Over time, this case has become a procedural motley. In its current iteration, defendant-appellant Barry Johnson emphasizes his association with the Johnson Law Firm (JLF) in attempting to compel the plaintiffs, Rickie Patton and his wife Cathleen Marquardt, to arbitrate various tort claims (including their claims of legal malpractice). The district court, adopting a magistrate judge's report and recommendation (R&R)1 and applying principles of collateral estoppel derived from Rhode Island law, determined that the appellant was barred from relitigating his contention that the claims should be heard before an arbitrator. The appellant assigns error. After threading our way through the labyrinth of prior proceedings, we affirm.
I. BACKGROUND
We briefly rehearse the background and travel of the case. In 2007, the plaintiffs retained defendants JLF and Steven M. Johnson to represent them in a products liability suit concerning an allegedly defective hernia mesh device (Kugel Mesh).2
*831The parties executed an Attorney Representation Agreement (the ARA), which contained a three-paragraph arbitration provision. The plaintiffs did not, however, initial or otherwise specifically acknowledge the arbitration paragraphs.
JLF filed the plaintiffs' products liability suit in the United States District Court for the Southern District of Texas. As part of a centralized multi-district litigation proceeding, see 28 U.S.C. § 1407, the suit was subsequently transferred to the District of Rhode Island, where it joined more than 1,000 similar suits brought against the Rhode Island-based Kugel Mesh manufacturer. In due course, JLF hired the appellant as an employed attorney. In that capacity, the appellant worked, inter alia, on the plaintiffs' suit.
When the suit was settled in 2015, a dispute arose among the plaintiffs, the appellant, JLF, and John Deaton (the Rhode Island-based local counsel retained by JLF). Central to this dispute were representations allegedly made by the appellant concerning settlement amounts. The dispute was not resolved, and the appellant came to believe that the plaintiffs would be filing a malpractice suit against him.
In an attempt to get out in front of such a suit, the appellant - in April of 2016 - filed a civil action against JLF and Patton in a Texas state court seeking to compel arbitration based on the provisions of the ARA. Patton challenged the court's jurisdiction over his person, as did Deaton (who had been impleaded by JLF). The Texas trial court rejected these jurisdictional challenges, striking the special appearances made on behalf of both Patton and Deaton. Deaton appealed, and the Texas Court of Appeals affirmed. See Deaton v. Johnson, No. 05-16-01221-CV, 2017 WL 2991939, at *4 (Tex. App. July 14, 2017), review dismissed (Aug. 10, 2018).
While Deaton's appeal was pending, JLF initiated a Judicial Arbitration and Mediation Service (JAMS) arbitration proceeding against Patton in Fort Worth, Texas. The appellant was not named as a party to the JAMS arbitration. Patton challenged JLF's right to arbitrate, arguing that the uninitialed arbitration paragraphs in the ARA were of no effect. By decision dated November 15, 2016, the arbitrator determined that the ARA did not contain a valid and enforceable agreement to arbitrate. Accordingly, the arbitrator dismissed the JAMS proceeding.
The plaintiffs made the next move. On April 3, 2017, they sued the appellant, JLF, and JLF's principal in a Rhode Island state court, asserting claims for malpractice, other torts, and unfair trade practices (all relating to the handling and settlement of the plaintiffs' Kugel Mesh suit). The defendants removed the suit to the United States District Court for the District of Rhode Island, noting diversity of citizenship and the existence of a controversy in the requisite amount. See 28 U.S.C. §§ 1332(a), 1441. At roughly the same time, the appellant initiated a second JAMS arbitration proceeding against Patton in Texas, premised upon the arbitration provision in the appellant's 2013 employment agreement with JLF - an agreement to which the plaintiffs were not parties. By means of this proceeding, the appellant sought what amounted to a declaration that the plaintiffs were bound to arbitrate their claims against him. The appellant proceeded to file a motion to compel arbitration in the United States District Court for the Northern District of Texas.
With this foundation in place, the appellant turned his attention to the Rhode Island case, moving to stay the civil action and compel arbitration pursuant to the Federal Arbitration Act (FAA). See *8329 U.S.C. §§ 3, 4. His motion sought to invoke the arbitration provisions of both his 2013 employment agreement and the ARA. While his motion was pending before the federal district court in Rhode Island, the federal district court in Texas denied the appellant's motion to compel arbitration on the ground that the 2013 employment agreement did not in any way bind Patton. Consequently, the court dismissed the Texas suit without prejudice.
