cir. 1996); In re Villa West Associates, 146 F.3d 798, 803 (10th Cir. 1998); William C. Atwater Co. v. Panama R.R., 246 N.Y. 519 159 N.E. 418, 419 (N.Y. 1927); Rubin v. Laser, 301 N.E.3d 60 234 Ill.Dec. 592, 703 N.E.2d 453, 459 (Ill.App. 1998); E. Allan Farnsworth, Contracts § 7.10, p. 466 (3d ed. 1999). To have the identical dispute litigated before different arbitration panels is a formula for duplication of effort and a fertile source, in this case, of disputes over esoteric issues in the law of res judicata (the kind of dispute that would also arise if the question of consolidation were for the arbitrators rather than the district court to answer). If separate arbitrations are ordered and the reinsurers lose the first one, will the decision by that arbitration panel have res judicata or collateral estoppel effect in the other arbitrations? See, e.g., W.R. Grace Co. v. Local Union 759, 461 U.S. 757, 764-65 (1983); Independent Lift Truck Builders Union v. NACCO Materials Handling Group, Inc., 202 F.3d 965, 968 (7th Cir. 2000); Chiron Corp. v. Ortho Diagnostic Systems, Inc., No. 99-15064, 2000 WL 309779, at *6 (9th Cir. Mar. 28, 2000); John Hancock Mutual Life Ins. Co. v. Olick, 151 F.3d 132, 139-40 (3d Cir. 1998); National Union Fire Ins. Co. v. Belco Petroleum Corp., 88 F.3d 129, 135-36 (2d Cir. 1996). Will it if the first order is confirmed first? See Miller v. Runyon, 77 F.3d 189, 193-94 (7th Cir. 1996); Chiron Corp. v. Ortho Diagnostic Systems, Inc., supra, at *7; John Hancock Mutual Life Ins. Co. v. Olick, supra, 151 F.3d at 137-39. What if the second order is confirmed first? See Consolidation Coal Co. v. United Mine Workers of America, District 12, Nos. 99-1640 and 99-1641 (7th Cir. appeal pending, argued Jan. 13, 2000). If the reinsurers win, this would not bind any other insurer than the one involved in the particular arbitration — unless the insurers are deemed to be in privity with each other because of the common agency of Unicover. E.g., We Care Hair Development, Inc. v. Engen, 180 F.3d 838, 842 (7th Cir. 1999); Canedy v. Boardman, 16 F.3d 183, 185 (7th Cir. 1994). All these problems are avoided by interpreting the contract to allow the reinsurers to demand a single arbitration, provided there is a single dispute, as appears to be the case; should this turn out not to be the case, severance would be possible.

The insurers have some practical arguments of their own, two related ones in fact. They ask: What if the insurers disagree about the choice of an arbitrator? Standing alone this is a very weak argument; the arbitration clause expressly requires the reinsurers to act as one party and thus agree on a single arbitrator, so apparently the parties thought this a feasible requirement to impose. The insurers seek to strengthen the argument by pointing out that two of the reinsurers are also insurers, and so are on both sides of the dispute. One of them, however, Phoenix, has thrown in its lot with the reinsurers, and does not claim — and obviously does not have — any right to participate in the choice of the insurers' arbitrator. The status of the other, Cologne, is unclear, but obviously it will have to decide which side it's on before the arbitrators are chosen.

We conclude that the balance of both the textual and the practical arguments favor the reinsurers, and we therefore reverse the judgment of the district court and remand for further proceedings consistent with this opinion.