This appeal primarily concerns the issue, surprisingly unsettled in this Circuit, as to what standards govern a district judge in adjudicating a motion for class certification under Rule 23 of the Federal Rules of Civil Procedure. Comprehended within this broad issue are subsidiary issues such as whether a definitive ruling must be made that each Rule 23 requirement has been met or whether only some showing of a requirement suffices, whether all of the evidence at the class certification stage is to be assessed or whether a class plaintiff's evidence, if not fatally flawed, suffices, and whether the standards for determination of a Rule 23 requirement are lessened when a Rule 23 requirement overlaps with an aspect of the merits of the proposed class action. Finally, the appeal presents the question whether granting a motion for class certification in the pending litigation exceeded the District Court's discretion.

These issues arise on an appeal by Defendants-Appellants Merrill Lynch & Co. and others ("the underwriters") from the October 13, 2004, order of the District Court for the Southern District of New York (Shira A. Scheindlin, District Judge) granting in part Plaintiffs-Appellees' motion for class certification in six securities fraud class actions. The six actions were selected by the District Court as "focus cases" out of 310 consolidated class actions, which themselves were consolidations of thousands of separate class actions. All of the lawsuits, including the six at issue on this appeal, involve claims of fraud on the part of several of the nation's largest underwriters in connection with a series of initial public offerings ("IPOs").

We conclude (1) that a district judge may not certify a class without making a ruling that each Rule 23 requirement is met and that a lesser standard such as "some showing" for satisfying each requirement will not suffice, (2) that all of the evidence must be assessed as with any other threshold issue, (3) that the fact that a Rule 23 requirement might overlap with an issue on the merits does not avoid the court's obligation to make a ruling as to whether the requirement is met, although such a circumstance might appropriately limit the scope of the court's inquiry at the class certification stage, and (4) that the cases pending on this appeal may not be certified as class actions. We therefore vacate the class certifications and remand for further proceedings.

Throughout 2001, thousands of investors filed class actions against 55 underwriters, 310 issuers, and hundreds of individual officers of the issuing companies, alleging that the Defendants had engaged in a scheme to defraud the investing public in violation of federal securities laws. The Assignment Committee of the Southern District of New York transferred all these suits to Judge Scheindlin for pretrial coordination. Judge Scheindlin consolidated the thousands of cases by issuer, resulting in 310 consolidated actions.

The complaints, as amended, consist of a set of "Master Allegations" applicable to all 310 consolidated actions and a "Class Action Complaint" specific to each of the 310 issuers. The Master Allegations describe three fraudulent devices used by the underwriters. First, they allege that the underwriters conditioned allocations of shares at the offer price on agreements to purchase shares in the aftermarket (the "Tie-in Agreements"). Second, they allege that the underwriters also required customers who received allocations of shares at the offer price to pay three forms of "Undisclosed Compensation" to the underwriters: (1) paying inflated brokerage commissions, (2) paying commissions on churned transactions in unrelated securities, and (3) purchasing other unwanted securities from the underwriters. Third, the Plaintiffs allege that the underwriters used their analysts in several improper ways: (1) setting unrealistic price targets, (2) promising a "hot" analyst to an issuer in exchange for underwriting the IPO, (3) tying analyst compensation to performance of the investment banking division, (4) allowing analysts to own shares of stocks they were touting, and (5) failing to disclose these conflicts of interest. The Master Allegations also allege that the underwriters facilitated receipt of quick profits by insiders of the issuer and that the issuers (also Defendants) "participated in and benefitted from" the underwriters' misconduct.

The Master Allegations detail the specific activities of each underwriter. These allegations include reports of the tie-in arrangements, undisclosed compensation, and analyst manipulation.

The issuers in the six focus cases involved in the pending appeal are Corvis Corp., Engage Technologies, Inc., FirePond, Inc., iXL Enterprises, Inc., Sycamore Networks, Inc., and VA Software Corp. All six complaints include the following six claims:

* claims under section 11 of the Securities Act, 15 U.S.C. § 77k, against the issuer, individual officers, and underwriters for untrue material statements of fact or material omissions from the registration statement, specifically the tie-in agreements and the undisclosed compensation;

* claims under section 15 of the Securities Act, 15 U.S.C. § 77o, against individual officers for derivative liability for an issuer's violation of section 11;

* claims under section 10(b) of the Securities and Exchange Act of 1934 ("the Exchange Act"), 15 U.S.C. § 78j, and Rule 10b-5, 17 C.F.R. § 240.10b-5, against the underwriters for deceptive and manipulative practices in connection with an IPO, specifically the tie-in agreements and the undisclosed compensation;

* claims under section 10(b) of the Exchange Act and Rule 10b-5 against the underwriters for materially false or misleading or material omissions from the registration statement/prospectus, specifically concealment of the tie-in agreements, undisclosed compensation, and analyst conflicts of interest;

* claims under section 10(b) of the Exchange Act and Rule 10b-5 against issuers and individual officers for materially false or misleading statements or material omissions, specifically concealment of the underwriters' wrongdoing; and

* claims under section 20(a) of the Exchange Act, 15 U.S.C. § 78t, against individual officers for derivative liability for an issuer's violation of Rule 10b-5.

Two of the complaints, those concerning iXL Enterprises, Inc. and Sycamore Networks, Inc., also included three additional claims related to secondary offerings that occurred with stocks of those issuers:

* claims under section 11 of the Securities Act against the issuer, individual officers, and underwriters for untrue material statements of fact or material omissions from the registration statement for the secondary offering, specifically the tie-in agreements and the undisclosed compensation;

* claims under section 15 of the Securities Act against individual officers for derivative liability for an issuer's violation of section 11 in connection with the secondary offering; and

* claims under section 10(b) of the Exchange Act and Rule 10b-5 against the underwriters for deceptive and manipulative practices in connection with the secondary offering, specifically the requirement that allocants in the IPO agree to purchase shares in the secondary offering.

Motions to Dismiss. In February 2003, Judge Scheindlin ruled on the Defendants' motions to dismiss. In re IPO Securities Litigation, 241 F. Supp. 2d 281 (S.D.N.Y. 2003). Judge Scheindlin denied the Defendants' motions except with respect to two sets of claims: the section 11 and section 15 claims of Plaintiffs who had sold their shares above the offering price, and some of the Rule 10b-5 claims against issuers and individual officers. Id. at 296-97. Judge Scheindlin granted the Plaintiffs leave to re-plead the latter claims. Id. at 399.

