Opinion for the Court filed by Circuit Judge HENDERSON.
Opinion concurring in the judgment filed by Circuit Judge ROGERS.
KAREN LeCRAFT HENDERSON, Circuit Judge:The Patent and Trademark Office of the United States Department of Commerce (PTO or Agency) seeks review of a decision of the Federal Labor Relations Authority (FLRA or Authority) upholding an arbitrator’s award in favor of the Patent Office Professional Association (POPA or Union). U.S. Dep’t of Commerce Patent & Trademark Office, 65 F.L.R.A. 290 (2010) (PTO II). The arbitrator concluded PTO committed an unfair labor practice in violation of the Federal Service Labor-Management Relations Statute (FSLMRS or Statute), 5 U.S.C. § 7116(a)(1) and (5), when it repudiated a provision in an agreement requiring that it make an annual request of the Office of Personnel Management (OPM) to increase PTO’s special schedule pay rates and, if OPM refuses, to discuss “substantially equivalent alternatives” with POPA. Arbitration Decision in re Patent Office Prof'l Ass’n v. U.S. Dep’t of Commerce, Patent & Trademark Office, FMCS Case No. 04-01463-3 (Arbitral Award of Arbitrator Arrigo) (July 25, 2006) (Award II). In particular, PTO challenges the Authority’s determination that the provision constitutes an “appropriate arrangement” under 5 U.S.C. § 7106(b)(3). We grant PTO’s petition on the ground that, under the collateral estoppel doctrine, the Authority was bound by *1097its earlier decision concluding the provision did not constitute an appropriate arrangement. See U.S. Dep’t of Commerce, Patent & Trademark Office, 60 F.L.R.A. 839 (2005) (PTO I), pet. for review dismissed, Patent Office Prof'l Ass’n v. FLRA, 180 Fed.Appx. 176 (D.C.Cir.2006).
I.
In 2000, PTO patent examiners’ wages, like those of most executive branch employees, were determined pursuant to the General Schedule (GS). Because it was experiencing problems recruiting and retaining employees, PTO requested and obtained OPM approval to pay employees special pay rates exceeding the comparable GS rates by ten or fifteen per cent, depending on the grade. Over time, however, special rates decrease in value relative to the corresponding GS rates because, while both rates receive annual general increases, only the latter include annual locality increases. Accordingly, PTO and POPA negotiated the following provision in an agreement effective January 2001:
The [PTO] shall request OPM approval for the next five years to increase the special pay schedule so as to maintain the 10% and 15% salary differentials relative to the updated GS rates, in a manner consistent with OPM regulations. If OPM refuses the request, the Agency shall enter into discussions with POPA in order to provide substantially equivalent alternatives.
Agreement on Initiatives for a New Millennium between [PTO and POPA], § A.2 (JA 69) (Millennium Agreement).
In 2002, federal employees in the Washington, D.C. region received a 3.6% general wage increase and a 1.17% locality pay increase. Pursuant to section A.2 of the Millennium Agreement, in February 2002, PTO requested that OPM increase the special pay rate by 1.17% to maintain the ten and fifteen per cent differentials, subsequently lowering the request to 1%. OPM denied PTO’s request on the ground PTO’s filings did not show it was “experiencing or ... likely to experience significant handicaps in recruiting or retaining patent professionals.” Award II at 11 (internal quotations omitted). OPM recommended that PTO explore “the strategic use of other compensation flexibilities to address targeted recruitment and retention problems.” Id. Accordingly, PTO entered into discussions with the Union regarding “substantially equivalent alternatives” pursuant to the second sentence of section A.2. When the discussions proved fruitless, the Union filed a grievance, which was then submitted to arbitration.
The arbitrator concluded that PTO had violated section A.2 of the Millennium Agreement and ordered it to “engage in ... discussions [with POPA] in good faith with a sincere resolve to find a way to make-up for the lost locality pay.” In re Arbitration Between Patent & Trademark Office & Patent Office Prof l Ass’n, FMCS Case No. 04-00138 at 16 (Oct. 1, 2001) (Arbitral Award of Arbitrator Evans) (Award I). In his order, Arbitrator Evans “found that Section A.2 was intended to address the adverse effect of special rate erosion that would occur over time as non-special rate employees received locality pay increases.” PTO I, 60 F.L.R.A. at 842 (citing Award I at 12).