Back in Rhode Island, the appellant abandoned his reliance on the 2013 employment agreement. Nevertheless, he continued to pursue his motion to compel arbitration, relying exclusively on the uninitialed arbitration paragraphs contained in the ARA. He alleged in relevant part that he was not a party to the first JAMS arbitration and, thus, was not bound by the decision of the first JAMS arbitrator (who had found the uninitialed arbitration paragraphs in the ARA impuissant as to Patton). The plaintiffs opposed this motion, arguing that the appellant was in privity with JLF and was therefore precluded from re-litigating the issue of arbitrability under principles of collateral estoppel.
The court below referred the appellant's motion to compel arbitration to a magistrate judge, who applied Rhode Island law and concluded that principles of collateral estoppel foreclosed the appellant's attempt to invoke the arbitration provision of the ARA. Accordingly, the magistrate judge recommended that the appellant's motion to compel arbitration be denied. See Patton I, 2018 WL 3655785, at *9. Represented by new counsel, the appellant served written objections to the R&R, but the district court overruled the objections, adopted the R&R, and denied the motion to compel arbitration. See id. at *1. This timely appeal followed.
II. ANALYSIS
Before beginning our analysis, we pause to smooth out a procedural wrinkle. We then proceed to the merits.
A. Judicial Review of the R&R.
"[A]s Article I judicial officers, magistrate judges ordinarily may not decide motions that are dispositive either of a case or of a claim or defense within a case." PowerShare, Inc. v. Syntel, Inc., 597 F.3d 10, 13 (1st Cir. 2010). While a magistrate judge may decide a non-dispositive motion, see Fed R. Civ. P. 72(a), she may only make a recommended disposition of a dispositive motion, see Fed. R. Civ. P. 72(b).
This dispositive/non-dispositive dichotomy has implications for judicial review. When a magistrate judge issues a recommended decision on a dispositive motion and an objection is interposed, district court review is de novo. See id. By contrast, when a magistrate judge enters an order resolving a non-dispositive motion and a first-tier appeal is taken to the district court, review is for clear error (that is, the district court must accept the magistrate judge's findings of fact and inferences drawn therefrom unless those findings and inferences are clearly erroneous). See Fed. R. Civ. P. 72(a) ; Phinney v. Wentworth Douglas Hosp., 199 F.3d 1, 4 (1st Cir. 1999).
In this case, the magistrate judge treated the appellant's motion to compel arbitration as a dispositive motion and recommended a decision. See Patton I, 2018 WL 3655785, at *1. This was error because a motion to compel arbitration is a non-dispositive motion. See PowerShare, 597 F.3d at 14. Accordingly, an order, not a recommended decision, would have been the appropriate vehicle for the magistrate judge's findings and conclusions.
*833But the district court came to the rescue: it recognized this discrepancy and treated the R&R as an order. See Patton I, 2018 WL 3655785 at *1. The district court's prophylactic action cured the defect and rendered any procedural error harmless. See United States v. Weissberger, 951 F.2d 392, 398 (D.C. Cir. 1991) (holding that district court's application of proper standard of review "cured any arguable defect" in magistrate judge's order).
That the error was harmless is all the more evident because the appellant's motion to compel turned on questions of law. See, e.g., PowerShare, 597 F.3d at 14 (explaining that "interpreting a contractual term [is] a question of law for the courts"); Monarch Life Ins. Co. v. Ropes & Gray, 65 F.3d 973, 978 (1st Cir. 1995) ("The applicability vel non of preclusion principles is a question of law."). This is significant because a magistrate judge's answers to questions of law, whether rendered in connection with a dispositive motion or a non-dispositive motion, engender de novo review. See PowerShare, 597 F.3d at 15 (explaining that, for questions of law, "there is no practical difference between review under Rule 72(a)'s 'contrary to law' standard and review under Rule 72(b)'s de novo standard"). It follows that whether the magistrate judge issued an R&R or an order, the district court was obliged to apply the same standard of review to the questions at issue.