In December 2003, Judge Scheindlin denied the Underwriter Defendants' renewed motion to dismiss. In re IPO Securities Litigation, 297 F. Supp. 2d 668 (S.D.N.Y. 2003). Judge Scheindlin held that the Plaintiffs' allegations of loss causation were sufficient when they alleged that the Defendants had manipulated the market. She also held that it was fair to infer dissipation of the inflated price over time in a manipulation case, notwithstanding the Second Circuit's intervening decision in Emergent Capital Investment Management, LLC v. Stonepath Group, Inc., 343 F.3d 189 (2d Cir.2003) (holding that, in a material misstatement or omission securities fraud action, plaintiffs must allege a price correction to adequately plead loss causation). 297 F.Supp.2d at 674-75.

Class Certification. In October 2004, Judge Scheindlin issued an order granting in part and denying in part the Plaintiffs' motions for class certification in the six focus cases. In re IPO Securities Litigation ("IPO Dist. Ct."), 227 F.R.D. 65 (S.D.N.Y.2004). For each focus case, Judge Scheindlin defined the class as follows:

The Class consists of all persons and entities that purchased or otherwise acquired the securities of [Specific Issuer] during the Class Period and were damaged thereby. Excluded from the Class are:

(1) Defendants herein, each of their respective parents, subsidiaries, and successors, and each of their respective directors, officers and legal counsel during the Class Period, and each such person's legal representatives, heirs, and assigns, members of each such person's immediate family, and any entity in which such person had a controlling interest during the Class Period;

(2) all persons and entities that, with respect to [Specific Issuer's] initial public offering: (a) received an allocation, (b) placed orders to purchase shares of that issuer's securities in the aftermarket within four weeks of the effective date of the offering, (c) paid any undisclosed compensation to the allocating underwriter(s), and (d) made a net profit (exclusive of commissions and other transaction costs), realized or unrealized, in connection with all of such person's or entity's combined transactions in [Specific Issuer's] securities during the Class Period; and

(3) all persons and entities who satisfy all of the requirements of subparagraph (2) with respect to any of the 309 initial public offerings that are the subject of these coordinated actions, if that offering occurred prior to [Specific Issuer's] offering.

Id. at 102.

Of particular pertinence to this appeal, Judge Scheindlin explicitly considered the issue of the standard of proof that the Plaintiffs must meet to obtain class certification. She noted that the Supreme Court has been silent on the question of what showing plaintiffs must make in support of their motion for class certification. The only parameters established by the Supreme Court in this regard, she further noted, were that a court must conduct a "rigorous analysis" in which it "may be necessary for the court to probe behind the pleadings," General Telephone Co. of the Southwest v. Falcon, 457 U.S. 147, 160-61, 102 S. Ct. 2364, 72 L. Ed. 2d 740 (1982), but the court cannot "conduct a preliminary inquiry into the merits of a suit," Eisen v. Carlisle & Jacquelin, 417 U.S. 156, 177, 94 S. Ct. 2140, 40 L. Ed. 2d 732 (1974). IPO (Dist.Ct.), 227 F.R.D. at 90-91. Judge Scheindlin noted recent decisions by the Fourth and Seventh Circuits that suggested that the plaintiffs must establish the requirements of Rule 23 by a preponderance of the evidence, even if resolving those issues requires a "preliminary inquiry into the merits," Szabo v. Bridgeport Machines, Inc., 249 F.3d 672, 676 (7th Cir.2001), or an "overlap with issues on the merits," Gariety v. Grant Thornton, LLP, 368 F.3d 356, 366 (4th Cir.2004). See IPO (Dist.Ct.), 227 F.R.D. at 91-92.

Judge Scheindlin concluded that applying the preponderance standard was inappropriate where those elements were "enmeshed" with the merits, because, as Eisen cautioned, 417 U.S. at 178, 94 S. Ct. 2140, that standard would prejudice a defendant. Instead, she adopted a "some showing" standard, which she derived from this Court's opinions in Caridad v. Metro-North Commuter Railroad, 191 F.3d 283, 292 (2d Cir.1999), and In re Visa Check/MasterMoney Antitrust Litigation ("Visa Check"), 280 F.3d 124, 134-35 (2d Cir.2001). Judge Scheindlin concluded:

In order to pass muster, plaintiffs — who have the burden of proof at class certification — must make "some showing." That showing may take the form of, for example, expert opinions, evidence (by document, affidavit, live testimony, or otherwise), or the uncontested allegations of the complaint.

IPO (Dist.Ct.), 227 F.R.D. at 93.

Judge Scheindlin then analyzed whether, under the "some showing" standard, the Plaintiffs had met the Rule 23 requirements. As to commonality, she found numerous common factual issues for the class, and noted that, apart from individual calculation of damages, all other individual issues "will arise because of issues defendants choose to raise." Id. at 94. Even these issues, she concluded, would have common questions, such as whether a certain publication put the Plaintiffs on inquiry notice of the scheme. As to typicality, Judge Scheindlin dispensed with the Defendants' principal argument—that some class representatives were inappropriate due to their involvement in the scheme— by altering the class definition to exclude such persons. Judge Scheindlin also found that the class representatives would adequately represent the class. Defendants did not contest that the putative classes were so numerous as to render joinder impracticable.

The implied requirement of ascertainability implicated Judge Scheindlin's revised class definition. The Plaintiffs had conceded that any persons who knowingly participated in the market manipulation would be barred from recovery. Viewing three components of the market manipulation scheme as "necessary," Judge Scheindlin created subparagraph (2) of the class definition, quoted above, which excluded Plaintiffs that had (1) received an allocation, (2) purchased additional shares within four weeks of the IPO, (3) paid undisclosed compensation, and (4) profited with respect to any of the 310 IPOs. The Defendants argued that determining which Plaintiffs had participated "would be a massive undertaking." Judge Scheindlin acknowledged that ascertainment would not be easy, but that the class definition was "objectively determinable," id. at 104, which satisfied the ascertainability criterion.

