The full case caption appears at the end of this opinion.
Posner, Circuit Judge. The plaintiff appeals fromthe dismissal under Fed. R. Civ. P. 12(b)(6) ofher far-ranging challenge to standard arbitrationprocedure. She had made a contract to selldefendant Argenbright her controlling interest inthe PIMMS Corporation for some $65 million. Thecontract provided that disputes under it would beresolved by arbitration in Chicago “in accordancewith the rules and regulations of the AmericanArbitration Association” and that the contractwas to be construed in accordance with the law ofMinnesota, where PIMMS was located. Shortly afterthe sale, Argenbright gave notice to Smith thatit believed that she had exaggerated PIMMS’srevenue potential, that the exaggerationconstituted a breach of warranty, thatArgenbright had sustained damages of $14 million,and that it wanted to arbitrate the claim. Itfiled the claim with the American ArbitrationAssociation’s Chicago office, which responded bysending the parties a list of 15 arbitratorstaken from the Association’s roster for “Largeand Complex Commercial Cases.” The list contained14 men and one woman. Pursuant to theAssociation’s rules, the parties were asked tostrike the names of any of the persons on thelist whom they did not want to have on thearbitration panel and to rank the remaining ones.One of the names struck by Argenbright was thatof the woman on the list (whom Smith had listedas her first choice), and as a result a panel ofthree male arbitrators was selected–whereuponSmith brought this suit in federal district courtagainst Argenbright and the Association,complaining primarily that the lack of genderdiversity of the list, coupled with Argenbright’saction in excluding the only woman on it, was abreach of contract. Federal jurisdiction is thusbased primarily on diversity of citizenship, seeCaudle v. American Arbitration Ass’n, No. 00-1423, 2000 WL 1528950, at *1 (7th Cir. Oct. 17,2000), but there is also a federal claim, thatthe defendants have denied the plaintiff theequal protection of the laws. The parties do notdiscuss which state’s law governs the state-lawclaim against the AAA, as distinct from Smith’sclaim against Argenbright, but imply by theircitations that it is Illinois law. Curiously, theAssociation, although served, filed no appearancein either the district court or this court. Thatwas taking a chance.