B. The Merits.
We review de novo the district court's denial of a motion to compel arbitration. See Nat'l Fed'n of the Blind v. The Container Store, Inc., 904 F.3d 70, 78 (1st Cir. 2018) ; Kristian v. Comcast Corp., 446 F.3d 25, 31 (1st Cir. 2006). We may affirm the district court's ruling "on any independent ground made apparent by the record." Escobar-Noble v. Luxury Hotels Int'l of P.R., Inc., 680 F.3d 118, 121 (1st Cir. 2012).
To compel arbitration, the movant must demonstrate "that a valid agreement to arbitrate exists, that [he] is entitled to invoke the arbitration clause, that the other party is bound by that clause, and that the claim asserted comes within the clause's scope." InterGen N.V. v. Grina, 344 F.3d 134, 142 (1st Cir. 2003). Here, the first JAMS arbitrator answered the question of whether the ARA contained a valid and enforceable arbitration agreement in the negative, and the magistrate judge - applying Rhode Island law - concluded that this determination was entitled to preclusive effect. See Patton I, 2018 WL 3655785, at *1-2. The appellant lays siege to this conclusion.
Some groundwork is helpful. "Collateral estoppel, sometimes called issue preclusion, bars parties from re-litigating issues of either fact or law that were adjudicated in an earlier proceeding" before a court or other tribunal of competent jurisdiction. Robb Evans & Assocs., LLC v. United States, 850 F.3d 24, 31 (1st Cir. 2017) ; see Ramallo Bros. Printing, Inc. v. El Día, Inc., 490 F.3d 86, 89 (1st Cir. 2007) (quoting S. Pac. R.R. Co. v. United States, 168 U.S. 1, 48, 18 S.Ct. 18, 42 L.Ed. 355 (1897) ). The doctrine serves the "dual purpose of protecting litigants from the burden of relitigating an identical issue with the same party or his privy and of promoting judicial economy by preventing needless litigation." Sutliffe v. Epping Sch. Dist., 584 F.3d 314, 329 (1st Cir. 2009) (quoting Parklane Hosiery Co. v. Shore, 439 U.S. 322, 326, 99 S.Ct. 645, 58 L.Ed.2d 552 (1979) ). As "issue preclusion prevent[s] relitigation of wrong decisions just as much as right ones," a court charged with applying collateral estoppel ought not inquire into the correctness of the earlier determination of a precluded issue.
*834Vargas-Colón v. Fundación Damas, Inc., 864 F.3d 14, 29 (1st Cir. 2017) (quoting B & B Hardware, Inc. v. Hargis Indus., Inc., --- U.S. ----, 135 S.Ct. 1293, 1308, 191 L.Ed.2d 222 (2015) ) (alteration in original).
As a threshold matter, the appellant posits that collateral estoppel principles are inapposite here because the arbitrator lacked the authority to decide the issue of whether an agreement to arbitrate existed. Although the plaintiffs argue that this issue was not properly preserved for appeal, our review of the record leaves us less sanguine. Thus, we proceed to consider the appellant's challenges to the arbitrator's authority to determine the arbitrability of claims arising in connection with the ARA.
To begin, the premise on which the appellant's argument rests is sound: as a customary tenant, collateral estoppel "is not implicated if the forum which rendered the prior 'judgment' (viz., the arbitral award) lacked 'jurisdiction' over the putatively precluded claim." Wolf v. Gruntal & Co., 45 F.3d 524, 527 (1st Cir. 1995) ; see, e.g., Montana v. United States, 440 U.S. 147, 153, 99 S.Ct. 970, 59 L.Ed.2d 210 (1979) ; S. Pac. R.R., 168 U.S. at 48, 18 S.Ct. 18. But as we explain below, the appellant's attempt to invoke this premise here is faulty.
The appellant's principal claim is that the arbitrator lacked authority to resolve the issue of arbitrability because that issue already had been resolved by the Texas state court when it rejected the jurisdictional challenges mounted by Patton and Deaton. In response to the magistrate judge's statement that "[i]t is difficult to discern a holding of this scope in the Texas state court materials filed by the parties," Patton I, 2018 WL 3655785, at *3 n.5, the appellant does not identify any such holding but, rather, notes only that the parties' briefing in the Texas court included arguments on arbitrability. The appellant, though, reads too much into this briefing: the mere fact that an issue is briefed before a court, without more, does not mean that the court decided the issue. See Wingard v. Emerald Venture Fla. LLC, 438 F.3d 1288, 1294 (11th Cir. 2006) ; Benoni v. Bos. & Me. Corp., 828 F.2d 52, 56 (1st Cir. 1987).