The Defendants raised four arguments relating to Rule 23(b)(3)'s requirement that common questions predominate over individual ones. First, they argued that individual questions surrounding transaction causation, or reliance, predominated because the fraud-on-the-market presumption of reliance, recognized in Basic Inc. v. Levinson, 485 U.S. 224, 245-47, 108 S. Ct. 978, 99 L. Ed. 2d 194 (1988), could not apply for lack of an efficient market. Judge Scheindlin rejected this argument, ruling that the Plaintiffs had made "some showing" of market efficiency, IPO (Dist.Ct.), 227 F.R.D. at 107, and that knowledge of the Defendants' scheme from publications presented a common question rather than individual ones, id. at 110. Second, the Defendants argued that the Plaintiffs' expert report did not establish loss causation. Judge Scheindlin concluded that weighing the competing expert reports was inappropriate and, citing Visa Check, that the Plaintiffs had "satisfied their burden at this stage to articulate a theory of loss causation that is not fatally flawed." Id. at 115. Third, Judge Scheindlin accepted the Plaintiffs' contention that they could prove damages class-wide by proposing a formula for the measure of damages over time. Id. at 116-17. Fourth, as to the Plaintiffs' section 11 claims, Judge Scheindlin agreed with the Defendants that once untraceable shares1 entered the market, the individual questions of whether an investor could trace his shares to the IPO would predominate, and so she ended the class periods with respect to these claims at the time when unregistered shares became tradeable. Id. at 118-19, 120.

Finally, Judge Scheindlin concluded that class adjudication was "clearly superior to any other form of adjudication," id. at 122, and granted the Plaintiffs' motion for class certification, subject to the modified definition and the limit on class period for section 11 claims set forth above, id.

Partial Settlement. In February 2005, Judge Scheindlin approved a settlement between the Plaintiff classes and the issuer and the individual officer Defendants in 298 of the 310 consolidated actions. The settlement provided the Plaintiffs with a guaranteed recovery of one billion dollars, offset by whatever amount the Plaintiffs recover from the underwriters.

Appeal. In June 2005, a panel of this Court granted the Defendants' petition for permission to appeal pursuant to Fed. R.Civ.P. 23(f). The order granting permission to appeal directed the parties to address the following issues:

(1) Whether the Second Circuit's "some showing" standard, see In re Visa Check/MasterMoney Antitrust Litigation, 280 F.3d 124, 134-35 (2d Cir.2001); Caridad v. Metro-North Commuter Railroad, 191 F.3d 283, 293 (2d Cir. 1999), is consistent with the 2003 amendments to Fed.R.Civ.P. 23; and

(2) Whether the presumption of reliance established in Basic [Inc.] v. Levinson, 485 U.S. 224 [108 S. Ct. 978, 99 L. Ed. 2d 194] (1988), was properly extended to plaintiffs' claims against non-issuer defendants and to the market manipulation claims.

"Provided that the district court has applied the proper legal standards in deciding whether to certify a class, its decision may only be overturned if it constitutes an abuse of discretion." Caridad, 191 F.3d at 291 (internal quotation marks omitted); accord Parker v. Time Warner Entertainment Co., 331 F.3d 13, 18 (2d Cir.2003); Moore v. PaineWebber, Inc., 306 F.3d 1247, 1252 (2d Cir.2002). The statement of this standard of review does not make it clear whether the abuse-of-discretion standard applies only to the trial judge's ultimate conclusion on the class certification motion or also to the subsidiary rulings on each of the six requirements for a Rule 23(b)(3) class.2 Since a district judge "may" certify a class where all the requirements of Rule 23 are met, see Fed.R.Civ.P. 23(b), it is arguable that review for abuse of discretion refers to the ultimate discretion whether or not to certify a class.

However, the abuse-of-discretion standard has regularly been applied in reviewing a district judge's conclusions with respect to individual requirements of Rule 23 both by this Court, see, e.g., Lundquist v. Security Pacific Automotive Financial Services Corp., 993 F.2d 11, 14 (2d Cir. 1993) (commonality and typicality); Johnpoll v. Thornburgh, 898 F.2d 849, 852 (2d Cir.1990) (adequacy of class definition and adequacy of representation); cf. In re Drexel Burnham Lambert Group, Inc., 960 F.2d 285, 292 (2d Cir.1992) (prohibition against opting out), and by other Circuits, see, e.g., Pederson v. Louisiana State University, 213 F.3d 858, 867-69 (5th Cir.2000) (numerosity); Castano v. American Tobacco Co., 84 F.3d 734, 752 (5th Cir.1996) (superiority); Hoxworth v. Blinder, Robinson & Co., 980 F.2d 912, 924, 925 (3d Cir.1992) (adequacy of representation, predominance, and duration of class period). We will apply the abuse-of-discretion standard both to Judge Scheindlin's ultimate decision on class certification as well as her rulings as to Rule 23 requirements, bearing in mind that whether an incorrect legal standard has been used is an issue of law to be reviewed de novo, see Parker, 331 F.3d at 18.

Our initial inquiry is whether Judge Scheindlin applied proper legal standards in determining the existence of the four prerequisites for every class action: numerosity, commonality, typicality, and adequacy of representation, Fed.R.Civ.P. 23(a), and the two additional requirements for a(b)(3) class action: predominance, i.e., law or fact questions common to the class predominate over questions affecting individual members, and superiority, i.e., class action is superior to other methods, id. 23(b)(3). Judge Scheindlin ruled that the Plaintiffs were required to make only "some showing" of compliance with these Rule 23 requirements. We conclude that use of a "some showing" standard was error, but we readily acknowledge that, until now, our Court has been less than clear as to the applicable standards for class certification, and on occasion, as we discuss below, we have used language that understandably led Judge Scheindlin astray. Before considering the relevant opinions of our Court, we start with the guidance provided by the Supreme Court.

Supreme Court decisions. The principal Supreme Court decision on determining Rule 23 requirements, General Telephone Co. of the Southwest v. Falcon, 457 U.S. 147, 102 S. Ct. 2364, 72 L. Ed. 2d 740 (1982), states, "[A] Title VII class action, like any other class action, may only be certified if the trial court is satisfied, after a rigorous analysis, that the prerequisites of Rule 23(a) have been satisfied." Id. at 161, 102 S. Ct. 2364. Although the Court's double use of the word "satisfied" is somewhat perplexing, the important point is that the requirements of Rule 23 must be met, not just supported by some evidence. As the Court added with respect to the four requirements of Rule 23(a), "[A]ctual, not presumed, conformance with Rule 23(a) remains . . . indispensable." Id. at 160, 102 S. Ct. 2364. Moreover, the certification decision requires "rigorous analysis."3 Id. at 161, 102 S. Ct. 2364. Significantly, the Court noted that "the class determination generally involves considerations that are enmeshed in the factual and legal issues comprising the plaintiff's cause of action." Id. at 160, 102 S. Ct. 2364 (internal quotation marks omitted). This last statement is especially important in light of the way circuit and district courts have understood (or, as we point out below, misunderstood) the Supreme Court's earlier decision in Eisen.4

In Eisen, the Court stated: "We find nothing in either the language or history of Rule 23 that gives a court any authority to conduct a preliminary inquiry into the merits of a suit in order to determine whether it may be maintained as a class action." Eisen, 417 U.S. at 177, 94 S. Ct. 2140. This statement has led some courts to think that in determining whether any Rule 23 requirement is met, a judge may not consider any aspect of the merits, and has led other courts to think that a judge may not do so at least with respect to a prerequisite of Rule 23 that overlaps with an aspect of the merits of the case.

