Several American Airlines, Inc. passengers claim that they and others similarly situated lost their luggage on international American flights. The passengers sued American in federal court seeking damages for their lost or damaged luggage and various forms of injunctive and declaratory relief. They sued under the Warsaw Convention, a treaty that governs claims for property damage arising out of international transportation of people and property.1 The individual plaintiffs also moved to certify their suit as a class action on behalf of two categories of passengers. The district court granted American partial summary judgment and declined to certify the class. Plaintiffs now appeal both of those rulings. Because they have shown no reversible error, we affirm the judgment of the district court.

This case arises from some bad luck the Cruz family purportedly had with their luggage. (We glean the statement of facts that follows from the parties' statements of material undisputed facts, unless otherwise indicated. See D.D.C. Local Civ. R. 56.1.) In 1995, five members of the Cruz family flew on an American Airlines flight from Washington D.C., Reagan National Airport to Santo Domingo, the Dominican Republic, checking two bags each. When they arrived in Santo Domingo, the Cruzes reported to American that five of their bags were missing.

The Cruzes subsequently filed a statement of property loss with American, claiming that the bags were worth $15,000. American, however, offered the Cruzes no compensation. American refused to offer compensation because, according to American's records, the Cruzes had filed their claims significantly more than 30 days after their loss. American's policy at the time was not to settle lost-baggage claims voluntarily if the claimant submitted a lost-property form more than 30 days after the date of loss, though there were (unspecified) exceptions to this internal policy (we refer to this policy as the "30-day rule").

The Cruzes' luggage travails did not end there. In 1997, Beato Cruz, who had been on the previous American flight, again flew on an American flight, this time from the Dominican Republic to New York City. When he arrived in New York, according to Cruz's deposition testimony, his bag was badly damaged and was missing its contents.

The next day, Cruz filed a statement of lost property with American, declaring that the value of his bag was $3,890. That same day American gave Cruz a $100 travel voucher. When he received the form, Cruz signed his name next to the following statement:

CUSTOMER RECEIPT AND RELEASE: THE ABOVE SUM RECEIVED FROM AMERICAN AIRLINES IS IN FULL SATISFACTION OF ALL CLAIMS, LIABILITIES AND DEMANDS THAT I MAY HAVE AGAINST SAID COMPANY.

Several months later, American issued Cruz a check for $634.90 as compensation for his damaged luggage. The check came with a letter stating that this figure was the maximum amount of compensation American was legally obligated to provide under the terms of its international tariff governing baggage loss and under the Warsaw Convention. Article 18 of the Warsaw Convention generally provides passengers a cause of action for damages against international carriers for lost or damaged checked bags. Under Article 22(2), that liability is limited to $9.07 per pound of lost or damaged baggage. American's international tariffs — which govern the rates for its international flights and which under federal law it must file with the Department of Transportation, see 49 U.S.C. § 41504 (2000) — specify a default "deemed weight" for Caribbean passengers' lost bags. This deemed weight, under the tariffs, is used to calculate American's liability under the Warsaw Convention. The tariffs, specifically, provide that the baggage weight of a Caribbean passenger with a single bag is assumed to be 100 pounds — the bag's maximum allowable weight — unless the passenger's ticket states the actual weight.

American calculated the $634.90 it offered Cruz based on a flawed understanding of the deemed weight of Cruz's bag. American computed that figure by multiplying $9.07 by 70 pounds, which it stated was the maximum allowable weight of Cruz's bag under its tariffs. The true maximum weight of Cruz's bag under the tariffs was 100 pounds. Therefore, the calculation underestimated the per-bag limit applicable to Cruz's lost bag by at least $272.10 ($907 minus $634.90).

Cruz cashed the $634.90 check. The back of the check had a legend of release on it, which stated that:

By endorsement or deposit of this check I (we) hereby release American Airlines, Inc., its agents, including other airlines providing transportation, its employee's [sic] and representatives from all claims rising in connection with the loss, damage or delay of my belongings transported or authorized to have been transported on the travel date indicated on the remittance advise.

