EASTERBROOK, Circuit Judge.

Martha Baker sued Sheena George in Illinois court following an automobile accident; Baker contends that George was at fault. Sheena is insured under a policy issued to her parents Timothy and Rebecca George. The policy, underwritten by Grinnell Select Insurance Co., covered two of the Georges' cars. The declarations page of the policy sets $100,000 as the per-person, per-accident maximum coverage. Grinnell has tendered $100,000 to Baker as the policy limit. Baker and the three Georges contend that Grinnell's exposure is $200,000, not $100,000, because each of the Georges' two cars contributed its own limit, which they say may be stacked for double coverage. To resolve the dispute, Grinnell initiated this action in federal court under the diversity jurisdiction, seeking a declaratory judgment that its payment of $100,000 exhausts all coverage. The district court entered summary judgment in favor of Baker and the Georges.

Grinnell relies on two anti-stacking clauses in the policy. One is implicit, the other explicit. The first is labeled "Limit of Liability" and reads:

The limit of liability shown in the Declarations for each person for Bodily Injury Liability is our maximum limit of liability for all damages, including damages for care, loss of services or death, arising out of "bodily injury" sustained by any one person in any one auto accident. Subject to this limit for each person, the limit of liability shown in the Declarations for each accident for Bodily Injury Liability is our maximum limit of liability for all damages for "bodily injury" resulting from one auto accident.

In other words, one injured person is matched against "the" limit of liability shown in the declarations (for this policy, $100,000) rather than against multiple limits. The explicit anti-stacking clause immediately following this text reinforces the point:

This is the most we will pay regardless of the number of:

1. "Insureds";

2. Claims made;

3. Vehicles or premiums shown in the Declarations; or

4. Vehicles involved in the auto accident.

It is hard to imagine clearer language. But it is not enough for one state appellate court. The Appellate Court of Illinois, Fifth District, has held in two decisions that, when the declarations page of a policy contains the language "insurance is provided where a premium is shown", the policy is ambiguous notwithstanding an explicit anti-stacking clause, because an insured might read the language "insurance is provided" to permit stacking. See Hall v. General Casualty Co., 328 Ill.App.3d 655, 262 Ill.Dec. 760, 766 N.E.2d 680 (5th Dist. 2002); Yates v. Farmers Automobile Insurance Ass'n, 311 Ill.App.3d 797, 244 Ill.Dec. 154, 724 N.E.2d 1042 (5th Dist. 2000). Two other districts of the state's appellate court, by contrast, have held that a clause identical to the one at issue in Hall forbids stacking. See Domin v. Shelby Insurance Co., 326 Ill.App.3d 688, 260 Ill.Dec. 563, 761 N.E.2d 746 (1st Dist. 2001); Pekin Insurance Co. v. Estate of Ritter, 322 Ill.App.3d 1004, 255 Ill.Dec. 900, 750 N.E.2d 1285 (4th Dist. 2001). Both Domin and Pekin rejected the holding of Yates; then Hall rejected the holding of Domin (it did not mention Pekin). In our case the district judge followed Hall and thus held that the policy allows stacking.

Illinois enforces clear anti-stacking clauses. See, e.g., Grzeszczak v. Illinois Farmers Insurance Co., 168 Ill.2d 216, 213 Ill.Dec. 606, 659 N.E.2d 952 (1995); Bruder v. Country Mutual Insurance Co., 156 Ill.2d 179, 189 Ill.Dec. 387, 620 N.E.2d 355 (1993). Hall conceded that the clause in that policy (materially identical to the clause in Grinnell's) was unambiguous. 328 Ill.App.3d at 658, 262 Ill.Dec. 760, 766 N.E.2d 680. What more is there to say? Put an unambiguous anti-stacking clause together with the holdings of Grzeszczak and Bruder, and you get the outcome of Domin and Pekin, not that of Hall or Yates.

Our task in a diversity action is to anticipate, as best we can, what the state's highest court will do. Usually decisions of intermediate state courts are good evidence about the meaning of local law, but when the state's appellate courts are divided they offer little useful guidance. We must decide independently. Given Grzeszczak and Bruder it is unlikely that the Supreme Court of Illinois would follow Hall or Yates.

As far as we can tell, the Fifth District stands alone among the 50 state judicial systems. The policy Grinnell issued — with a declarations page listing multiple cars, premiums, and coverages separately, and then a clause stating that the limit for one car and one accident is the total available no matter how many vehicles or premiums are shown in the declarations — is the standard auto-liability form devised by the Insurance Services Office and is in use across the nation. Defendants did not cite, and we could not find, any decision outside the Fifth District allowing stacking. Plenty of decisions in other states hold that this or similar language forecloses stacking. See, e.g., Rodriguez v. General Accident Insurance Co., 808 S.W.2d 379 (Mo. 1991); Saccucci v. State Farm Mutual Automobile Insurance Co., 32 Ohio St.3d 273, 512 N.E.2d 1160 (1987); Antanovich v. Allstate Insurance Co., 507 Pa. 68, 488 A.2d 571 (1985); Upshaw v. Trinity Cos., 842 S.W.2d 631 (Texas 1992); Folkman v. Quamme, 264 Wis.2d 617, 665 N.W.2d 857 (2003). We expect the Supreme Court of Illinois to follow them.

Even a mound of decisions would not deflect a powerful argument, but Hall and Yates do not offer one. What they say is that the language of the declarations page stating that "insurance is provided where a premium is shown" could be understood by a reasonable insured to mean that all listed coverages may be combined. The court then construes ambiguity in favor of the insureds. Let us assume that the declarations page is ambiguous (though we think it is not, for a reason to be explained); still, how does this justify stacking, unless the no-stacking clause is read out of the policy? Its function is to say that even if some other clause suggests the possibility of stacking, that is not what the policy means. It is a disambiguator. To see ambiguity in the policy is to learn why the anti-stacking clause was included; it is not remotely to justify overriding the anti-stacking clause. Anyway, the declarations page is straight-forward. A policy that covers two vehicles, with a premium and limit attached separately, says that even if each vehicle has an accident, the limit for each remains available. A policy covering two cars and multiple drivers is twice as likely to be called on as a policy covering one car and one driver; the separate premium compensates the insurer for this marginal risk. On the holding of Hall and Yates, however, a policy covering two cars (each at the same premium as one car) quadruples rather than doubles the insurer's exposure, because it doubles the number of cars and doubles the limit for each. Reasonable insureds would not expect quadruple the coverage for double the premium. Cf. Great Lakes Dredge Dock Co. v. Chicago, 260 F.3d 789 (7th Cir. 2001); Sybron Transition Corp. v. Security Insurance of Hartford, 258 F.3d 595 (7th Cir. 2001). The anti-stacking clause makes clear that adding a car to the policy increases the number of vehicles covered, but not the limits for any one car or accident.

REVERSED