However, careful examination of Eisen reveals that there is no basis for thinking that a specific Rule 23 requirement need not be fully established just because it concerns, or even overlaps with, an aspect of the merits. The oft-quoted statement from Eisen was made in a case in which the district judge's merits inquiry had nothing to do with determining the requirements for class certification. In Eisen, the district court, after determining that the case was appropriate for class certification, was concerned with which side should bear the cost of notice to the class. Id. at 166-68, 94 S. Ct. 2140. As recounted by the Supreme Court, the district court had ruled that, without a class action, no one plaintiff could bear the cost of the notice, but that it would be unfair to impose the cost on the defendants unless the plaintiffs could show a probability of success on the merits. Id. at 168, 94 S. Ct. 2140. Concluding that such a probability existed, the district court had ordered the defendants to pay 90 percent of the costs of notice, id., and had devised a scheme of individual notice for some plaintiffs and notice by publication for others, id. at 167, 94 S. Ct. 2140. The court of appeals had rejected that approach and had required individual notice with the cost borne by the plaintiffs. Id. at 169, 94 S. Ct. 2140. The court of appeals had also ruled that the action was "unmanageable" and had rejected class certification. Id.

The Supreme Court ruled that Rule 23 required individual notice. Id. at 175-77, 94 S. Ct. 2140. Then the Court ruled that the plaintiffs must bear the cost. It was in this context that the Court said that the district court could not "conduct a preliminary inquiry into the merits." Id. at 177, 94 S. Ct. 2140. Doing so, the Court said, would allow the class representative to obtain a determination on the merits "without any assurance that a class action may be maintained." Id. at 177-78, 94 S. Ct. 2140. The Court said it was also concerned that the court's tentative findings "may color the subsequent proceedings and place an unfair burden on the defendant." Id. at 178, 94 S. Ct. 2140. Then, since the class representative had said he would not bear the cost of notice, the Court ordered the class action dismissed. Id. at 179, 94 S. Ct. 2140.

The point is that the Supreme Court was not faced with determination of any particular Rule 23 requirement or a requirement that overlapped with the merits. The district court had preliminarily assessed the merits to decide the collateral issue of who should pay for the notice.

The Fifth Circuit case on which the Supreme Court principally relied in Eisen, Miller v. Mackey International, Inc., 452 F.2d 424 (5th Cir.1971), also did not involve determination of any Rule 23 requirement or even one that overlapped with a merits inquiry. The Supreme Court said:

In short, we agree with Judge Wisdom's conclusion in Miller v. Mackey International, 452 F.2d 424 (5th Cir.1971), where the court rejected a preliminary inquiry into the merits of a proposed class action:

"In determining the propriety of a class action, the question is not whether the plaintiff or plaintiffs have stated a cause of action or will prevail on the merits, but rather whether the requirements of Rule 23 are met."

Eisen, 417 U.S. at 178, 94 S. Ct. 2140.

But the district court in Miller, just like the district court in Eisen, had not looked at the merits in order to determine whether any one of the Rule 23 requirements was met. Instead, the district court in Miller had simply concluded that because of a deficiency on the merits of the plaintiff's securities claim, i.e., an alleged competitor, omitted from the prospectus, was not in fact in competition with the defendant, a class action was inappropriate. Miller, 452 F.2d at 426. Significantly, after ruling that this merits inquiry was not a proper basis for denying class certification, Judge Wisdom's opinion remanded the case to the district court for further proceedings "including a full hearing on the question presented [Rule 23 certification] and findings by the district judge." Id. at 431 (emphasis added).

Unfortunately, the statement in Eisen that a court considering certification must not consider the merits has sometimes been taken out of context and applied in cases where a merits inquiry either concerns a Rule 23 requirement or overlaps with such a requirement. The evolution of case law in our Circuit, to which we now turn, illustrates what has happened.

Case law within the Second Circuit. An early example is Professional Adjusting Systems of America, Inc. v. General Adjustment Bureau, Inc., 64 F.R.D. 35 (S.D.N.Y.1974), in which then-District Judge Gurfein, explicitly mindful of the admonitions in Eisen and Miller, said that the choice for a district court must be

somewhere between the pleading and the fruits of discovery . . . . Enough must be laid bare to let the judge survey the factual scene on a kind of sketchy relief map, leaving for later view the myriad of details that cover the terrain. But to find its way, the Court must know something of the commonality of action or frustration that binds the class.

Id. at 38 (emphasis added). Most of Judge Gurfein's statement was expressly quoted by our Court in Sirota v. Solitron Devices, Inc., 673 F.2d 566, 571-72 (2d Cir.1982), in addition to the no-merits-inquiry language from Eisen itself, id. at 570.

Eisen and Sirota were prominently cited in our Circuit's decision in Caridad, 191 F.3d at 291, which was principally relied on by Judge Scheindlin in the pending case. As many other decisions have done, Caridad took the "no merits inquiry" language of Eisen out of its context of a merits inquiry unrelated to a specific Rule 23 class certification requirement and applied it to consideration of the Rule 23 threshold requirements. In addition, Caridad contained the following sentence, on which Judge Scheindlin based her "some showing" standard for Rule 23 requirements: "Of course, class certification would not be warranted absent some showing that the challenged practice is causally related to a pattern of disparate treatment or has a disparate impact on African-American employees at Metro-North." Caridad, 191 F.3d at 292 (emphasis added).5 Although it is not entirely clear whether the "some showing" sentence in Caridad is a comment on the standard for satisfying the Rule 23(a) requirement of commonality or a requirement concerning the merits issue of causality, it seems clear that the Eisen caution was a major influence on the Caridad decision. Thus, under the influence of Eisen, Caridad condemned "statistical dueling" between experts, id. (internal quotations marks omitted), and ruled that the report of the plaintiffs' expert plus anecdotal evidence "satisfies the Class Plaintiffs' burden of demonstrating commonality for purposes of class certification," id. at 293, without requiring the district court to have made a clear determination of commonality in light of all the evidence bearing on that issue that had been presented at the class certification stage. The condemnation of "statistical dueling" by experts was drawn from a careful opinion by District Judge Koeltl, which had noted that the experts' disagreement on the merits — whether a discriminatory impact could be shown—was not a valid basis for denying class certification. See Krueger v. New York Telephone Co., 163 F.R.D. 433, 440 (S.D.N.Y.1995). Caridad, by the imprecision of its language, left unclear whether the merits dispute between the experts was not to be resolved at the class certification stage or whether their dispute about a class certification requirement was not to be resolved at that stage.6