Critically, there is nothing in the Texas state court's succinct jurisdictional determination that indicates it was predicated upon the arbitrability vel non of disputes under the ARA. Given the nature of the jurisdictional issue, it is equally likely that the Texas state court's retention of jurisdiction relied on the facts surrounding the plaintiffs' engagement of JLF. These facts indicated, among other things, that Texas was the place where the contract was formed and that Texas was the anticipated place of performance and payment. See, e.g., Griffith Techs., Inc. v. Packers Plus Energy Servs. (USA), Inc., No. 01-17-00097-CV, 2017 WL 6759200, at *3 (Tex. App. Dec. 28, 2017) (holding that contract's place of performance is an important consideration with respect to personal jurisdiction); Hoagland v. Butcher, 474 S.W.3d 802, 815 (Tex. App. 2014) (same). Thus, there is no principled way in which we can read the Texas state court's jurisdictional determination as a determination that a valid and enforceable agreement to arbitrate existed.
The appellant has a fallback position. He argues that the first JAMS arbitrator exceeded his authority because the parties did not agree to submit the question of arbitrability to an arbitrator. This is whistling past the graveyard.
Parties to a contract may, by mutual agreement, place before an arbitrator "not only the merits of a particular dispute but also 'gateway' questions of 'arbitrability,'
*835such as whether the parties have agreed to arbitrate or whether their agreement covers a particular controversy." Henry Schein, Inc. v. Archer & White Sales, Inc., [--- U.S. ----, ----, 139 S.Ct. 524, --- L.Ed.2d ----, 2019 WL 122164, at *3 (2019) ] (quoting Rent-A-Ctr., W., Inc. v. Jackson, 561 U.S. 63, 68-69, 130 S.Ct. 2772, 177 L.Ed.2d 403 (2010) ). For such gateway questions, a court "should not assume that the parties agreed to arbitrate arbitrability unless there is clear and unmistakable evidence that they did so." Id. at 531 [2019 WL 122164, at *6 ] (quoting First Options of Chi., Inc. v. Kaplan, 514 U.S. 938, 944, 115 S.Ct. 1920, 131 L.Ed.2d 985 (1995) ).
The "clear and unmistakable evidence" standard is demanding. See Shank/Balfour Beatty v. Int'l Bhd. Of Elec. Workers Local 99, 497 F.3d 83, 89-90 (1st Cir. 2007) ; Marie v. Allied Home Mortg. Corp., 402 F.3d 1, 14 (1st Cir. 2005). Generally speaking, a court must look to the language of the parties' agreement to determine whether the agreement to arbitrate extends to questions of arbitrability. See, e.g., Rent-A-Ctr., 561 U.S. at 66-67, 130 S.Ct. 2772 ; PowerShare, 597 F.3d at 15-18. Even so, the language of the contract is not always the exclusive source of relevant information; the parties' conduct also may herald an agreement to arbitrate the question of arbitrability. See Local 36 Sheet Metal Workers' Int'l Ass'n v. Whitney, 670 F.3d 865, 869 (8th Cir. 2012) ; Cleveland Elec. Illuminating Co. v. Util. Workers Union of Am., 440 F.3d 809, 813 (6th Cir. 2006) ; see also Coady v. Ashcraft & Gerel, 223 F.3d 1, 9 n.10 (1st Cir. 2000) (explaining that "[p]arties may supplement by their submissions the authority granted an arbitration panel under a contract"). Relatedly, "a court must defer to an arbitrator's arbitrability decision when the parties submitted that matter to arbitration." First Options, 514 U.S. at 943, 115 S.Ct. 1920.
