
516 F.3d 546 (2008)
EDSTROM INDUSTRIES, INC., Plaintiff-Appellant,
v.
COMPANION LIFE INSURANCE COMPANY, Defendant-Appellee.
No. 07-2165.
United States Court of Appeals, Seventh Circuit.
Argued January 11, 2008.
Decided February 11, 2008.
*547 *548 John E. Murray (argued), Simandl & Murray, Waukesha, WI, for Plaintiff-Appellant.
Anne W. Reed (argued), Reinhart, Boerner, Van Deuren, Milwaukee, WI, for Defendant-Appellee.
Charlotte Gibson, Office of the Attorney General, Wisconsin Dept. of Justice, Madison, WI, for Amicus Curiae State of Wisconsin.
Noreen J. Parrett, Parrett & O'Connell, Madison, WI, for Amicus Curiae, National Association of Insurance Commissioners.
Before BAUER, POSNER, and EVANS, Circuit Judges.
POSNER, Circuit Judge.
Edstrom, a manufacturing company that is the plaintiff in this diversity suit, which is governed by Wisconsin law, sponsors a group health insurance plan for its employees and their dependents. It pays claims under the plan out of its own pocketup to $65,000. Above that, an insurance company, the defendant, Companion, which has sold Edstrom what is called a "stop loss" insurance policy, pays. As explained in Jerry S. Rosenbloom, The Handbook of Employee Benefits: Design, Funding and Administration, 98 (2005), "If an organization utilizes a cost-plus or self-insured method of financing, it may choose to limit its potential aggregate medical claims exposure by purchasing insurance that would make payment if claims exceeded a certain predetermined amount for the entire group. This insurance coverage for capping the total claims experience of the group is known as aggregate stop loss. A firm might also limit its liability using specific stop loss. Specific stop loss sets a limit on the amount that a plan sponsor will pay for an individual case. If a catastrophic medical case occurs, the employer will only be responsible for paying covered medical costs on that individual case up to the stop-loss amount." Companion's policy specifies an aggregate as well as a specific stop-loss amount, but the former is not involved in this case and we can therefore ignore it.
As a condition of issuing the policy, Companion required Edstrom to identify any participant in its group insurance health plan who could reasonably be expected to incur more than $32,500 in medical expenses in 2004. In December 2003, Edstrom told Companion there was no such participant, and the policy was issued to Edstrom on January 1, 2004. Four months before Edstrom had made the required representation, however, one of the *549 plan participants had had a child who shortly after birth had developed a grave medical condition. It has not been determined whether Edstrom learned this before or after it made the representation. When Companion discovered the child's condition, it altered the policy to raise the child's deductible from $65,000 to $450,000, pursuant to a provision of the policy that after noting Companion's reliance on information provided by the insured states that "should subsequent information become known which, if known prior to the issuance of this [policy], would affect the rates, deductibles, terms or conditions hereunder, [Companion] will have the right to revise [them] as of the effective date of issuance, by providing written notice to the [insured]." By the end of 2004, in reliance on this provision, Companion had refused to reimburse Edstrom for $890,000 in medical expenses that Edstrom had incurred for treatment of the child.
Edstrom invoked arbitration pursuant to the insurance policy, lost, sought unsuccessfully in the district court to overturn the arbitrator's decision, and now appeals to us.
The arbitration clause included an "express stipulation that the arbitrator shall strictly abide by the terms of this [policy] and shall strictly apply rules of law applicable thereto," namely the rules of Wisconsin law. This stipulation persuaded the parties and the district judge that the arbitration is governed by Wisconsin's arbitration statute rather than by the Federal Arbitration Act (title 9 of the U.S. Code). It is true that the contract in which the clause is embedded affects interstate commerce, and so the federal act is applicable. 9 U.S.C. § 2; Allied-Bruce Terminix Cos. v. Dobson, 513 U.S. 265, 115 S.Ct. 834, 130 L.Ed.2d 753 (1995). But the Supreme Court has held that parties can opt out of the federal act, provided the state arbitration statute does not contain provisions that would undermine the federal act's aim of facilitating the resolution of disputes involving maritime or interstate commerce by arbitration. Compare Volt Information Sciences, Inc. v. Board of Trustees of Leland Stanford Junior University, 489 U.S. 468, 476-79, 109 S.Ct. 1248, 103 L.Ed.2d 488 (1989), with Doctor's Associates, Inc. v. Casarotto, 517 U.S. 681, 686-87, 116 S.Ct. 1652, 134 L.Ed.2d 902 (1996); see also Flexible Mfg. Systems Pty. Limited v. Super Products Corp., 86 F.3d 96 (7th Cir.1996); Securities Industry Ass'n v. Connolly, 883 F.2d 1114, 1120 (1st Cir.1989). The proviso is satisfied here; the Wisconsin and federal statutes do not differ in any particular that bears on this appeal. Cf. Flexible Mfg. Systems Pty. Limited v. Super Products Corp., supra, 86 F.3d at 98-99.