Caridad was soon followed by Visa Check, which upheld a district court's conclusion as to commonality on the lenient basis that the plaintiffs' methodology to show common questions of fact "was not fatally flawed," Visa Check, 280 F.3d at 135. Visa Check began its consideration of the issue by citing Eisen, id. at 133, and quoting Caridad for the proposition, based on Eisen, that "`a motion for class certification is not an occasion for examination of the merits of the case,'" id. at 135 (quoting Caridad, 191 F.3d at 291). Then Visa Check asserted that a district judge "must ensure that the basis of the expert opinion [for the theory supporting common issues subject to classwide determination] is not so flawed that it would be inadmissible as a matter of law." Id. For this proposition, the Court cited Cruz v. Coach Stores, Inc., No. 96 Civ. 8099, 1998 WL 812045, at *4 n. 3 (S.D.N.Y. Nov.18, 1998), aff'd in part, vacated in part on other grounds, 202 F.3d 560 (2d Cir.2000). In the cited footnote in the district court opinion in Cruz, Judge Rakoff had said that the plaintiff's expert's report, offered to show commonality, was "fatally flawed" and for that reason inadmissible. In affirming in part, our Court said that "[the plaintiff] has not shown that the [district] court abused its discretion in finding the report methodologically flawed." Cruz, 202 F.3d at 573. Ultimately, Visa Check approved what it characterized as the district court's conclusion that it was obliged to determine only "whether [the plaintiffs] had shown, based on methodology that was not fatally flawed, that the requirements of Rule 23 were met."7 Visa Check, 280 F.3d at 135. However, the fact that an expert's report was rejected as admissible evidence in Cruz because it was fatally flawed was not a sufficient basis for saying in Visa Check that a report suffices to establish a Rule 23 requirement as long as it is not fatally flawed. Visa Check also stated that a district judge, at the class certification stage, "may not weigh conflicting expert evidence or engage in `statistical dueling' of experts," id. (quoting Caridad, 191 F.3d at 292-93), without clarifying whether the district judge should refrain from resolving a merits dispute or a dispute about a class certification requirement.

After Visa Check, our decision in Parker appeared to move away from the lenient approach of Caridad and Visa Check and toward a district court's obligation to determine that Rule 23 requirements are met. In Parker, we rejected a denial of certification by a district judge who had ruled that a class action was not superior to individual actions where the aggregate liability of the defendant was grossly disproportionate to the harm suffered by each individual. 331 F.3d at 21. We concluded that the district judge had made assumptions of fact concerning the size of the class, and we remanded for "findings of fact." Id.

More recently, our Court's decision in Heerwagen v. Clear Channel Communications, 435 F.3d 219 (2d Cir.2006), marked a major shift away from the "some showing" and "not fatally flawed" language of Caridad and Visa Check. Heerwagen began its consideration of the appropriate standard for meeting class certification requirements by repeating the admonitions of Caridad and Visa Check that the court is not "to conduct a preliminary inquiry into the merits of plaintiff's case at the class certification stage." Id. at 231. There was even an invocation of Sirota's reliance on Judge Gurfein's statement in Professional Adjusting Systems that a class certification judge need only look "somewhere between the pleading and the fruits of discovery" to make a class certification. See id. (internal quotation marks omitted). However, without mentioning the "some showing" language from Caridad, Heerwagen then asserted that the district court must determine whether Rule 23 requirements have been met. Heerwagen also referred to "the express language of Rule 23(b)(3), which requires that a court find predominance." Id. at 233 (emphasis added). Heerwagen somewhat straddled the issue of whether such a determination could include some inquiry into the merits:

Some overlap with the ultimate review on the merits is an acceptable collateral consequence of the "rigorous analysis" that courts must perform when determining whether Rule 23's requirements have been met, see Falcon, 457 U.S. at 161, 102 S. Ct. 2364, 72 L. Ed. 2d 740, so long as it does not stem from a forbidden preliminary inquiry into the merits, Eisen, 417 U.S. at 177, 94 S. Ct. 2140, 40 L. Ed. 2d 732.

435 F.3d at 232. Declining to go as far as other circuits in permitting broad inquiry into the merits in order to determine whether Rule 23 requirements have been met, see id. (citing, e.g., Gariety, 368 F.3d at 366; Szabo, 249 F.3d at 676), Heerwagen, apparently still laboring under the influence of Eisen, identified one circumstance where the need for findings would not require weighing all the relevant evidence. We relied on Caridad "to prohibit weighing evidence in connection with Rule 23 determinations to the extent those determinations are effectively identical to merits issues." Id. (emphasis added). Satisfied that the merits issue considered by the district court was not identical with a Rule 23 requirement, Heerwagen affirmed the denial of class certification. Thus, the Eisen caution was disregarded as to Rule 23 requirements that somewhat overlap with the merits, but apparently retained as to a requirement that completely overlaps with the merits.

Heerwagen also considered the putative class plaintiff's claim that the district court had improperly required her to meet Rule 23's predominance requirement by a preponderance of the evidence. Initially, we expressed doubt whether the district court had used the preponderance standard. See id. at 233. Then, without determining what standard had been used, we said, in what may well have been dictum, that "[e]ven if a preponderance of the evidence standard was invoked, that was not in error." Id. Indeed, we asserted: "Complying with Rule 23(b)(3)'s predominance requirement cannot be shown by less than a preponderance of the evidence."8 Id. Case law in other circuits. The case law that has developed outside our Circuit since Eisen has generally supported an obligation of the district court to make a determination that the requirements of Rule 23 are met, and has not accepted a weak "some showing" standard.