The decision in Cleveland Electric is instructive. There, the Sixth Circuit determined that parties who "submitted the question of arbitrability to the arbitrator for his determination" and manifested no intent to "reserve the question of arbitrability for the court" had "clearly and unmistakably consented" to arbitrate questions of arbitrability. 440 F.3d at 813. In making this determination, the court convincingly distinguished First Options, in which the Supreme Court found that because parties had filed written objections to the arbitration in which they challenged the arbitrators' jurisdiction over questions of arbitrability, those parties "did not clearly agree to submit the question of arbitrability to arbitration." 514 U.S. at 947, 115 S.Ct. 1920.
Here, we discern much the same type of factual mosaic that the Sixth Circuit found persuasive in Cleveland Electric. JLF took the unequivocal position before the first JAMS arbitrator that, pursuant to JAMS rules, the arbitrator had the authority to adjudicate any "[j]urisdictional and arbitrability disputes, including disputes over the formation, existence, validity, interpretation or scope of the agreement under which Arbitration is sought." All of the parties to the first JAMS arbitration submitted briefs to the arbitrator on the issue of whether the claims asserted were arbitrable at all, and no one questioned the arbitrator's authority to decide that issue. Nor did any party seek to vacate the arbitrator's decision on such a ground. Given this history, we conclude that the parties to the first JAMS arbitration clearly and unmistakably accepted the proposition that the arbitrator possessed the requisite authority to determine *836whether claims arising under the ARA were arbitrable.
Our conclusion that the first JAMS arbitrator had authority to decide the issue of arbitrability brings us to the next facet of the appellant's asseverational array. The magistrate judge, following the parties' lead, applied Rhode Island law and concluded that collateral estoppel principles demanded the denial of the appellant's motion to compel arbitration. See Patton I, 2018 WL 3655785, at *7. The appellant now submits that the court below should not have applied Rhode Island law in resolving this question. Instead, he contends that Texas law should control.
With respect to the preclusive effect of an unconfirmed arbitral award,3 it is an open question whether, in this diversity action, we should apply the choice-of-law rules of the forum state (Rhode Island), see Cochran v. Quest Software, Inc., 328 F.3d 1, 6 (1st Cir. 2003), or the choice-of-law rules dictated by federal common law, see McDonald v. City of W. Branch, Mich., 466 U.S. 284, 288, 104 S.Ct. 1799, 80 L.Ed.2d 302 (1984). The absence of controlling authority is not surprising as "[t]he source of the law that governs the preclusion consequences of an [unconfirmed] arbitration award has not been much developed." 18B Charles Alan Wright et al., Federal Practice and Procedure § 4475.1 (2d ed. 2002) ; see W.J. O'Neil Co. v. Shepley, Bulfinch, Richardson & Abbott, Inc., 765 F.3d 625, 629 (6th Cir. 2014) (referring to the source-of-law issue for unconfirmed arbitral awards as "underdeveloped and murky").
Here, however, we need not explore this uncertain source-of-law terrain. In his briefing before the magistrate judge, the appellant stated unequivocally that the preclusive effect of the arbitrator's ruling "should be determined under Rhode Island law, because this issue does not involve the construction of the ARA and is therefore not subject to determination under Texas law." The other parties acquiesced. Where, as here, all parties agree to the application of a particular source of law, a court is "free to 'forego an independent analysis and accept the parties' agreement.' " Hershey v. Donaldson, Lufkin & Jenrette Sec. Corp., 317 F.3d 16, 20 (1st Cir. 2003) (quoting Borden v. Paul Revere Life Ins. Co., 935 F.2d 370, 375 (1st Cir. 1991) ). The magistrate judge followed this praxis, stating explicitly that she was applying Rhode Island law at the parties' behest. See Patton I, 2018 WL 3655785, at *7 n. 10.
In this venue, the appellant reverses direction and assigns error to the district court's reliance on Rhode Island collateral estoppel law. But a party cannot so easily change horses in midstream, abandoning a position that he advocated below in search of a swifter steed. We think it self-evident that a party cannot invite the trial court to employ one source of applicable law and then - after the trial *837court has accepted his invitation - try to convince the court of appeals that some other source of law would be preferable. See Lott v. Levitt, 556 F.3d 564, 568 (7th Cir. 2009) ; Ortiz v. Gaston Cty. Dyeing Mach. Co., 277 F.3d 594, 597 (1st Cir. 2002). After all, the appellant "is not entitled to get a free peek at how his dispute will shake out under [Rhode Island] law and, when things don't go his way, ask for a mulligan under the laws of a different jurisdiction." Lott, 556 F.3d at 568. The opposite is true: "[w]hen the parties agree on the substantive law that should govern, 'we may hold the parties to their plausible choice of law.' " Lluberes v. Uncommon Prods.,LLC, 663 F.3d 6, 23 (1st Cir. 2011) (quoting Perry v. Blum, 629 F.3d 1, 8 (1st Cir. 2010) ).
