233 F.3d 502 (7th Cir. 2000)
Lisa A. Smith, Plaintiff-Appellant,v.American Arbitration Association, Inc.  and Argenbright, Inc., Defendants-Appellees,
No. 00-1204
In the  United States Court of Appeals  For the Seventh Circuit
Argued September 22, 2000Decided September 25, 2000Opinion December 1, 2000*

Appeal from the United States District Court  for the Northern District of Illinois, Eastern Division.  No. 99 C 7368--John F. Grady, Judge.[Copyrighted Material Omitted]
Before Posner, Manion, and Evans, Circuit Judges.
Posner, Circuit Judge.


1
The plaintiff appeals from  the dismissal under Fed. R. Civ. P. 12(b)(6) of  her far-ranging challenge to standard arbitration  procedure. She had made a contract to sell  defendant Argenbright her controlling interest in  the PIMMS Corporation for some $65 million. The  contract provided that disputes under it would be  resolved by arbitration in Chicago "in accordance  with the rules and regulations of the American  Arbitration Association" and that the contract  was to be construed in accordance with the law of  Minnesota, where PIMMS was located. Shortly after  the sale, Argenbright gave notice to Smith that  it believed that she had exaggerated PIMMS's  revenue potential, that the exaggeration  constituted a breach of warranty, that  Argenbright had sustained damages of $14 million,  and that it wanted to arbitrate the claim. It  filed the claim with the American Arbitration  Association's Chicago office, which responded by  sending the parties a list of 15 arbitrators  taken from the Association's roster for "Large  and Complex Commercial Cases." The list contained  14 men and one woman. Pursuant to the  Association's rules, the parties were asked to  strike the names of any of the persons on the  list whom they did not want to have on the  arbitration panel and to rank the remaining ones.  One of the names struck by Argenbright was that  of the woman on the list (whom Smith had listed  as her first choice), and as a result a panel of  three male arbitrators was selected--whereupon  Smith brought this suit in federal district court  against Argenbright and the Association,  complaining primarily that the lack of gender  diversity of the list, coupled with Argenbright's  action in excluding the only woman on it, was a  breach of contract. Federal jurisdiction is thus  based primarily on diversity of citizenship, see  Caudle v. American Arbitration Ass'n, 230 F.3d 920, 922 (7th Cir. Oct. 17,  2000), but there is also a federal claim, that  the defendants have denied the plaintiff the  equal protection of the laws. The parties do not  discuss which state's law governs the state-law  claim against the AAA, as distinct from Smith's  claim against Argenbright, but imply by their  citations that it is Illinois law. Curiously, the  Association, although served, filed no appearance  in either the district court or this court. That  was taking a chance.


2
The district court rebuffed Smith's effort to  obtain a preliminary injunction against the  arbitration and so the arbitration went forward  before the all-male panel. The court then  dismissed Smith's suit for failure to state a  claim. Her appeal asks us to order the  arbitration rerun before a new panel that  contains at least one woman. Shortly before the  appeal was argued to us, the trial phase of the  arbitration ended and the arbitrators announced  that they would issue their decision shortly. (We  have not been told whether they have yet done  so.) Lest the pendency of the appeal influence  the arbitration in any way, we accelerated our  consideration and issued an order affirming the  district court with a notation that the opinion  would follow. This is the opinion.


3
Smith expresses concern that because she is a  woman and her opponent is a corporation  presumably controlled by men (though there is no  allegation to that effect), an all-male panel  will be unsympathetic to her. No effort to  substantiate the suggestion that male judges or  arbitrators are prejudiced against wealthy women  who have purely commercial disputes with  corporations has been made; nor has Smith pointed  to any issue in this litigation to which a man  might be insensitive. The relief sought, which  seems premised on the belief that a female  litigant is entitled to be judged by a panel that  includes at least one woman, borders on the  fantastic.


4
But we do not suppose that there is anything in  the law that would forbid private parties to  stipulate to a mode of private dispute resolution  that specified a particular gender composition of  the tribunal, assuming the arbitrators are not  employees of the American Arbitration Association  or of some other dispute-resolution agency  conducting the arbitration, which might bring  Title VII into play. So if Smith has a  contractual right to be judged by an arbitration  panel that contains at least one woman, she can  enforce it, though just how and when are  questions, as we'll see; but let's start with the  question whether there is a possible breach of  contract.