Several circuits have strongly supported a requirement of findings that Rule 23 requirements are met, and some have explicitly rejected the idea that something less than a clear finding is adequate just because a Rule 23 requirement overlaps with the merits. The Seventh Circuit has stated that "a judge should make whatever factual and legal inquiries are necessary under Rule 23" even if "the judge must make a preliminary inquiry into the merits." Szabo, 249 F.3d at 676. Judge Easterbrook added, "[T]he judge would receive evidence (if only by affidavit) and resolve the disputes before deciding whether to certify the class." Id. (emphasis added). The Fourth Circuit has followed Szabo and stated that "the factors spelled out in Rule 23 must be addressed through findings, even if they overlap with issues on the merits." Gariety, 368 F.3d at 366. The Third Circuit has also followed Szabo and cited approvingly this statement from 5 Moore's Federal Practice § 23.46[4]: "[B]ecause the determination of a certification request invariably involves some examination of factual and legal issues underlying the plaintiffs' cause of action, a court may consider the substantive elements of the plaintiff's case . . . ." Newton v. Merrill Lynch, Pierce, Fenner & Smith, Inc., 259 F.3d 154, 166 (3d Cir.2001). The Eighth Circuit has stated that "in ruling on class certification, a court may be required to resolve disputes concerning the factual setting of the case," including "the resolution of expert disputes concerning the import of evidence." Blades v. Monsanto Co., 400 F.3d 562, 575 (8th Cir.2005) (emphasis added). The Fifth Circuit, following Gariety, has stated that "a careful certification inquiry is required and findings must be made" and has rejected a class certification because the district court "applied too lax a standard of proof," Unger v. Amedisys, Inc., 401 F.3d 316, 319 (5th Cir.2005). The Eleventh Circuit has stated:

While it is true that a trial court may not properly reach the merits of a claim when determining whether class certification is warranted, this principle should not be talismanically invoked to artificially limit a trial court's examination of the factors necessary to a reasoned determination of whether a plaintiff has met her burden of establishing each of the Rule 23 class action requirements.

Love v. Turlington, 733 F.2d 1562, 1564 (11th Cir.1984) (citation omitted).

The Fourth Circuit in Gariety considered and fully answered the concern expressed in Eisen (with respect to a merits inquiry on an issue unrelated to a Rule 23 requirement) that a merits inquiry on an issue that is related to the merits would prejudice the defendant. The Fourth Circuit noted that such an inquiry would not bind the ultimate fact-finder.9 See Gariety, 368 F.3d at 366. A trial judge's finding on a merits issue for purposes of a Rule 23 requirement no more binds the court to rule for the plaintiff on the ultimate merits of that issue than does a finding that the plaintiff has shown a probability of success for purposes of a preliminary injunction.

The First Circuit has expressed a mild disagreement with this strong line of authority. See In re PolyMedica Corp. Securities Litigation, 432 F.3d 1 (1st Cir. 2005). Although aligning itself with "the majority view" permitting merits inquiry, see id. at 6 (citing Waste Management Holdings, Inc. v. Mowbray, 208 F.3d 288 (1st Cir.2000)), the First Circuit invoked Eisen for the limited proposition that the Supreme Court "prohibits a district court from inquiring into whether a plaintiff will prevail on the merits at class certification," id. (emphasis added). Ultimately, in considering the issue of how much evidence a class plaintiff must present to show the efficient market necessary to invoke the Basic presumption of reliance, the First Circuit stated that the "[t]he question of how much evidence of efficiency is necessary for a court to accept the fraud-on-the-market presumption of reliance at the class-certification stage is . . . one of degree." Id. at 17. The court acknowledged that its "generalities" on the issue "are the best we can do." Id.

Significance of the 2003 amendments to Rule 23. In 2003, the Civil Rules Advisory Committee made several changes to Rule 23, but neither the amended Rule nor the Committee's commentary explicitly resolves the split of authority between our Circuit's ambiguous Caridad/Visa Check/Heerwagen approach to determining Rule 23 requirements and the predominant view of the other circuits that class certification requires findings as to such requirements, even if such findings involve consideration of merits issues. Two changes arguably combine to permit a more extensive inquiry into whether Rule 23 requirements are met than was previously appropriate. First, the amended rule removes from prior Rule 23(c)(1)(C) the provision that class certification "may be conditional." Second, the amended rule replaces the provision of prior Rule 23(c)(1)(A) that a class certification decision be made "as soon as practicable" with a provision requiring the decision "at an early practicable time." And the Advisory Committee states that "[a] court that is not satisfied that the requirements of Rule 23 have been met should refuse certification until they have been met." Fed. R.Civ.P. 23(c)(1)(C) Adv. Comm. Notes 2003.10

Clarifying the standards for the Second Circuit. The foregoing discussion demonstrates the need for some clarification of a district court's role in assessing a motion for class certification. Obviously, we can no longer continue to advise district courts that "some showing," Caridad, 191 F.3d at 292, of meeting Rule 23 requirements will suffice and that "findings" are required, see Parker, 331 F.3d at 21, or that an expert's report will sustain a plaintiff's burden so long as it is not "fatally flawed," see Visa Check, 280 F.3d at 135, and that the plaintiff must prove Rule 23 requirements, see Heerwagen, 435 F.3d at 233.11

It would seem to be beyond dispute that a district court may not grant class certification without making a determination that all of the Rule 23 requirements are met. We resist saying that what are required are "findings" because that word usually implies that a district judge is resolving a disputed issue of fact. Although there are often factual disputes in connection with Rule 23 requirements, and such disputes must be resolved with findings, the ultimate issue as to each requirement is really a mixed question of fact and law. A legal standard, e.g., numerosity, commonality, or predominance, is being applied to a set of facts, some of which might be in dispute. The Rule 23 requirements are threshold issues, similar in some respects to preliminary issues such as personal or subject matter jurisdiction. We normally do not say that a district court makes a "finding" of subject matter jurisdiction; rather, the district court makes a "ruling" or a "determination" as to whether such jurisdiction exists. The judge rules either that jurisdiction exists or that it does not. Of course, in making such a ruling, the judge often resolves underlying factual disputes, and, as to these disputes, the judge must be persuaded that the fact at issue has been established. The same approach is appropriate for Rule 23 requirements. For example, in considering whether the numerosity requirement is met, a judge might need to resolve a factual dispute as to how many members are in a proposed class. Any dispute about the size of the proposed class must be resolved, and a finding of the size of the class, e.g., 50, 100, or more than 200, must be made. At that point, the judge would apply the legal standard governing numerosity and make a ruling as to whether that standard, applied to the facts as found, establishes numerosity.12

