In the

United States Court of Appeals

For the Seventh Circuit

No. 00-1204

Lisa A. Smith,

Plaintiff-Appellant,

v.

American Arbitration Association, Inc.

 and Argenbright, Inc.,

Defendants-Appellees,

Appeal from the United States District Court

for the Northern District of Illinois, Eastern Division.

No. 99 C 7368--John F. Grady, Judge.

Argued September 22, 2000--Decided September 25, 2000

Opinion December 1, 2000

 Before Posner, Manion, and Evans, Circuit Judges.

 Posner, Circuit Judge. 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, No. 00-

1423, 2000 WL 1528950, at *1 (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.

 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.

 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.

 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.

 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."

 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).

 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.

 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.

 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).

 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.

 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.

 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.

 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).

Affirmed.

FOOTNOTE

/* 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.