On review, the Authority set aside the arbitral award as violating section 7106 of the FSLMRS. The Statute generally imposes on a federal agency a duty to bargain in good faith with a public employee union over conditions of employment but section 7106(a) exempts from the duty certain “management rights,” including the right to retain its employees. See U.S. Dep’t of the Treasury v. FLRA 670 F.3d *10981315, 1317 (D.C.Cir.2012); 5 U.S.C. § 7106(a)(2)(A). Nonetheless, an agency must bargain over a proposal — including one that affects a management right — if the proposal constitutes an “ ‘appropriate arrangement! ] for employees adversely affected’ by the exercise of management rights.” Nat’l Ass’n of Gov’t Emps., Inc. v. FLRA 179 F.3d 946, 948 (D.C.Cir.1999) (quoting 5 U.S.C. § 7106(b)(3)). In PTO I, the Authority concluded section A.2 affected PTO’s management right to retain employees and was not an “appropriate arrangement” within the meaning of 5 U.S.C. § 7106(b)(3) because, “as interpreted and enforced by the Arbitrator,” it sought to “ameliorate!] adverse effects” that result not from the exercise of a management right but from “the operation of law, specifically, the fact that under 5 C.F.R. § 531.606, special rate employees are not permitted to receive locality pay adjustments.” 60 F.L.R.A. at 842. Thus, the Authority concluded section A.2 was not a statutory “arrangement” at all and set aside the arbitral award as “contrary to management’s right to retain employees under § 7106(a)(2)(A).” Id. at 842, 843. In making this determination, the Authority specifically rejected as “unsupported” POPA’s claim that section A.2 was intended as an arrangement for employees adversely affected by PTO’s decision “to eliminate paper files and to include a customer service element in the performance plans.”1
In 2003, the locality pay rate for the Washington, D.C. region again increased by 1.17%. PTO determined it could not certify to OPM that a special pay rate increase was “critical to the mission of the Agency” and, accordingly, notified POPA it would not submit a request that OPM increase the rate. PTO II, 65 F.L.R.A. at 291. POPA again filed a grievance, which was again submitted to arbitration.
Arbitrator Arrigo found section A.2 affected the Agency’s management right to retain employees because “ ‘the essential facts and circumstances’ ” were “ ‘substantially identical’ ” to PTO I. Id. at 292 (quoting Award II at 24). He further concluded that section A.2 was an “appropriate arrangement” because “ ‘the entirety of [§] A,’ including § A.2, ‘was negotiated as a quid pro quo for the elimination of paper patents and the addition of customer service duties for employees!,]’ two changes desired by the Agency and opposed by the Union.” Id. (quoting Award II at 24) (alteration in original). Arbitrator Arrigo specifically found that “the linkage between a special pay schedule and the paper file and customer service issues was established ‘in every document concerning the discussions between the parties,’ ” id. (quoting Award II at 25), and the special pay rate provisions were “a ‘balm’ to ‘ameliorate the adverse effects upon employees for the Union’s acceding to the Agency’s desire to exercise its management rights regarding the elimination of paper files ... and employees being assigned additional duties’ and were enforceable as appropriate arrangements under § 7106(b)(3).” Id. (quoting Award II at 25-26). He further determined PTO’s breach of both sentences of section A.2 — by declining to submit a request to OPM, then failing to enter *1099discussions with POPA — ‘“went to the heart of the parties’ agreement’ ” because it was a “ ‘critical part’ of § A, which was, in turn, necessary to [POPA’s] acceptance of the rest of the [Millennium Agreement].” Id. (quoting Award II at 27). Accordingly, Arbitrator Arrigo concluded PTO repudiated the agreement in violation of 5 U.S.C. § 7116(a)(1) and (5).2 He decided that “the appropriate remedy was to ‘require the Agency to fulfill its obligations under the agreement and to “enter discussions with [the Union] in order to provide substantially equivalent alternatives” to the erosion of the agreed-upon pay differentials set forth in the agreement,’ ” to include “interest ‘on any money the employees might receive pursuant to the discussions envisioned in [§] A.2.’ ” Id. at 292-93 (quoting Award II at 29-30 (quoting § A.2)).