5
Smith relies primarily on a "Guide to Mediation  and Arbitration for Business People," published  by the American Arbitration Association. The  guide states that the Association "monitors the  integrity of the process, the quality of roster  composition and balance in terms of gender,  racial and ethnic diversity," all aimed at a  "bottom line" consisting of "a roster of neutrals  crafted to meet the needs of the parties."  Another publication of the Association, "A Brief  Overview of the American Arbitration  Association," states that the Association  maintains "a national panel of experts, diverse  in gender and ethnicity." These statements alone  cannot support a breach of contract suit against  either the Association or Argenbright. The fact  that the contract provides for arbitration in  accordance with the Association's rules and  regulations no more made the Association a party  to the contract than a building contract that  specifies that the builder will install Kohler  plumbing fixtures makes Kohler a party to the  building contract. The Association did agree to  administer the arbitration between Smith and  Argenbright in exchange for a fee, and by doing  so it undertook to administer the arbitration in  accordance with the Association's rules. But the  "Guide" and the "Brief Overview" are not a part  of those rules, and the rules of the Association  (which, remember, are incorporated in the stock  purchase agreement) are explicit that the  Association's "authority and duties . . . are  prescribed in the agreement of the parties and in  these rules."


6
We doubt, moreover, that a "promise," if that is  how the statements we quoted should be read, to  "monitor . . . balance in terms of gender, racial  and ethnic diversity" or maintain "a national  panel of experts, diverse in gender and  ethnicity," is sufficiently definite to be  enforceable in a suit for breach of contract.  Shields v. Local 705, International Brotherhood  of Teamsters Pension Plan, 188 F.3d 895, 900-01  (7th Cir. 1999); Beraha v. Baxter Health Care  Corp., 956 F.2d 1436, 1441 (7th Cir. 1992). No  guidance is found in the Association's rules, or  statements, or any place else that we can find,  on what these duties of monitoring and  maintenance consist of and how compliance or  noncompliance with them is determined. The  language is not promissory, and this  distinguishes the employee-handbook cases on  which Smith relies. See, e.g., Duldulao v. Saint  Mary of Nazareth Hospital Center, 505 N.E.2d 314,  318 (Ill. 1987); Pine River State Bank v.  Mettille, 333 N.W.2d 622, 627 (Minn. 1983); see 1  E. Allan Farnsworth, Farnsworth on Contracts sec.  2.9a, pp. 93-94 (1990). The closest analogy is to  the federal statute that seeks to prevent  discrimination in the creation of jury venires,  28 U.S.C. sec.sec. 1861-1867, but the analogy is  weak because jurors are drafted and arbitrators  are volunteers. A venire can be compared with the  population from which it was drawn to see whether  it is a representative sample of that population.  But even if a list of lawyers could be compiled  who would be capable of arbitrating large and  complex commercial cases, it would be impossible  to determine how many would be willing to serve  on AAA panels. Either the "promise" on which  Smith relies is too vague to be enforceable or  the AAA never intended (and never manifested an  intent) that the promise be legally enforceable,  or, most likely, both. See, e.g., Architectural  Metal Systems, Inc. v. Consolidated Systems,  Inc., 58 F.3d 1227, 1229 (7th Cir. 1995).


7
The breach of contract claim against Argenbright  is, if anything, weaker than the claim against  the AAA. Argenbright never undertook to exercise  its discretion over arbitrator selection in a  particular way. We do not know why Argenbright  objected to the one woman on the AAA's list; but  even if it did so for precisely the reason that  Smith suspects, this was not the breach of any  express or implied contract between Smith and  itself. We take it that Smith's real complaint  about Argenbright is that Argenbright took  advantage of the Association's having supplied a  list that made it easy for a party to obtain an  all-male panel. The argument in other words is  that the panel composition was contaminated to  Argenbright's advantage and that having thus been  the beneficiary of the Association's breach  Argenbright should, by principles of unjust  enrichment, be forced to relinquish the unfair  advantage that it obtained from that breach.


8
So viewed, however, Smith's claim against  Argenbright is premature. The time to challenge  an arbitration, on whatever grounds, including  bias, is when the arbitration is completed and an  award rendered. E.g., Dean v. Sullivan, 118 F.3d  1170 (7th Cir. 1997); Michaels v. Mariforum  Shipping, S.A., 624 F.2d 411, 414 n.4 (2d Cir.  1980). To allow a party to bring an independent  suit to enjoin the arbitration is inconsistent  with fundamental procedural principles that apply  with even greater force to arbitration than to  conventional litigation. If during jury voir dire  a Batson objection to the exercise of a  peremptory challenge is rejected by the trial  judge, the disappointed litigant cannot bring a  suit to enjoin the litigation. But that is what  Smith tried to do here. It is true that in rare  instances a litigant can interrupt the litigation  by filing an interlocutory appeal or seeking  mandamus. But a party who wants to have such an  option should not (and of course need not)  consent to arbitration, which generally and here  does not have an appellate component. The choice  of arbitration is a choice to trade off certain  procedural safeguards, such as appellate review,  against hoped-for savings in time and expense  (other than the expense of the tribunal), a  measure of procedural simplicity and informality,  and a differently constituted tribunal. Harter v.  Iowa Grain Co., 220 F.3d 544, 553 (7th Cir.  2000); see also Generica Ltd. v. Pharmaceutical  Basics, Inc., 125 F.3d 1123, 1129-30 (7th Cir.  1997). That choice would be disrupted by allowing  a party to arbitration to obtain an interlocutory  appeal to a federal district court, as Smith has  tried to do.


9
The parties are of diverse citizenship, so  Argenbright if it obtains an award in the  arbitration will be able to seek confirmation  (that is, enforcement) of the award in federal  district court under the Federal Arbitration Act.  9 U.S.C. sec. 9; International Union of Operating  Engineers, Local No. 841 v. Murphy Co., 82 F.3d  185 (7th Cir. 1996); P & P Industries, Inc. v.  Sutter Corp., 179 F.3d 861, 866 (10th Cir. 1999).  Smith points out that while she will be able to  object to confirmation, the grounds for objection  permitted by the act (or by judicial extension of  it, First Options of Chicago, Inc. v. Kaplan, 514  U.S. 938, 942 (1995); Cole v. Burns International  Security Services, 105 F.3d 1465, 1486 (DC Cir.  1997)) are extremely limited, and though one of  them is "evident partiality" by the arbitrators,  9 U.S.C sec. 10(a)(2); Harter v. Iowa Grain Co.,  supra, 220 F.3d at 553; Dawahare v. Spencer, 210  F.3d 666, 669 (6th Cir. 2000), this will be  impossible as a practical matter to prove;  therefore she should be permitted to sue now.  That's a non sequitur. The right to object to the  composition of the tribunal on broader grounds  than evident partiality was one of the procedural  rights that Smith gave up when she agreed to the  arbitration clause in the stock purchase  agreement. By agreeing to arbitrate in a setting  in which Argenbright if it prevailed could seek  confirmation under the Federal Arbitration Act,  Smith bound herself to accept the limited  judicial review which that act allows. First  Options of Chicago, Inc. v. Kaplan, supra, 514  U.S. at 942; Connecticut General Life Insurance  Co. v. Sun Life Assurance Co., 210 F.3d 771, 774  (7th Cir. 2000); UHC Management Co. v. Computer  Sciences Corp., 148 F.3d 992, 997 (8th Cir.  1998).


10
We mentioned the principle of Batson v.  Kentucky, 476 U.S. 79, (1986), that peremptory  challenges cannot be based on racial or other  invidious grounds, now including gender. J.E.B.  v. Alabama, 511 U.S. 127 (1994); United States v.  Brisk, 171 F.3d 514, 522-23 (7th Cir. 1999);  United States v. Tipton, 90 F.3d 861, 881 (4th  Cir. 1996). Smith argues that this principle,  which is based on the equal protection clause  (more precisely, where federal rather than state  action is concerned, on the due process clause of  the Fifth Amendment, interpreted as containing an  equal-protection component), should be extended  to arbitration, since the courts through the  Federal Arbitration Act and cognate state  statutes lend their assistance to arbitration. We  disagree. Arbitration is a private self-help  remedy. The American Arbitration Association is a  private organization selling a private service to  private parties who are under no legal obligation  to agree to arbitrate their disputes or, if they  decide to use arbitration to resolve disputes, to  use the services of the Association, which is not  the only provider of such services. Compare  Dunham v. Frank's Nursery & Crafts, Inc., 919  F.2d 1281, 1286 (7th Cir. 1990). When arbitrators  issue awards, they do so pursuant to the  disputants' contract--in fact the award is a  supplemental contract obligating the losing party  to pay the winner. The fact that the courts  enforce these contracts, just as they enforce  other contracts, does not convert the contracts  into state or federal action and so bring the  equal protection clause into play. Parks v. "Mr.  Ford", 556 F.2d 132, 156 (3d Cir. 1977)  (concurring opinion). This is not Shelley v.  Kraemer, 334 U.S. 1 (1948), or Marsh v. Alabama,  326 U.S. 501 (1946), cases in which the  enforcement of private contracts had the effect  of establishing private governments exercising  governmental power under delegation from the  state.


11
Smith also appeals to a provision of Minnesota's  arbitration statute that if the method for  appointing arbitrators agreed upon by the parties  fails, the court shall appoint the arbitrators.  Minn. Stat. sec. 572.10(1). Smith's invocation of  the Minnesota statute is frivolous, first,  because the invocation is premature; second,  because the choice of law provision in the stock  purchase agreement does not appear in the  arbitration clause but is instead a direction to  the arbitrators as to what law to apply (and the  arbitrators, we are told, have so interpreted  it); and third because the agreed method of  selection did not fail, since there was never an  agreement that the list of possible arbitrators  would contain a particular number or percentage  of women.


12
Finally, Smith makes two statutory claims  against the American Arbitration Association. The  first is that the Association's representations  about gender balance violate Illinois's Uniform  Deceptive Trade Practices Act, 815 ILCS 510/2.  The point we made earlier about the vagueness of  the representations is equally applicable here.  Laws forbidding deceptive advertising are  inapplicable to "puffing," which is to say to  general quality claims too vague to create  warranted reliance. Totz v. Continental Du Page  Acura, 602 N.E.2d 1374, 1383 (Ill App. 1992); see  also Lionel Trains, Inc. v. Albano, 831 F.Supp.  647, 651 (N.D. Ill. 1993), aff'd without opinion,  35 F.3d 568 (7th Cir. 1994). That is the nature  of the alleged "promise" of balance and  diversity. Moreover, the statutory remedy is an  injunction against the deceptive advertising, 815  ILCS 510/3; Smith v. Prime Cable of Chicago, 658  N.E.2d 1325, 1337 (Ill. App. 1995); Empire Home  Services, Inc. v. Carpet America, Inc., 653  N.E.2d 852 (Ill. App. 1995), which is not the  relief sought here. Stated otherwise, Smith being  undeceived and the arbitration conducted, her  claim for prospective relief against the  allegedly deceptive advertising, the only relief  sought, is moot.


13
The second statutory claim is of a violation of  the prohibition against gender discrimination in  Illinois' Human Rights Act, 775 ILCS 5/5-102.  Smith argues that the AAA is a "place of public  accommodation" within the meaning of the act  because it is a business whose services are  "offered, sold or otherwise made available to the  public." But there is no allegation of  discrimination by the AAA. Argenbright is accused  of having taken advantage of the opportunity that  the Association created for it to strike the  woman from the list of possible arbitrators, and  that action (depending on the company's motive)  could conceivably be a form of gender  discrimination (by analogy to Batson), though  that we need not decide since there is no  suggestion that Argenbright is a place of public  accommodation. The charge against the AAA is that  it failed to maintain gender diversity or  balance, but such a failure, while it might  conceivably violate an undertaking by the AAA, is  not discrimination. Efforts to achieve gender  diversity can constitute reverse discrimination;  but failure to achieve diversity, failure in  other words to engage in affirmative action,  cannot. The law permits affirmative action in  some circumstances, but it does not require it  except as a remedy for discrimination by the  defendant. E.g., Texas Dept. of Community Affairs  v. Burdine, 450 U.S. 248, 259 (1981); Yatvin v.  Madison Metropolitan School District, 840 F.2d  412, 415 (7th Cir. 1988).


14
Affirmed.



Notes:


*
 The plaintiff filed a petition for rehearing  within 14 days following the issuance of our  decision, without waiting for us to issue the  opinion explaining our decision. She cannot be  faulted for doing this, since the period for  filing a petition for rehearing runs from the  date of the judgment rather than from the date of  the opinion, Fed. R. App. P. 40(a)(1), but for  future reference we note that the court's policy,  in cases in which decision precedes opinion, is  to allow the losing party a 14-day extension of  time following the issuance of the opinion for  seeking rehearing. We shall therefore give Smith  14 days to file a supplementary petition if she  wishes.