Cruz signed his name next to this statement when he endorsed the check. At that point, Cruz had already retained his current attorney and was a party to this lawsuit against American, which at the time only involved the Cruz family's 1995 trip. Cruz also testified at his deposition that, when he cashed the check, he believed he could sue American for "the additional amount [he] believed [he] was owed," which, according to positions he later took, was the bag's fair value. Again, Cruz's position at the time was that the fair value of his bag was $3,890.

On December 20, 1996, five Cruz family members, including Beato Cruz, sued American in federal district court to recover the value of their bags. Relying on the Warsaw Convention, they sought damages equal to the fair value of the contents of their lost and damaged luggage. They also alleged that American unlawfully required them to complete a lost-property form and illegally applied the 30-day rule to them. The Cruzes accordingly sought both a declaration that these procedures were illegal and an injunction preventing American from applying the procedures to future passengers.

The district court dismissed plaintiffs' declaratory and injunctive claims for lack of Article III standing. The court reasoned that as American admitted, it had incorrectly required the Cruzes to fill out a claim form, mistakenly applied the 30-day rule to the Cruzes' claims, and agreed to process the Cruzes' claims as timely filed, the Cruzes personally stood to gain little from the requested declaratory and injunctive relief. Moreover, reasoned the court, the possibility that American would in similar circumstances again misapply those procedures to the Cruzes was highly improbable. The district court concluded, therefore, that the Cruzes had no standing to raise the declaratory and injunctive claims.

American also moved for partial summary judgment on the Cruzes' damages claims to the extent the Cruzes sought damages in excess of the Warsaw Convention's $9.07 per pound liability limit. American, however, conceded that it was liable to the Cruzes to the extent of $9.07 per pound of their lost bags. Consequently, American also moved for entry of final judgment in the Cruzes' favor to the extent of $9.07 times the poundage of the Cruzes' bags.

The district court granted both of American's motions, holding that American's liability to the Cruzes under the Warsaw Convention was limited to $9.07 per pound of lost luggage. The Cruzes had argued that the Warsaw Convention's liability limit did not apply because American had failed to state the weight of each suitcase on the Cruzes' baggage stubs, as required by Article 4(3)(f) of the Convention. The district court rejected this argument. Because American conceded liability to the Cruzes and moved for partial judgment in the Cruzes' favor, the district court entered a judgment in the Cruzes' favor to the extent of $9.07 times the poundage of their bags.

While American's summary-judgment motions were pending, the Cruzes moved to amend their complaint. Their motion sought to transform their individual claims into class action claims on behalf of others who had lost their luggage in similar circumstances. That motion was pending when the district court ruled on American's summary-judgment motions. After its ruling, the district court dismissed the Cruzes' motion to amend as moot.

The Cruzes successfully appealed the district court's judgment to this Court. On appeal, the Cruzes attacked, among other things, the district court's ruling regarding the Warsaw Convention's liability limit. In particular, they argued that the liability limit did not apply to the Cruzes' damages claims, because American had failed to record the baggage weight of each suitcase on the Cruzes' baggage stubs. We accepted that argument and accordingly vacated and remanded the district court's judgment. Cruz v. Am. Airlines, Inc., 193 F.3d 526, 528-30 (D.C.Cir.1999). Cruz did not, however, address whether the district court's standing rulings were correct. Nor did Cruz address whether the district court correctly dismissed as moot the Cruzes' motion to amend their complaint. Cruz merely reinstated the Cruzes' action to its prior, pre-summary judgment status and thus revived the Cruzes' motion to amend their complaint to a class action. Id. at 528 n. 2.

After remand, the Cruzes, in April 2000, filed an amended complaint asserting two class-action claims. The complaint described the "Claim I" class as

consist[ing] of all persons who during the period beginning two years prior to initiation of this suit, December 20, 1994, and ending on the date of Final Judgment herein (the "Claim I class period") (a) checked their baggage for transport for an international air journey to or from the United States in whole or part performed by American, (b) sustained the loss of or damage to their checked baggage in circumstances where American is made liable for such loss/damage under Warsaw Article 30(3), (c) gave timely notice of such loss/damage consistent with Warsaw Article 26 or applicable carrier tariff rules, (d) made claim for the fair value of such loss/damage, and (e) suffered the non-processing or rejection of their claim because of their alleged failure to comply with the requirements of defendant's 30-day Rule.