The Rule 23 requirements differ from other threshold issues in that, once a district court has ruled, the standard for appellate review is whether discretion has been exceeded (or abused). This standard of review implies that a district judge has some leeway as to Rule 23 requirements, and, unlike rulings as to jurisdiction, may be affirmed in some circumstances for ruling either that a particular Rule 23 requirement is met or is not met. Of course, this leeway, as with all matters of discretion, is not boundless. To the extent that the ruling on a Rule 23 requirement is supported by a finding of fact, that finding, like any other finding of fact, is reviewed under the "clearly erroneous" standard. And to the extent that the ruling involves an issue of law, review is de novo. See Parker, 331 F.3d at 18. To illustrate, again using the example of numerosity, review of the factual finding as to the size of the proposed class would be for clear error, review of the judge's articulation of the legal standard governing numerosity would be de novo, and review of the ultimate ruling that applied the correct legal standard to the facts as found would be for abuse of discretion. Thus a ruling on numerosity, based on a finding of fact that is not clearly erroneous and with application of a legal standard that is correct, could be affirmed as within allowable discretion, in some circumstances, whether the ruling determined that this Rule 23 requirement was met or not met.

The more troublesome issue arises when the Rule 23 requirement overlaps with an issue on the merits. With Eisen properly understood to preclude consideration of the merits only when a merits issue is unrelated to a Rule 23 requirement, there is no reason to lessen a district court's obligation to make a determination that every Rule 23 requirement is met before certifying a class just because of some or even full overlap of that requirement with a merits issue. We thus align ourselves with Szabo, Gariety, and all of the other decisions discussed above that have required definitive assessment of Rule 23 requirements, notwithstanding their overlap with merits issues. As Gariety usefully pointed out, the determination as to a Rule 23 requirement is made only for purposes of class certification and is not binding on the trier of facts, even if that trier is the class certification judge. 368 F.3d at 366.

In one respect, however, overlap between a Rule 23 requirement and a merits issue justifies some adjustment in a district court's procedures at the class certification stage. To avoid the risk that a Rule 23 hearing will extend into a protracted mini-trial of substantial portions of the underlying litigation, a district judge must be accorded considerable discretion to limit both discovery and the extent of the hearing on Rule 23 requirements. But even with some limits on discovery and the extent of the hearing, the district judge must receive enough evidence, by affidavits, documents, or testimony, to be satisfied that each Rule 23 requirement has been met.

In light of the foregoing discussion, we reach the following conclusions: (1) a district judge may certify a class only after making determinations that each of the Rule 23 requirements has been met; (2) such determinations can be made only if the judge resolves factual disputes relevant to each Rule 23 requirement and finds that whatever underlying facts are relevant to a particular Rule 23 requirement have been established and is persuaded to rule, based on the relevant facts and the applicable legal standard, that the requirement is met; (3) the obligation to make such determinations is not lessened by overlap between a Rule 23 requirement and a merits issue, even a merits issue that is identical with a Rule 23 requirement; (4) in making such determinations, a district judge should not assess any aspect of the merits unrelated to a Rule 23 requirement; and (5) a district judge has ample discretion to circumscribe both the extent of discovery concerning Rule 23 requirements and the extent of a hearing to determine whether such requirements are met in order to assure that a class certification motion does not become a pretext for a partial trial of the merits.

In drawing these conclusions, we add three observations. First, our conclusions necessarily preclude the use of a "some showing" standard, and to whatever extent Caridad might have implied such a standard for a Rule 23 requirement, that implication is disavowed. Second, we also disavow the suggestion in Visa Check that an expert's testimony may establish a component of a Rule 23 requirement simply by being not fatally flawed. A district judge is to assess all of the relevant evidence admitted at the class certification stage and determine whether each Rule 23 requirement has been met, just as the judge would resolve a dispute about any other threshold prerequisite for continuing a lawsuit. Finally, we decline to follow the dictum in Heerwagen suggesting that a district judge may not weigh conflicting evidence and determine the existence of a Rule 23 requirement just because that requirement is identical to an issue on the merits.

II. Application of the Correct Standards to the Pending Case

In some circumstances, it would be appropriate to remand a case such as this to the District Court for reconsideration of the class certification motion under the proper standards as we have explained them. We conclude, however, that remand is not appropriate because the Plaintiffs' own allegations and evidence demonstrate that the Rule 23 requirement of predominance of common questions over individual questions cannot be met under the standards as we have explicated them.

Reliance. The predominance requirement fails initially with respect to the issue of reliance. The Plaintiffs recognize that they must establish that they relied on the misrepresentations that they have alleged, and they also recognize that establishing reliance individually by members of the class would defeat the requirement of Rule 23 that common questions of law or fact predominate over questions affecting only individual members. See Fed.R.Civ.P. 23(b)(3). To satisfy the predominance requirement the Plaintiffs invoke the presumption from the Supreme Court's decision in Basic, 485 U.S. at 245-47, 108 S. Ct. 978, that purchasers of securities relied on price in an efficient market. "The fraud-on-the-market doctrine, as described by the Supreme Court in Basic [Inc.] v. Levinson, creates a rebuttable presumption that (1) misrepresentations by an issuer affect the price of securities traded in the open market, and (2) investors rely on the market price of securities as an accurate measure of their intrinsic value." Hevesi v. Citigroup Inc., 366 F.3d 70, 77 (2d Cir. 2004). Applying the lenient "some showing" standard, which we have now discarded, the District Court in the pending case ruled that the Plaintiffs had sufficiently shown the existence of an efficient market to invoke the Basic presumption. IPO (Dist.Ct.), 227 F.R.D. at 107. However, the Plaintiffs' own allegations and evidence demonstrate that an efficient market cannot be established in this case under the proper standards set forth in this opinion.

In the first place, the market for IPO shares is not efficient. As the late Judge Timbers of our Court has said, sitting with the Sixth Circuit, "[A] primary market for newly issued [securities] is not efficient or developed under any definition of these terms." Freeman v. Laventhol & Horwath, 915 F.2d 193, 199 (6th Cir.1990) (internal quotation marks omitted); accord Berwecky v. Bear, Stearns & Co., 197 F.R.D. 65, 68 n. 5 (S.D.N.Y.2000) (The fraud-on-the-market "presumption can not logically apply when plaintiffs allege fraud in connection with an IPO, because in an IPO there is no well-developed market in offered securities."). As just one example of why an efficient market, necessary for the Basic presumption to apply, cannot be established with an IPO, we note that during the 25-day "quiet period," analysts cannot report concerning securities in an IPO, see 17 C.F.R. §§ 230.174(d), 242.101(b)(1), thereby precluding the contemporaneous "significant number of reports by securities analysts" that are a characteristic of an efficient market. See Freeman, 915 F.2d at 199.