PTO excepted to the award and the FLRA sustained it. The FLRA first upheld Arbitrator Arrigo’s unchallenged finding that section A.2 affected management’s right to retain employees. The Authority further affirmed his determination that section A.2 was an arrangement, relying on his finding “that the entire subject of special pay was negotiated ‘to provide a “balm” to the Union which would ameliorate the adverse effects upon employees’ of ‘the Agency’s desire to exercise its management rights regarding the elimination of paper files.’ ” 65 F.L.R.A. at 295 (quoting Award II at 25-26). Finally, the Authority considered whether the arrangement was “appropriate” under the “abrogation” standard, which it recently re-adopted in U.S. Environmental Protection Agency, 65 F.L.R.A. 113 (2010) (U.S. EPA)3 Under the abrogation standard, the Authority assesses “whether the arbitration award ‘precludes [the] agency from exercising’ the affected management right” — if it does not, the Authority will “find that the arrangement is appropriate within the meaning of § 7106(b)(3).” PTO II, 65 F.L.R.A. at 296 (quoting Dep’t of the Treasury, U.S. Customs Serv., 37 F.L.R.A. 309, 314 (1990)) (alteration in PTO II). In PTO II, the Authority decided section A.2 satisfied the standard because PTO “provided no basis for finding that the award precludes the Agency from exercising its right to retain employees.” Id. at 296. Having approved section A.2, the Authority upheld Arbitrator Arrigo’s finding that PTO repudiated the first sentence of section A.2 in failing to submit a request to OPM and thereby committed an unfair labor practice in violation of 7116(a)(1) and (5) of the Statute. Asserting that Arbitrator Arrigo’s “finding of repudiation of the first sentence of § A.2 provides a separate and independent basis for his finding of a violation of § 7116(a)(1) and (5),” the Authority found it “unnecessary to determine whether the Arbitrator erroneously found a repudiation of the sec*1100ond sentence of § A.2.” 65 F.L.R.A. at 297. PTO filed a timely notice of appeal.
II.
PTO contends, inter alia, that collateral estoppel precluded the Authority from finding section A.2 constituted an “arrangement.” We agree.4
Under FLRA precedent, collateral estoppel, or issue preclusion, requires a showing of five elements:
Before the doctrine of collateral estoppel can be applied, it must be demonstrated that: (1) the same issue was involved in both cases; (2) that issue was litigated in the first case; (3) resolving it was necessary to the decision in the first case; (4) the decision in the first case, on the issue to be precluded, was final; and (5) the party attempting to raise the issue in the second case was fully represented in the first case.
U.S. Dep’t of Energy W. Area Power Admin., Golden, Colo., 56 F.L.R.A. 9, 11 (2000) (citing U.S. Dep’t of the Air Force, Scott Air Force Base, III, 35 F.L.R.A. 978, 982 (1990)). If all five elements are met, the Authority is bound by its findings in the earlier case. See Scott Air Force Base, 35 F.L.R.A. at 981. All five are met here.
Regarding the first and second elements, in each proceeding the parties litigated the issue whether section A.2 constituted an appropriate arrangement or, more fundamentally, whether it constituted an arrangement at all. In Award I, Arbitrator Evans “found that Section A.2 was intended to address the adverse effect of special rate erosion that would occur over time as non-special rate employees received locality pay increases.” PTO I, 60 F.L.R.A. at 842 (citing Award I at 12). The Authority upheld this finding of intent but concluded that section A.2 was not— indeed, could not — be an “arrangement” within the meaning of section 7106(b)(3) because it “ameliorate[d] adverse effects that result from the operation of law, not the exercise of a management right.” Id.
In Award II, Arbitrator Arrigo addressed the same issue, reaching a contrary conclusion. Recognizing that “ ‘the essential facts and circumstances’ in the case before him were ‘substantially identical’ to those found by the Authority in PTO I,” he therefore “found, in accordance with that decision, that § A.2 of the [Millennium Agreement] affected management’s right to retain employees.” PTO II, 65 F.L.R.A. at 292 (quoting Award II at 24-25). He nonetheless found that section A.2 was indeed an arrangement because “ ‘the entirety of [§] A,’ including § A.2, ‘was negotiated as a quid pro quo for the elimination of paper patents and the addition of customer service duties for employees’[ — ]two changes desired by the Agency and opposed by the Union.” Id. (quoting Award II at 24) (bracketed material deleted).5 In PTO II, the Authority upheld this determination notwithstanding it had rejected the very same finding in PTO I “as unsupported.” 60 F.L.R.A. at *1101842-43. In short, despite contrary outcomes, the two FLRA decisions involved the same issue — namely, whether section A.2 constitutes an (appropriate) arrangement.