The courts of appeals are divided over a question related to opting out of the Federal Arbitration Actwhether parties can alter the standard of judicial review of arbitral awards, and specifically can make it more searching, without running afoul of the Act. Most of the cases answer yes. Compare Puerto Rico Telephone Co. v. U.S. Phone Mfg. Corp., 427 F.3d 21, 31 (1st Cir.2005); Jacada (Europe) Ltd. v. International Marketing Strategies, 401 F.3d 701, 710-12 (6th Cir.2005); Roadway Package System, Inc. v. Kayser, 257 F.3d 287, 292-93 (3d Cir.2001), and Gateway Technologies, Inc. v. MCI Telecommunications Corp., 64 F.3d 993, 997 (5th Cir. 1995), with Kyocera Corp. v. Prudential-Bache Trade Services, Inc., 341 F.3d 987, 1000 (9th Cir.2003) (en banc), and Bowen v. Amoco Pipeline Co., 254 F.3d 925, 936-37 (10th Cir.2001). The question is before the Supreme Court. Hall Street Associates, L.L.C. v. Mattel, Inc., 196 Ved.Appx. 476 (9th Cir.2006), cert. granted, ___ U.S. *550 ___, 127 S.Ct. 2875, 167 L.Ed2d 1151 (May 29, 2007).
The question in our case is different. It is whether the arbitrator can be directed to apply specific substantive norms and held to the application. The Supreme Court held in the Volt case that parties to a contract may include in the contract's arbitration clause a choice of law provision defining, by reference to a state's arbitration law (provided it does not undermine the federal arbitration law), "the rules under which that arbitration will be conducted." 489 U.S. at 479, 109 S.Ct. 1248; see also Dr. Kenneth Ford v. NYL-Care Health Plans of Gulf Coast, Inc., 141 F.3d 243, 246-49 (5th Cir.1998). We cannot think of any reason why the choice of law provision could not designate the governing substantive norms. Cf. 1 Jay E. Grenig, Alternative Dispute Resolution, § 7.2, p. 149-51 (3d ed.2005). The alternative would be to leave every arbitrator free to make up his own law of contracts.
It shouldn't matter that the arbitrator was directed to "strictly" apply, rather than just apply, Wisconsin law. If parties add, in the provision designating what body of law shall apply to disputes referred to arbitration, "and we mean it!" which is in essence what they did hereno federal policy requires the arbitrator to ignore that directive. Nowhere in the Federal Arbitration Act is it written that arbitrators are always to apply loosely whatever body of law the parties have specified to guide the arbitrators in resolving disputes.
The arbitrator ruled that the insurance policy gave Companion "the complete and unfettered right at its sole election" to raise the deductible "when it became aware of [the child's] medical condition. . . . It is of no moment whether omission of [the child] was, in the word[s] of Edstrom's counsel, `an honest mistake,' or the product of Edstrom's failure to exercise due care or worse. This is because, first and foremost, the contract gave [Companion] the unqualified right to revise deductibles upon disclosure of previously undisclosed conditions." Edstrom argues that the ruling violates a Wisconsin statute which provides that a misrepresentation cannot affect an insurer's obligations unless the insured "knew or should have known that the representation was false." Wis. Stat. § 631.11(1)(b). So if Edstrom neither knew nor had reason to know, when it represented to Companion that no plan participant or dependent was likely to incur medical expenses in excess of $32,500 in 2004, that the representation was false, it should be home free. The arbitrator did not mention the statute, but the magistrate judge ruled that it did not apply in this case because it does not apply to contracts of reinsurance, Wis. Stat. § 631.01(2), and he held that the stop-loss policy was a contract of reinsurancethat Edstrom was the insurer of claims under its group health plan and Companion was the reinsurer. If this is right, it is irrelevant whether Edstrom knew or should have known that a participant in its plan was likely to incur medical expenses in excess of the deductible. As the arbitrator said, the policy, makes that irrelevant, so that only if the statute is applicable, preempting the policy provision, is Companion's right to raise the deductible on the basis of an innocently undisclosed preexisting condition constrained.