Moreover, the Plaintiffs' own allegations as to how slow the market was to correct the alleged price inflation despite what they also allege was widespread knowledge of the scheme indicate the very antithesis of an efficient market. Indeed, the Plaintiffs claim on appeal, in an effort to support their theory of loss causation, that whatever artificially inflated effects on share prices were allegedly caused by the Defendants' conduct continued even past the December 6, 2000, end date of the class period. See Brief for Appellees at 81. It is also doubtful whether the Basic presumption can be extended, beyond its original context, to tie-in trading, underwriter compensation, and analysts' reports. See West v. Prudential Securities, Inc., 282 F.3d 935, 938 (7th Cir.2002).

Without the Basic presumption, individual questions of reliance would predominate over common questions.

Knowledge. There is no dispute that a section 10(b) claimant "must allege and prove" that the claimant traded "in ignorance of the fact that the price was affected by the alleged manipulation." Gurary v. Winehouse, 190 F.3d 37, 45 (2d Cir. 1999). The Plaintiffs must show lack of knowledge to recover on their section 11 claims as well. DeMaria v. Andersen, 318 F.3d 170, 175 (2d Cir.2003) ("[Section] 11 provides a cause of action for `any person acquiring' a security issued pursuant to a materially false registration statement unless the purchaser knew about the false statement at the time of acquisition."). The Plaintiffs' allegations, evidence, and discovery responses demonstrate that the predominance requirement is defeated because common questions of knowledge do not predominate over individual questions. The claim that lack of knowledge is common to the class is thoroughly undermined by the Plaintiffs' own allegations as to how widespread was knowledge of the alleged scheme. Obviously, the initial IPO allocants, who were required to purchase in the aftermarket, were fully aware of the obligation that is alleged to have artificially inflated share prices. Those receiving or seeking allocations number in the thousands.13 With respect to one IPO alone (Engage Technologies, Inc.), 540 institutions and 1,850 others received allocations. And there were more than 900 IPOs allegedly manipulated by aftermarket purchase requirements. Equally obviously, that, in response more than 11,000 induced to enter the requirements would have been known not just to the entities receiving allocations, but also to many thousands of people employed by the institutional investors. In addition, two cable television networks, MSNBC and CNBC, reported on the aftermarket purchase requirements in 1999, and in 2000 the practice was the subject of an SEC Staff Legal Bulletin and a report in Barron's discussing the bulletin. The Plaintiffs themselves refer to the "industry-wide understanding" that those who agreed to purchase in the aftermarket received allocations. See Master Allegations ¶¶ 30, 31.

The District Court sought to minimize the extent of individual questions of knowledge by redefining the proposed class to exclude "those investors who exhibit the hallmarks of full participation in the alleged scheme." 227 F.R.D. at 103 (emphasis added). However, that exclusion leaves within the class those who participated in part and those who were required to remain "ready" to purchase in the aftermarket if the underwriters so desired, Master Allegations ¶ 15, all of whom knew of the alleged scheme. Moreover, the exclusion of full participants from the class does nothing to lessen the broad extent of knowledge of the scheme throughout the community of market participants and watchers, and it is this widespread knowledge that would precipitate individual inquiries as to the knowledge of each member of the class, even as redefined.14

Payment of undisclosed compensation. Yet a further example of an aspect of this litigation bristling with individual questions is ascertainment of which putative class members have "paid any undisclosed compensation to the allocating underwriter(s)," IPO (Dist.Ct.), 227 F.R.D. at 102, a circumstance that, along with others, would exclude them from the class. Passing the somewhat paradoxical point as to how someone is to determine whether compensation that was "undisclosed" was paid, we note that individual issues arise even as to those aspects of compensation that a Plaintiff might be able to determine were within the Plaintiffs' definition of "Undisclosed Compensation." As described in the Master Allegations, such compensation comprises:

(a) paying inflated brokerage commissions; (b) entering into transactions in otherwise unrelated securities for the primary purpose of generating commissions; and/or (c) purchasing equity offerings underwritten by the Underwriter Defendants, including, but not limited to, secondary (or add-on) offerings that would not be purchased but for the Underwriter Defendants' unlawful scheme.

Id. at 100 (quoting Master Allegations ¶ 17) (emphases added).

Each category of undisclosed compensation would require individualized determinations. Whether a brokerage commission was inflated would depend on a comparison between what brokerage the putative class member was charged and the customary commission for trades of a similar nature. Whether shares unrelated to the IPO were purchased for the purpose of generating commissions and whether shares purchased in the aftermarket would not have been bought but for the allegedly unlawful scheme would require inquiry into the subjective intent of the purchaser. A purchaser would not have paid undisclosed compensation if shares were bought entirely at the behest of the purchaser and because of an independent interest in buying shares of a particular company. Obviously, ascertaining each purchaser's intent would require an individualized determination. See Simer v. Rios, 661 F.2d 655, 669 (7th Cir.1981) (class difficult to ascertain where "membership in the class depends on each individual's state of mind"); Dunnigan v. Metropolitan Life Insurance Co., 214 F.R.D. 125, 135 (S.D.N.Y.2003) ("Where membership in the class requires a subjective determination, the class is not identifiable."). Although it has been stated that class members must be ascertainable "at some point in the case," but not necessarily prior to class certification, see In re Methyl Tertiary Butyl Ether ("MTBE") Products Liability Litigation, 209 F.R.D. 323, 337 (S.D.N.Y.2002) (internal quotation marks omitted), we point out the need for numerous individualized determinations of class membership in order to provide further support for our basic conclusion that individual questions will permeate this litigation. Although ascertainability of the class is an issue distinct from the predominance requirement for a(b)(3) class, the problems we have identified on this topic further indicate the obstacles to proceeding with the focus cases as class actions.

Under the standards we have today set forth, it is clear that, with respect to at least the factors of reliance and lack of knowledge of the scheme, the Plaintiffs cannot satisfy the predominance requirement for a(b)(3) class action. Accordingly, we vacate the District Court's order granting class certifications in each of the six focus cases and remand for further proceedings.