The FLRA contends the two cases did not involve the same issue because they involved different arbitrators interpreting section A.2 in different awards under different circumstances. According to the Authority, one arbitrator’s interpretation of a contract provision should not be binding on a subsequent arbitrator’s interpretation in a different proceeding. But it is not Arbitrator Evans’s interpretation in Award I that is binding here — rather, it is the Authority’s legal conclusion in PTO I that section A.2 does not qualify as an appropriate arrangement because it “ameliorates adverse effects that result from the operation of law, not the exercise of a management right.” 60 F.L.R.A. at 842; see Scott Air Force Base, 35 F.L.R.A. at 981 (on exceptions from arbitrator decision, “Authority is bound by its finding” in previous decision reviewing administrative law judge’s unfair labor practice decision); Resp’t’s Br. 21 (“The Authority’s decision in PTO I set aside the First Award as contrary to law....”). The force of the Authority’s conclusion applies no less to the facts in PTO II as to those in PTO I.
The Authority further attempts to distinguish the cases by asserting that PTO I involved a violation of section A.2’s second sentence while PTO II found a breach only of its first sentence only. PTO I, however, made no distinction between the intent behind the first and the second sentences, stating: “Section A.2, as interpreted and enforced by the Arbitrator, ameliorates adverse effects that result from the operation of law, not the exercise of a management right.” 60 F.L.R.A. at 842. Moreover, we do not see how the two intertwined sentences can be viewed in isolation from each other (or assigned different purposes) inasmuch as they operate together, in sequence, to offset the annual pay erosion resulting from “the fact that under 5 C.F.R. § 531.606, special rate employees are not permitted to receive locality pay adjustments,” 60 F.L.R.A. at 842; see also Award I at 12 (“Section A.2 set up a two-track process to deal with the potential of locality pay erosion. The first track is set forth in the first sentence of Section A.2. It requires PTO to submit a request to OPM for a special pay rate adjustment to keep-up with the locality pay awarded in the Washington, DC metropolitan area to GS employees. If that failed, which happened here, the parties ultimately agreed to go down a second track to find an alternative way to make-up for locality pay erosion (for 5 years).”). Thus, the “arrangement” issue was both involved and litigated in each proceeding.6
The third through fifth collateral estoppel elements are plainly satisfied: In PTO I, the resolution of the “arrangement” issue was necessary in order to decide whether section A.2 was an appropriate arrangement so as to be enforceable under section 7106(b)(3) notwithstanding it affected the management right to retain employees; PTO I was a final FLRA decision which was judicially unreviewable, see Patent Office Prof'l Ass’n v. FLRA, 180 Fed.Appx. 176 (D.C.Cir.2006) (dismissing petition for review for lack of jurisdiction because “FLRA decision reviewing an arbitration award is statutorily foreclosed *1102‘unless the order involves an unfair labor practice under section 711[6].’ ” (quoting 5 U.S.C. § 7123(a)(1))); see also Scott Air Force Base, 35 F.L.R.A. at 983 (“[U]nless and until a Federal court of appeals denies enforcement to a decision of the Authority, that decision must be treated as a final adjudicatory action.”); and POPA and PTO were fully represented by counsel throughout each proceeding.
Finally, we reject Intervenor POPA’s claim that the court lacks jurisdiction to address the collateral estoppel claim because PTO failed to raise it before the Authority. See 5 U.S.C. § 7123(c) (“No objection that has not been urged before the Authority, or its designee, shall be considered by the court, unless the failure or neglect to urge the objection is excused because of extraordinary circumstances.”). Unlike our concurring colleague, we do not find it “questionable” whether PTO adequately raised the objection below. See Concurrence at 1103. While it did not use the magic words “collateral estoppel,” PTO nonetheless argued the substance of a collateral estoppel defense in its exceptions to Award II. There, it cited PTO I as “binding Authority precedent,” in which “[t]he Authority has already determined that Section (A)(2) of the Millennium Agreement is not an arrangement” because it “ ‘ameliorates adverse effects that result from the operation of law, not the exercise of a management right.’ ” Agency’s Exceptions to Arbitrator’s Award at 14, PTO II (Aug. 28, 2006) (JA 14) (quoting PTO I, 60 F.L.R.A. at 842). The Authority understood this argument to implicate collateral estoppel. See PTO II, 65 F.L.R.A. at 295 n. 5 (rejecting argument “Arbitrator was collaterally es-topped from finding § A.2 to be an appropriate arrangement” “[t]o the extent that the Agency’s exceptions can be construed as [so] arguing”); id. at 301 (Member Beck, dissenting in part) (“[T]he arbitral proceedings and the Agency’s exceptions are rife with collateral estoppel implications. Both parties and the Arbitrator recognized the implications of the Authority’s prior decision and the Agency addressed the impact of that decision throughout its exceptions.” (internal citations omitted)). We do as well.