The magistrate judge's ruling that stop-loss insurance is reinsurance under Wisconsin law is perhaps understandable, because "unlike traditional group health insurance, stop-loss insurance is akin to reinsurance in that it does not provide coverage directly to plan members or beneficiaries." Travelers Ins. Co. v. Cuomo, 14 F.3d 708, 723 (2d Cir.1993), *551 reversed on other grounds, 514 U.S. 645, 115 S.Ct. 1671, 131 L.Ed.2d 695 (1995). But kinship is not enough. It is a mistake to think that anything someone does to "insure" someone else against a risk is "insurance" within the meaning of statutes that regulate insurance. If you sign an accommodation note, you guarantee another's debt; in effect, you "insure" the creditor. If a contract contains a warranty, the promisor is "insuring" the promisee against the consequences of a defect in the product covered by the warranty. Strict products liability is likewise a system of insurance against product defects (though that is not all it is). A debtor's promise to indemnify his creditor for the costs of collection if the debtor defaults is still another example of "insurance" in the broad sense. And if a company promises a "golden parachute" to one of its executives, it is "insuring" the executive against his not being able to find as good a job should he lose his present one. But as in the other examples, the golden parachute is not an "insurance" policy within the meaning of the insurance statutes. Finally, a person who has a $5,000 deductible in his automobile collision policy is "self-insured" for damage up to the amount, but that does not make him an insurance company and his auto insurance policy a reinsurance policy. Stop-loss insurance is an insurance policy for losses that the insured self-insures up to the limit of the deductible.
Reinsurance contracts are (largely) unregulated because they are contracts between insurance companies, Ott v. All-Star Ins. Corp., 99 Wis.2d 635, 299 N.W.2d 839, 843 (1981); Franklin Mutual Ins. Co. v. Meeme Town Mutual Fire Ins. Co., 68 Wis.2d 179, 228 N.W.2d 165, 166 (1975) ("reinsurance, to an insurance lawyer, means one thing onlythe ceding by one insurance company to another of all or a portion of its risks for a stipulated portion of the premium" (internal quotation marks, and citation, omitted)), and insurance companies are heavily regulated. The insurance policies they issue are regulated in order to protect insureds from insurers (and to an extent the reverse as well), rather than to protect insurance companies from each other. Edstrom is not an insurance company, but an insured. See. Wis. Stat. § 600.03(27), and with specific reference to stop-loss insurance, Wisconsin Office of Commissioner of Insurance, "Opinion Letter Regarding `Single Employer Self-Insured Group Medical Plan" 2 (July 22, 2002), and "Regulatory Alert to Stop Loss Carriers and Third Party Administrators" 2 (June 4, 2003), www.oci.wi.gov/ bulletin/0603mewa.htm (visited Jan. 18, 2008); Terry Humo, Employer's Guide to Self-Insuring Health Benefits ¶ 600, p. 2 (2007); cf. 29 U.S.C. § 1144(b)(2)(B) (employee welfare benefit plans governed by ERISA may not be deemed to be insurance companies). Companion is not a reinsurance company, but an insurance company. True, Edstrom is a company rather than a hapless individual, but chapter 31 of the Wisconsin statutes, the chapter that contains the protective provision at issue in this case, does not exempt from its protections insureds that happen not to be natural persons.
The magistrate judge's interpretation would not only strip the purchasers of stop-loss insurance, even when they are small companies, of the extensive protections that Wisconsin law provides to insureds, see, e.g., Wis. Stat. §§ 631.20, 645.68(3), (5), but it would disrupt the Wisconsin Health Insurance Risk Sharing Plan. The plan provides health insurance to persons who cannot obtain private coverage, and finances the program by imposing fees on health-insurance companies including companies that sell stop-loss insurance to employers who sponsor self-funded employee welfare benefit plans. *552 See Safeco Life Ins. Co. v. Musser, 65 F.3d 647 (7th Cir.1995); Wis. Stat. §§ 149.10(b)(5), 149.13. Were Companion classified as a reinsurance company rather than a seller of health insurance, it would be exempt from the tax.
Companion argues that it doesn't matter whether the arbitrator interpreted the statute correctly, or, as we believe, incorrectlya belief consistent with how other courts have interpreted similar statutes in other states. Kitchell v. Public Service Co. of New Mexico, 126 N.M. 525, 972 P.2d 344, 348 (1998); South Carolina Property & Casualty Ins. Guaranty Ass n v. Carolinas Roofing & Sheet Metal Contractors Self-Insurance Fund, 315 S.C. 555, 446 S.E.2d 422, 424-25 (1994); Stamp v. Department of Labor & Industries, 122 Wash.2d 536, 859 P.2d 597, 599-601 (1993); Iowa Contractors Workers' Compensation Group v. Iowa Ins. Guaranty Ass'n, 437 N.W.2d 909, 914-16 (Iowa 1989); Zinke-Smith, Inc. v. Florida Ins. Guaranty Ass'n, Inc., 304 So.2d 507 (Fla.App.1974); Tennessee Department of Commerce and Insurance, "Regulation of Excess Stop-Loss Coverage," Tenn. Ins. Bulletin 7-1-94 (1994). All that matters, according to Companion, is that we be able to imagine an "interpretive path" connecting the statute to the arbitrator's conclusion that the statute does not apply to a stop-loss insurer. Chicago Typographical Union No. 16 v. Chicago Sun-Times, Inc., 935 F.2d 1501, 1504-06 (7th Cir.1991). And it is true that errors of law committed by arbitrators are not grounds for setting aside an arbitral award. That would transform the judicial role in arbitration into appellate review of the award. George Watts & Son, Inc. v. Tiffany & Co., 248 F.3d 577, 579 (7th Cir.2001). The parties' effort to shift the resolution of their dispute from the court system, by agreeing to arbitration, would be thwarted.