To be sure, in the memorandum of law that accompanied his objections to the magistrate judge's R&R, the appellant couched his arguments in terms of Texas collateral estoppel law. But this was little more than an attempt to lock the barn door after the horses had galloped away. A party cannot successfully urge a magistrate judge to apply a particular body of law and then, dissatisfied with the outcome that he invited, ask the district court to apply some other body of law. See Robb Evans & Assocs., 850 F.3d at 35, ("[T]he law is settled that a litigant must put its best foot forward before a magistrate judge, and cannot introduce new arguments for the first time on the district court's review of the magistrate judge's ruling or recommendation."). "[I]t would be fundamentally unfair to permit a litigant to set its case in motion before the magistrate, wait to see which way the wind was blowing, and - having received an unfavorable recommendation - shift gears before the district judge." Paterson-Leitch Co. v. Mass. Mun. Wholesale Elec. Co., 840 F.2d 985, 991 (1st Cir. 1988).
To say more on this point would be to paint the lily. Since the appellant has waived any argument for an alternative choice of law, we conclude that Rhode Island collateral estoppel principles must be applied here. To hold otherwise would be to sanction the use of misdirection as a tool for subsequent appellate advocacy. See id. ("[A party cannot] feint and weave at the initial hearing, and save its knockout punch for the second round.").
Under Rhode Island law, the doctrine of collateral estoppel provides that an issue "that has been actually litigated and determined cannot be re-litigated between the same parties or their privies in future proceedings." Commercial Union Ins. Co. v. Pelchat, 727 A.2d 676, 680 (R.I. 1999). "Subject to situations in which application of the doctrine would lead to inequitable results," Foster-Glocester Reg'l Sch. Comm. v. Bd. of Review, 854 A.2d 1008, 1014 (R.I. 2004), collateral estoppel under Rhode Island law requires that there is an identity of issues; that the prior proceeding resulted in a final judgment on the merits; and that the party against whom collateral estoppel is asserted is the same as or in privity with a party from that proceeding, see E.W. Audet & Sons, Inc. v. Fireman's Fund Ins. Co., 635 A.2d 1181, 1186 (R.I. 1994). The district court found that this case fit comfortably within the Rhode Island collateral estoppel framework: there was a sufficient identity of issues; the arbitral decision, though unconfirmed, was a final judgment warranting preclusive effect; the appellant was in privity with JLF and, therefore, was bound by the arbitral decision; and application of the doctrine would not lead to any inequitable results. See Patton I, 2018 WL 3655785, at *1-9.
In his briefs before this court, the appellant does not challenge the correctness of the district court's application of Rhode *838Island collateral estoppel principles. Rather, the appellant makes a more limited argument, submitting only that Texas collateral estoppel law should be applied. He does not argue at all that the court below misapplied Rhode Island collateral estoppel law.
"It is axiomatic that arguments not developed on appeal are abandoned." Soto-Cintrón v. United States, 901 F.3d 29, 32 n.3 (1st Cir. 2018) (citing United States v. Zannino, 895 F.2d 1, 17 (1st Cir. 1990) ); see Rivera-Gomez v. de Castro, 843 F.2d 631, 635 (1st Cir. 1988) (explaining that "a litigant has an obligation 'to spell out its arguments squarely and distinctly' or else forever hold its peace" (quoting Paterson-Leitch, 840 F.2d at 990 ) ). It follows inexorably, as night follows day, that the appellant has waived any claim of error regarding the magistrate judge's analysis under Rhode Island collateral estoppel law. Accordingly, the denial of the appellant's motion to compel arbitration must stand.
III. CONCLUSION
We need go no further. For the reasons elucidated above, the judgment of the district court is affirmed, and the case is remanded for further proceedings consistent with this opinion.