Claim I sought, inter alia, a declaration that American's "application of its 30-day rule to checked baggage claims" was unlawful and an injunction preventing American from applying the 30-day rule to the claims of future passengers, and noting damages.

The complaint defined the "Claim II class" as

consist[ing] of all persons all persons [sic] who during the period beginning two years prior to initiation of this suit, December 20, 1994, and ending on March 3, 1999 (the "Claim II class period") (a) checked their baggage for transport for an international air journey to or from the United States in whole or part performed by American and without the weight of that baggage having been recorded on the passenger's combined passenger ticket and baggage check, (b) sustained the loss of or damage to their checked baggage in circumstances where American is made liable for such loss/damage under Warsaw Article 30(3), (c) gave timely notice of such loss/damage consistent with Warsaw Article 26 or applicable carrier tariff rules, (d) made claim for the fair value of such loss/damage, and (e) thereafter received from American for such claim a payment of compensation less than the claimed fair value of such loss/damage, being an amount (usually $634.90 but sometimes $907) which American asserted was the limit of its liability for such baggage loss/damage under Warsaw's Article 22(2) liability limit and its tariff rules.

Claim II asked the district court to award this class compensatory damages equal to the fair value of their lost or damaged bags. Claim II also alleged that American had typically (as it did with Beato Cruz) settled the Claim II class members' damages claims for $634.90 per bag, based on American's representation that this figure was the limit of its liability under the Warsaw Convention. As discussed, those settlement offers (70 pounds times $9.07) erroneously assumed that, for a single bag, the maximum weight provided in American's tariff was 70 pounds, not 100.

American moved for partial summary judgment, arguing, as it had before the first appeal, that the Claim I plaintiffs lacked standing to obtain a declaration that American's 30-day rule was unlawful and an injunction preventing American from applying that procedure to future customers. As to Claim II, American argued that Beato Cruz's claim was barred by the two American claim-release forms he signed. The Cruzes, for their part, moved to certify both Claim I and Claim II as class actions.

In their reply to American's opposition to the Cruzes' motion to certify the two classes, filed on November 3, 2000, the Cruzes for the first time requested an additional form of relief under Claim I, one mentioned in neither their complaints nor their previous certification and summary-judgment documents. The Cruzes asked the district court to declare that American had an obligation to "process" the Claim I class members' claims without regard to American's (since repudiated) 30-day rule, and for American to offer the Claim I class compensation. The Cruzes requested that the district court issue an injunction requiring American to do both of those things.

The district court granted American's partial summary-judgment motion. The court decided to address American's summary-judgment motion before addressing the Cruzes' certification motion. As to summary judgment, the court concluded that Beato Cruz had released his claim for money damages by cashing the $634.90 check. Cruz had argued that this release should be rescinded on grounds of misrepresentation or mutual mistake. American, Cruz claimed, mistakenly represented to Cruz in the letter accompanying the $634.90 offer of settlement that the maximum weight of his bag, as defined in American's tariffs, was 70, not 100, pounds. As a result, American had underestimated the maximum extent of its Warsaw Convention liability to him. The district court rejected that argument, in part because American pointed to Cruz's deposition testimony showing that this mistake or misrepresentation did not contribute in any material way to Cruz's decision to sign the release. Cruz's testimony at his deposition was that, at the time he cashed the $634.90 check, he was represented by his present attorney and believed that he could successfully sue American for more than this amount even after he signed the release.

The district court also agreed with American that none of the Claim I putative class representatives had standing to seek declaratory and injunctive relief to remedy American's misapplication of the 30-day rule to them. That relief, the court reasoned, only would address American's prospective application of the rule, and therefore would not redress the putative representatives' actual injury — their lost bags. Moreover, the court continued, the possibility that these same plaintiffs would again fly on an international American flight, lose their bags, and have the 30-day rule again applied to them was simply too speculative an injury to establish Article III standing. The district court did not address whether the Cruzes had standing to seek relief under their newly articulated theory — specifically, whether they had standing to seek a declaration and injunction ordering American to "process" their claims and make offers to them. Having dismissed much of the Cruzes' case on the merits, the district court directed the Cruzes to file a new class-certification motion in light of the trimmed-down posture of the case.

The Cruzes filed exactly three post-summary-judgment motions. First, they renewed their motion to certify the Claim I class. They claimed that their complaint, even after the district court's summary-judgment ruling, still presented three common issues: (1) whether American was legally obligated to compensate the Claim I class members; (2) whether the district court should issue an injunction requiring American to process their damages claims on their merits without regard to the 30-day rule; and (3) whether the Cruzes were entitled to a declaration that the Warsaw Convention liability limit did not apply to those class members whose baggage weight American did not record on their claim tickets.

Second, the Cruzes requested that the district court reconsider its summary-judgment ruling. The sole ground on which the Cruzes sought reconsideration was that the district court had mistakenly granted American summary judgment as to the Claim II representatives' claims. Specifically, they repeated their argument that the release signed by the representatives, contrary to the district court's ruling, was fatally tainted by American's misrepresentation of the deemed weight of their bags. That motion, however, did not challenge the district court's ruling that the Cruzes lacked standing to assert their Claim I injunctive claims. Because the Cruzes interpreted the district court's summary-judgment ruling to have implicitly denied their motion to certify the Claim II class, the Cruzes did not formally renew that motion in their reconsideration petition.

Finally, the Cruzes filed a motion they styled as a "contingent motion for disclosure and notification." This motion asked the district court to direct American to disclose to the Cruzes the identities of the Claim I putative class members and to invite them to intervene as plaintiffs, assuming the district court concluded that "the existing complement of plaintiffs seeking to serve as the [Claim I] class representatives requires supplementation or substitution."

The district court denied all three motions. As for the Cruzes' claims for declaratory and injunctive relief, the district court noted that it had already ruled that the Cruzes lacked standing to challenge "the legitimacy of the 30-day rule." Thus, the court concluded, the Cruzes only had standing to seek damages for their lost bags. On the issue of damages, the district court declined to certify a class. The court relied primarily on Federal Rule of Civil Procedure 23(a), which requires that there be "questions of law or fact common to the class" before a court may certify a class. The court reasoned that the class members' claims for damages did not present a common issue. Resolution of any individual damage claim, the court said, would require a detailed, individualized inquiry into the value of each person's lost luggage, miring the court in an "unmanageable series of mini-trials that would destroy the efficiency rationale undergirding Rule 23." For substantially the same reason, the court concluded, alternatively, that the Cruzes' remaining damages claims did not present "question[s] of law or fact [that] predominate over any questions affecting only individual members." Fed. R.Civ.P. 23(c)(3). The district court also denied the Cruzes' motion for disclosure and intervention and their motion for reconsideration of its earlier summary-judgment ruling.

Following the district court's disposition, the Cruzes settled their individual damages claims with American. The district court accordingly entered an order granting American judgment on Beato Cruz's Claim II claim and dismissing the Claim I and Claim II class claims with prejudice. This appeal followed.

The Cruzes raise two sets of issues on appeal. The first relates to the district court's disposition of the motion to certify the Claim I putative class. As to this claim, the Cruzes argue that the district court mistakenly found they lacked standing to pursue declaratory and injunctive relief on behalf of that class. They also say that the district court abused its discretion in declining to certify the class. And they complain that the district court violated Rule 23(d)(2) by denying their contingent request for the court to order American to disclose the identities of the Claim I putative class members and to invite those people to intervene in this action.

The second set of issues relates to the Claim II class. Plaintiffs attack the district court's ruling that Beato Cruz's damages claim was released. Plaintiffs also appear to argue in their reply brief that the district court mistakenly declined to consider the propriety of certifying the Claim II class.

For the reasons that follow, we reject all of these assertions and affirm the judgment of the district court. We first address the Claim I issues, then the Claim II issues.

We review de novo the district court's decision to grant American summary judgment, viewing the evidence in the light most favorable to the Cruzes, the nonmoving parties. The district court's summary-judgment ruling should be affirmed only if American has satisfied its burden of showing that there is no genuine issue of material fact about whether it is entitled to judgment. Tao v. Freeh, 27 F.3d 635, 638 (D.C.Cir.1994). We may reverse a district court's refusal to certify a class only if it abused its discretion or applied incorrect legal criteria in doing so. Hartman v. Duffey, 19 F.3d 1459, 1471 (D.C.Cir.1994). The district court's decision not to order notice to the class is also a matter within the district court's "discretion," Larionoff v. United States, 533 F.2d 1167, 1186 n. 44 (D.C.Cir.1976), and so we will also reverse that only if the decision was an abuse of discretion.

1. Plaintiffs' challenge to the prospective enforcement of the 30-day rule.

The district court correctly found that the Cruzes lack Article III standing to obtain an injunction forbidding American from enforcing its 30-day rule and a declaration that this rule is unlawful. To establish standing, the Cruzes must show that American's actions have caused them some concrete injury that this declaratory and injunctive relief will redress. Fla. Audubon Soc'y v. Bentsen, 94 F.3d 658, 663 (D.C.Cir.1996) (en banc). The Cruzes have made no such showing.

In particular, they have not shown that their challenge to the prospective enforcement of American's 30-day policy will redress any concrete injury they have asserted. Plaintiffs have alleged the loss of their luggage on American flights; but a prospective injunction against future applications of the 30-day rule will do nothing to remedy that past harm. There is a chance that plaintiffs could lose their luggage on a future American flight; but plaintiffs have not alleged, much less presented evidence, that they have any such travel plans. Even if they did, the likelihood that American would, once again, lose plaintiffs' luggage is minuscule. And even assuming plaintiffs lost their luggage on another international American flight, the likelihood that they would again file their claims late is small, given their previous experience with American; indeed, Beato Cruz's actions — he filed his second claim for reimbursement on time — shows that these once-wronged plaintiffs are unlikely to file their claims late again. Even then, it is unlikely that American would again reject any late-filed claim, given the litigation its 30-day rule spawned and given that it has disavowed the 30-day rule.

Plaintiffs' speculative interest in prospectively challenging the 30-day rule parallels the one the Supreme Court found fell short of establishing a concrete interest in City of Los Angeles v. Lyons, 461 U.S. 95, 103 S. Ct. 1660, 75 L. Ed. 2d 675 (1983). In Lyons, a person whom police officers stopped and applied a chokehold to sued the City of Los Angeles and the officers for money damages and an injunction declaring that this practice was unlawful. Id. at 97-98, 103 S.Ct. at 1662-63. The Supreme Court held that the plaintiff lacked standing to seek the injunctive remedy, since it was highly unlikely that the plaintiff would be again stopped by the police and subjected to the same sort of chokehold. Id. at 107-08, 103 S. Ct. 1660 at 1668. Therefore, the Court reasoned, the plaintiff had no concrete interest in obtaining a prospective injunction.

The reasoning of Lyons applies to the claims before us. It is not likely that plaintiffs will again lose their luggage on an international American flight, much less again be denied compensation as a result of the misapplication of the 30-day rule. Though plaintiffs dismiss Lyons as involving a "wholly concluded and unlikely to be repeated incident of a police choke-hold," that characterization aptly describes plaintiffs' asserted injury as well.

2. Plaintiffs' request for a retrospective injunction ordering American to process their claims and offer to settle their claims.

Plaintiffs argue that the district court's decision to grant American summary judgment failed to consider a separate claim for injunctive relief — a claim for a retrospective injunction ordering American to "process" plaintiffs' compensation claims without regard to American's 30-day rule. This assertion challenges the district court's summary-judgment ruling that the Cruzes lacked standing to assert their Claim I requests "for declaratory and injunctive relief regarding [American's] 30-day rule." The district court never addressed plaintiffs' request for a retrospective, as opposed to a prospective, injunction and declaration, but that was because the Cruzes' lawyer failed to apprise the district court of it sufficiently. We therefore decline to address its merits.

We root this decision in our well-established discretion not to consider claims that litigants fail to raise sufficiently below and on which district courts do not pass. See Singleton v. Wulff, 428 U.S. 106, 120-21, 96 S. Ct. 2868, 2877, 49 L. Ed. 2d 826 (1976). The issue is whether, in light of the policy of this rule to "encourage[] parties to communicate with each other and the trial judge," Edmond v. U.S. Postal Serv., 949 F.2d 415, 422 (D.C.Cir.1991), plaintiffs apprised the district court with sufficient clarity of this challenge to its summary-judgment ruling.

They did not. Plaintiffs never mentioned this request in their pleadings. Their revised complaint, in particular, contained no hint of this odd request for an injunction, as plaintiffs' counsel conceded when pressed at oral argument. Nor did their summary-judgment papers, although those papers did stress the uncontroversial (and distinct) proposition that American has a duty to compensate passengers whose luggage it loses. The first clue plaintiffs gave the district court of their new theory came in their reply to American's opposition to their motion to certify the Claim I class — filed nearly four years after the Cruzes' filed their initial complaint.

This tardy, oblique assertion of the claim was not sufficient to apprise the district court of the need to address this issue in its summary-judgment ruling. Because plaintiffs asserted it only in their class-certification papers, rather than their summary-judgment papers, they did not give the district court a square chance to decide the question at the summary judgment stage. Plaintiffs, in particular, never made the argument that they had standing to assert this claim, and thus that American's motion to dismiss the Claim I claims for injunctive relief should have been denied.

Nor did plaintiffs make this argument clear to the district court after the district court entered its order dismissing Claim I to the extent it requested "declaratory and injunctive relief regarding [American's] 30-day rule." Plaintiffs, most damningly, never raised their retrospective injunctive claim as a reason for the district court to reconsider its summary-judgment ruling, although plaintiffs moved for reconsideration on other grounds. True, plaintiffs, in their renewed motion for class certification, identified the claim as a common issue that might warrant certifying the class. By then, however, the district court had granted American's motion for summary judgment as to Claim I injunctive relief related to the 30-day rule, removing those claims from the case. When plaintiffs belatedly argued that their new injunctive claim presented a common issue ripe for class adjudication, the district court, understandably, rejected it on the ground that it had already dismissed plaintiffs' injunctive claims. The district court properly treated the unchallenged portions of its summary-judgment order as the law of the case. Summary-judgment motions could not perform their function of simplifying and narrowing disputed issues if district courts had an obligation to reconsider, in light of the implications of other positions taken by litigants, such rulings sua sponte.

Plaintiffs' attempt to excuse their 11th-hour change of course does not succeed. They attempt to assign the blame to American, asserting that their shift simply reacted to "American's assertion, first made in its summary judgment papers, that it was free, as a matter of business policy, to reject or refuse to process, class member damage claims, whether or not its 30-day rule was unlawful or properly applied." This is both backward and wrong. It is wrong because American, to our knowledge, has never made such an assertion. American conceded below, in its brief, and at oral argument, that it may have a duty to compensate some (but not all) class members whose claims it rejected on the basis of its (now-abandoned) 30-day rule, and thus that it was not "free" to reject those claims.

It is backward because plaintiffs, not American, are the ones who shifted course. Nothing prevented the Cruzes from making this argument either in the four years that passed before the district court granted summary judgment against them or in their reconsideration motion. This inaction moves us, in our discretion, to decline to consider the merits of the issue now.

Finally, it is appropriate for us to determine that the claim was not sufficiently raised below, and therefore is not properly before us, without addressing whether plaintiffs have Article III standing to raise the claim. This approach is entirely consistent with the rule that courts must address issues relating to subject matter jurisdiction before reaching the merits of a case. See Steel Co. v. Citizens for a Better Env't, 523 U.S. 83, 101-02, 118 S. Ct. 1003, 1016, 140 L. Ed. 2d 210 (1998). As the Supreme Court has explained, "a court that dismisses on other non-merits grounds ... makes no assumption of law-declaring power that violates the separation of powers principles" underlying the Steel Company rule. Ruhrgas AG v. Marathon Oil Co., 526 U.S. 574, 585, 119 S. Ct. 1563, 1570, 143 L. Ed. 2d 760 (1999) (internal quotation marks and citation omitted). By declining to consider plaintiffs' retrospective injunctive claim, we are, within our discretion, simply declining to exercise jurisdiction over it. As Steel Company itself recognized, it is permissible to do that without determining whether plaintiffs have Article III standing to assert their claim for a retrospective injunction. See 523 U.S. at 100 n. 3, 118 S.Ct. at 1015 n. 3.

Because plaintiffs' claim for retrospective injunctive relief is not properly before us, we can easily dispose of plaintiffs' assertion that the district court abused its discretion in not certifying the Claim I class. As discussed more fully above, the district court declined to certify the Claim I class because the class members' damages claims presented individualized issues not common to all class members. Plaintiffs do not challenge this conclusion on appeal. Instead, plaintiffs assert that their injunctive claims, rather than their damages claims, are common issues that can be adjudicated class wide.

Those claims, however, are out of this case now that we have concluded that plaintiffs either lack standing to raise their injunctive claims or have not preserved them for appeal. These conclusions therefore also refute plaintiffs' certification argument. The district court neither erred nor abused its discretion in declining to certify the class on a ground that plaintiffs do not challenge on appeal.

The district court did not abuse its discretion in denying plaintiffs' "contingent motion for disclosure and notification" — in essence, a request that the district court order notice, pursuant to Rule 23(d)(2), to a non-certified class. We doubt, as a threshold matter, that a district court has any discretion to order notice "in the conduct of [an] action[]" in which it has declined to certify any class whatsoever, for such an action may well not be one "to which [Rule 23] applies." Fed.R.Civ.P. 23(d)(2). Setting that point aside, however, the district court, at a minimum, did not abuse its discretion by declining to order notice to this putative class given that it found the remaining issues in the case were unsuitable for class treatment at all, and given that there was no reversible error in that finding.

We also affirm the district court's decision to grant American summary judgment on Beato Cruz's individual damages claim and to deny his motion to certify the Claim II class. As to the summary-judgment issue, the district court concluded that Cruz's individual damages claim was barred by the release Cruz signed in exchange for American's $634.90 payment to him. Cruz challenges this ruling on appeal, claiming that the release is voidable because American, in its letter accompanying that payment, mistakenly represented the extent of its liability to Cruz under the Warsaw Convention. Cruz also appears to argue in his reply brief that the district court erroneously declined to address whether the Claim II class should have been certified given that it granted American summary judgment on the representative plaintiffs' individual claims. We reject both challenges.

The parties disagree on the law applicable to the issue of the validity of the release. Cruz argues that federal common law applies; American says, and the district court agreed, that state law applies. In any event, American continues, Cruz's release is valid regardless whether state law or federal common law applies.

We agree with American that there is no conflict of law for this Court to resolve. The parties have identified only three possible sources of law: Maryland, Virginia, and federal common law. Cruz argues that the federal common law rule of decision to apply is the rule of the Second Restatement of Contracts. That rule, as Cruz quotes approvingly in his brief, is that "[a]n agreement is voidable" on grounds of mutual mistake "where both parties were mistaken as to a basic assumption of the agreement which has a material effect on the exchange of performances." Restatement (Second) of Contracts § 152. In like fashion, Cruz relies on the Second Restatement's unilateral misrepresentation rule. That rule, as stated in his brief, is that the release is voidable if Cruz's manifestation of assent was induced by a material misrepresentation by American that "substantially contributed" to Cruz's decision to sign the release. Id. §§ 164, 167.

In American's view, under the law of Virginia and Maryland, Cruz may rescind the agreement on the ground of mistake if he agreed to it with a mistaken belief concerning a fact of significance. As for misrepresentation, American's understanding of the law of Virginia and Maryland is that Cruz may rescind the agreement if he reasonably relied on American's material misrepresentation.

The standards advocated by the parties do not conflict in any respect relevant to our resolution of this appeal. While the standards are not linguistically identical, all place the burden on Cruz to make out this defense to enforcing the release. The only difference is that the mutual mistake standard labels whether Cruz relied on the misrepresentation in terms of whether the mistake had a "material effect on the exchange of performances" or whether the mistaken belief concerned a "fact of significance," rather than in terms of his "reliance" on the misrepresentation. These formulations all go to whether the misrepresentation or mutual mistake was important to Cruz in his decision to accept the release. Therefore, the distinctions among them, in our view, make no substantive difference, at least in this case, and so we need not make a choice of law.

Turning to the merits, Cruz has shown no triable issue of fact as to whether he relied on American's mistaken misrepresentation. To review: American's letter that accompanied its $634.90 check to Cruz understated the limit of its Warsaw Convention liability by $272.10. It is true, as Cruz points out, that this was indeed a misrepresentation or mistake; but Cruz has not established a triable issue of fact on the essential element of Cruz's reliance on this misrepresentation or mistake.

Uncontradicted evidence in the summary-judgment record establishes that this is not a triable issue. Cruz testified that, at the time he signed the release, he believed that the release would not prevent him from recovering even more money from American. That belief demonstrates that he did not rely on American's representations about the state of the law of Warsaw Convention liability. If Cruz, in accepting the release, had relied on American's representation about the limit of its liability, he would not have believed that he could, in his words, recover an "additional amount." Rather, he would have thought that American's payment fully discharged its payment obligation. That is because American paid him exactly what it represented it owed him. The fact that he thought he was owed more shows that he did not believe that representation, i.e., American's view of the law.

Therefore, Cruz's deposition testimony, together with the fact that he was represented by his current lawyer at the time, proves that he accepted a totally different measure, one that did not depend on deemed weight. This evidence shows that at the time — no doubt influenced by advice from his lawyer in the pending litigation against American — Cruz believed that he could recover the full $3,890 value of his bag regardless of its weight, deemed or otherwise. That is clear enough from positions his lawyer later took on his behalf, and given the summary-judgment record the parties compiled, it is not reasonable to read the record any other way. Because Cruz did not accept deemed weight as a method for calculating liability at all, he could not have cared that American got the deemed weight wrong. Cruz's belief shows that he accepted the release for totally different reasons, ones that had nothing to do with American's mistaken representation as to deemed weight, and thus as to the limit of its liability under the Warsaw Convention. Cruz's failure to produce any evidence creating a genuine issue as to this fact entitles American to summary judgment on the question of this defense to enforcing the release.

We recognize, as Cruz takes pains to highlight in his brief, that the mistake at issue in this case is different from the one in Curtin v. United Airlines, Inc., 275 F.3d 88 (D.C.Cir.2001), but this distinction does not require a different result in this case. In Curtin, United Airlines had offered to settle the lost-baggage claims of certain of its passengers and, in connection with these offers, had represented to these passengers that its liability was limited to $635 under the Warsaw Convention. Id. at 89-90. This Court held that this representation did not allow the passengers who had settled their claims with United to rescind the releases on the ground of mutual or unilateral mistake. Id. at 96-97. United made the representations before Cruz was decided, the Court reasoned, when the law regarding the limit of United's liability under the Warsaw Convention was unsettled. Because that representation was reasonable in light of the unsettled state of the law at the time the parties agreed to the release, United made no "mistake," the Court held. Id.

Cruz is right that, unlike Curtin, American, in light of its understanding of the law at the time of the release, made a mistake. Given American's belief that the Warsaw Convention liability limits applied, and its view of how to calculate those liability limits, American mistakenly stated the limit of that liability. We rest our holding not on the fact that American made no "mistake," but rather on the fact that that Cruz has not established genuine issues of material fact about whether he relied on that mistake, given that he did not think American's liability was limited at all.

Cruz does not argue in his opening brief that the district court mistakenly declined to address whether the Claim II class should be certified given that it dismissed only the representative plaintiffs' claims on the merits at the summary judgment stage, rather than all of the claims of the Claim II putative class. Although we may discern a hint of such an argument after a close reading of plaintiffs' reply brief (albeit not a hint supported by both citations to authority and argument, as is required by Federal Rule of Appellate Procedure 28(a)(9)), plaintiff was required to present, argue, and support this claim in his opening brief for us to consider it. See, e.g., Nat'l Lime Ass'n v. EPA, 233 F.3d 625, 633 (D.C.Cir.2000). We are not "self-directed boards of legal inquiry and research, but essentially ... arbiters of legal questions presented and argued by the parties." Carducci v. Regan, 714 F.2d 171, 177 (D.C.Cir.1983).

We therefore do not consider whether the district court correctly declined to address the propriety of certifying the Claim II class after it dismissed the individual plaintiff's damages claims. Although we do not decide the point, we note that many of the reasons the district court gave in declining to certify the Claim I class equally apply to whether the Claim II class should have been certified. Once the injunctive claims are gone, the issues in both Claim I and Claim II are individualized.

For the reasons expressed above, the judgment of the district court is affirmed.