But precisely because arbitration is a creature of contract, the arbitrator cannot disregard the lawful directions the parties have given them. If they tell him to apply Wisconsin law, he cannot apply New York law. Id.; Milwaukee Board of School Directors v. Milwaukee Teachers' Education Ass'n, 93 Wis.2d 415, 287 N.W.2d 131, 135-36 (1980). "When parties agree to arbitrate their disputes they opt out of the court system, and when one of them challenges the resulting arbitration award he perforce does so not on the ground that the arbitrators made a mistake but that they violated the agreement to arbitrate, as by corruption, evident partiality, exceeding their powers, etc.conduct to which the parties did not consent when they included an arbitration clause in their contract." Wise v. Wachovia Securities, LLC, 450 F.3d 265, 269 (7th Cir.2006).
The arbitration clause in this case told the arbitrator to apply Wisconsin law "strictly." This unusual stipulation, like other exact directive language in arbitration clauses, see, e.g., Poland Spring Corp. v. United Food & Commercial Workers Int'l Union, AFL-CIO-CLC, Local 1445, 314 F.3d 29 (1st Cir.2002); Roadway Package System, Inc. v. Kayser, 257 F.3d 287 (3d Cir.2001); Milwaukee Board of School Directors v. Milwaukee Teachers' Education. Ass'n, supra, 287 N.W.2d at 135-36, limited the extent to which the arbitrator could indulge his fancy, here in interpreting Wisconsin insurance law. It is unrealistic to think that the arbitrator was even trying to interpret Wisconsin law. For though the misrepresentation statute, Wis. Stat. § 631.11(1)(b), on which Edstrom relies was argued to the arbitrator, he did not mention it in his opinion, let alone try to show that it is inapplicable because stop-loss insurance is really reinsurance. He seems not to have interpreted *553 it at all but merely to have ignored it, which was inconsistent with the directive, that he strictly apply Wisconsin lawand would have been inconsistent even if "strictly" had been omitted.
It might be replied that had the arbitrator not written an opinion (and he was not required to do so), we would attribute to him whatever interpretive path might lead to a conclusion that the statute was indeed inapplicable; and so if we pick apart arbitrators' opinions as we are doing here the result will be to deter arbitrators from writing opinions and "this would be undesirable for a well-reasoned opinion tends to engender confidence in the integrity of the process and aids in clarifying the underlying agreement." United Steelworkers of America v. Enterprise Wheel & Car Corp., 363 U.S. 593, 598, 80 S.Ct. 1358, 4 L.Ed.2d 1424 (1960). We doubt that there is an interpretive path in this case. Chicago Typographical Union No. 16 v. Chicago Sun-Times, Inc., supra, 935 F.2d at 1504-06. Companion has tried to persuade us that there is, but has failed. And we can no more ignore what an arbitrator says than what a jury says when it returns a special verdict rather than a general verdict or what a judge says who explains the basis for a ruling excluding evidence rather than just saying "objection sustained." Had the arbitrator in this case said to hell with Wisconsin law, we could not enforce his award on the ground that had he said nothing we would imagine what he might have said to make it seem that he was applying that law. Westerbeke Corp. v. Daihatsu Motor Co., 304 F.3d 200, 212 (2d Cir.2002); Ottley v. Sheepshead Nursing Home, 688 F.2d 883, 891-92 and n. 2 (2d Cir.1982) (concurring opinion).
Companion further argues that we must uphold the arbitrator's ruling if he could have found that the statute, even if strictly applied, would not forbid raising the deductible. There was evidence that Edstrom knew or should have known that its representation was false, and if that is right the statute would not protect it. But by saying only that the sincerity of Edstrom's representation was irrelevant (which it would be, if the Wisconsin statute were inapplicable), the arbitrator implied that he had not decided, and would not decide, the issue.
The district court is directed to vacate the arbitration award and return the matter to the arbitrator to determine whether Edstrom knew or should have known that its representation to Companion was false.
REVERSED AND REMANDED, WITH DIRECTIONS.