For the foregoing reasons, we conclude that POPA was estopped from arguing section A.2 is an appropriate arrangement intended to lessen the adverse effects from the elimination of paper files and addition of customer service duties and that the Authority should have so held.7 Accordingly, we grant PTO’s petition for review.
So ordered.
. According to the FLRA, POPA asserted in PTO I
that elimination of the paper files adversely affects employees by requiring them to spend virtually their entire work day tethered to a computer screen!,] that computer images of patents are inferior to paper copies, that there are problems with conducting key word searches of old patents on computers, and that computer patents do not include examiners’ notes that were in paper patents and which facilitated the patent search for examiners.
60 F.L.R.A. at 842 (quotation marks omitted; brackets in original).
. The two subsections provide:
(a) For the purpose of this chapter, it shall be an unfair labor practice for an agency— (1) to interfere with, restrain, or coerce any employee in the exercise by the employee of any right under this chapter; ... [or]
(5) to refuse to consult or negotiate in good faith with a labor organization as required by this chapter;....
5 U.S.C. § 7116(a)(1), (5).
. Before its decision in U.S. EPA, the Authority reviewed arbitral awards using its “excessive interference standard” under which the enforcement of a contract provision in the award is appropriate unless it "excessively interferes with management's rights.” U.S. Dep’t of Justice, Fed. Bureau of Prisons, 58 F.L.R.A. 109, 111 (2002). In U.S. EPA, the Authority re-adopted the abrogation standard, which it had previously applied to arbitral awards from 1990 until 2002. See Dep't of the Treasury, U.S. Customs Serv., 37 F.L.R.A. 309, 313-14 (1990) (replacing excessive interference standard with abrogation standard); Fed. Bureau of Prisons, supra (reinstating excessive interference standard).
. In light of our disposition, we do not address PTO's alternative grounds for review, including its challenge to the Authority’s adoption of the abrogation standard. See supra p. 1099 note 3 & accompanying text.
. The "entirety” of section A covers the "Uniform Special Pay Schedule,” including the directive in section A.l that PTO submit an initial request for special rates in 2001 as well as the language in section A.2 governing the request procedure for subsequent years. In PTO I, the Authority stated: "Special rates are, by law, a means to ameliorate recruitment and retention problems.” (citing 5 C.F.R. § 530.303(a) ("OPM may increase the minimum rates otherwise payable under the pay schedules ... to the extent it considers necessary to overcome existing or likely significant handicaps in the recruitment or retention of well-qualified personnel____”)). 60 F.L.R.A. at 841.
. POPA argues the appropriate arrangement issue was not "litigated” in the first proceeding, asserting: "In PTO I, Arbitrator Evans did not address the issue of whether the [Millennium Agreement], or any part of it, was intended as an 'appropriate arrangement’ within the meaning of § 7106(b)(3). It simply was not an issue in the first arbitration case.” Intervenor’s Br. 24-25 (emphasis in original). The issue was thoroughly addressed, however, on review before the Authority.
. We see no reason to deviate, as our concurring colleague suggests, from the general rule that "a valid and final adjudicative determination by an administrative tribunal has the same effects under the rules of res judicata, subject to the same exceptions and qualifications, as a judgment of a court.” Restatement (Second) of Judgments § 83(1). It is true that the rules are " 'applied more flexibly to administrative adjudications than to judicial proceedings,'” Concurrence at 1107 (quoting Clark-Cowlitz Joint Operating Agency v. FERC, 826 F.2d 1074, 1080-81 n. 5 (D.C.Cir.1987) (en banc)) — to take into account that "an ambiguous or broadly worded statute may admit of more than one interpretation.” Id. at 1080-81 n. 5 — but the rules nonetheless are applied. And this case involves no administrative peculiarity requiring that they be modified. Nor does this case suffer from the flaw — fatal in Clark-Cowlitz that the party asserting preclusion (a losing power plant license applicant) was not a losing party in the earlier proceeding on which preclusion was premised. Rather, the applicant and the Commission had been "fellow travelers” on the prevailing side of the earlier proceeding. Id. at 1080. Accordingly, the purpose underlying preclusion — which is "meant to provide an affirmative defense that one parly to a prior proceeding may raise against another party that took an adverse position in that proceeding” and "to prevent parties from rearguing issues they have already lost,” id. at 1080 n. 5 — would not have *1103been served. See id. Here, by contrast, the POPA sought to relitigate in PTO II the issue it had lost in PTO I. We thus face the classic issue preclusion scenario.