
636 F.3d 305 (2011)
Osyp FIRISHCHAK, Petitioner,
v.
Eric H. HOLDER, Jr., Attorney General of the United States, Respondent.
No. 09-2238.
United States Court of Appeals, Seventh Circuit.
Argued October 20, 2010.
Decided February 14, 2011.
Rehearing and Rehearing En Banc Denied April 12, 2011.
*306 James Maher, III (argued), Chicago, IL, for Petitioner.
William H. Kenety (argued), OIL, Department of Justice, Washington, DC, for Respondent.
Before FLAUM, RIPPLE, and EVANS, