Posner, Circuit Judge.

Jefferies LLC, a securities and investment-banking firm, in 2012 hired Michael Frawley to be the firm's vice chairman and global head of metals and listed products. Nicholas Webb, a sales executive in the global metals group headed by Frawley of a firm they had previously worked for, and Thad Beversdorf, a director of that group, were hired by Jefferies on the same day that Frawley was hired. Webb and Beversdorf signed employment contracts with Jefferies in which they "consent[ed] that any arbitration proceeding brought with respect to matters related to your employment or this Agreement shall be brought before FINRA ... or if the parties are permitted to bring such action in a state or federal court, then you hereby consent to the personal jurisdiction of the state and federal courts ... [in New York City] with respect to matters related to your employment or this Agreement."

FINRA is an acronym for Financial Industry Regulatory Authority, Inc., a "not-for-profit organization authorized by Congress to protect America's investors by making sure the broker-dealer industry operates fairly and honestly ... [by] writing and enforcing rules governing the activities of 3,800 broker-dealers with 633,800 brokers; examining firms for compliance with those rules; fostering market transparency; and educating investors." FINRA, "About FINRA," www.finra.org/about (visited May 23, 2017).

All three of Jefferies' new employees were metals traders, primarily in iron ore. But in 2013 Jefferies decided to get out of the iron ore business, and so ordered Frawley to tell Webb and Beversdorf to stop trading iron ore. Frawley did not tell them, and instead pushed them to do more iron ore trades. Some months later, Jefferies fired Webb and Beversdorf; the record does not indicate whether Frawley was fired, although it's clear that he no longer is employed by Jefferies. Webb and Beversdorf brought this suit against Frawley in an Illinois state court in 2015, charging him with having defrauded them and interfered with their contracts with Jefferies — in short with having cost them their jobs. Frawley sought to remove the case to federal court on the ground that the plaintiffs were citizens of a different state (Illinois) from the defendant (New York) and that "the amount in controversy exceeds $75,000, exclusive of interest and costs." Frawley's notice of removal noted that "Plaintiffs Webb and Beversdorf each seek damages in excess of $100,000 against Defendant, or an amount in excess of $50,000 for each count of their two-count Complaint." The following day Frawley moved the district court to compel Webb and Beversdorf to arbitrate their dispute with him before FINRA; he also asked the district court to stay the litigation pending the arbitration.

Webb and Beversdorf responded by filing a motion to remand the case to the state court on the ground that Frawley had failed to establish that the amount in controversy exceeded $75,000 (as required for a suit based on diversity of citizenship, see 28 U.S.C. § 1332(a)) because the $100,000 figure had been arrived at by aggregation of duplicative claims — the two counts in their complaints had been nothing more than different theories under which the plaintiffs could recover the single $50,000 loss that each had suffered; therefore Frawley had double-counted. The district judge denied the motion to remand the case to the state court, and shortly afterward Frawley renewed his motion (on which the judge had not ruled) to compel the plaintiffs to arbitrate their dispute with him. Webb and Beversdorf submitted affidavits which stated that they'd never agreed to arbitrate disputes with Frawley and after being fired by Jefferies had not been associated with any member of FINRA. But the judge granted Frawley's motion to compel arbitration, and having done so dismissed the plaintiffs' suit (the suit by Webb and Beversdorf that had originally been brought in state court, later removed to federal court), precipitating their appeal to us.

The judge was correct not to remand the case to state court, but instead retain it in the federal district court, if Webb and Beversdorf were each seeking more than $75,000 in damages from Frawley, for if they were he was entitled to have removed the case to the federal court. Our best guess — though no stronger statement is possible — is that they were seeking higher damages. They had received high annual salaries at Jefferies — about $175,000 for Webb and $250,000 for Beversdorf, each with the potential to earn additional bonuses. They are unlikely to have obtained comparable salaries elsewhere, for they complain in their complaint that Frawley's actions had "resulted in their [Webb's and Beversdorf's] commercial reputations being irreparably damaged in the industry." That assertion has led Frawley to assert that the stakes of the case exceed $75,000 for each of the two plaintiffs, and we have said that a defendant's "estimate of the stakes is acceptable if it is plausible and supported by a preponderance of the evidence." Oshana v. Coca-Cola Co., 472 F.3d 506, 511 (7th Cir. 2006). Had Webb and Beversdorf wanted to remain in state court, they could have stipulated that they would collect no more than $75,000 in damages each. They did not.

The district court allowed limited discovery on the amount in controversy, and Frawley sent each plaintiff a request to admit that the damages he suffered had not exceeded $75,000. Each plaintiff had replied that he could not "truthfully admit or deny this request." As we said in Workman v. United Parcel Service, Inc., 234 F.3d 998, 1000 (7th Cir. 2000), "if [the plaintiff] doesn't make such a stipulation, the inference arises that he thinks his claim may be worth more."

As for Frawley's motion to compel the plaintiffs to arbitrate, it is based on FINRA Rule 13200(a), which states that "except as otherwise provided in the Code [FINRA's code of arbitration procedure], a dispute must be arbitrated under the Code if the dispute arises out of the business activities of a member or an associated person and is between or among Members; Members and Associated Persons; or Associated Persons." Frawley argues that Webb and Beversdorf were persons associated with a FINRA member, namely Jefferies, even though they had ceased to work for Jefferies. FINRA Rule 13100(u) defines a person associated with a member to include "a person formerly associated with a member." But since FINRA is a private organization, the court could not order Webb and Beversdorf to follow its arbitration rules unless they'd agreed to do so. See Howsam v. Dean Witter Reynolds, Inc., 537 U.S. 79, 83, 123 S.Ct. 588, 154 L.Ed.2d 491 (2002). Beversdorf agreed; he signed a U-4 form, and, as explained in subsection (1) of an accompanying disclosure, "[by signing] you are agreeing to arbitrate any dispute, claim or controversy that may arise between you and your firm, or a customer, or any other person[,] that is required to be arbitrated under the rules of the self-regulatory organizations [including FINRA] with which you are registering. This means you are giving up the right to sue a member, customer, or another associated person in court, including the right to a trial by jury, except as provided by the rules of the arbitration forum in which a claim is filed." Webb, however, signed neither a U-4 form nor any other agreement requiring him to arbitrate before FINRA. Frawley points to the arbitration provision in Webb's employment contract with Jefferies, quoted earlier in the opinion, but that's just a venue provision — it simply requires that if Webb agrees to arbitrate his dispute with Frawley, he must arbitrate it before FINRA. Having not so agreed he remains free to litigate his dispute with Frawley in federal court.

We therefore affirm in part and reverse in part the district court's order compelling arbitration: Beversdorf must arbitrate his dispute with Frawley pursuant to the form U-4, while Webb's suit against Frawley may proceed in the district court.

So ordered.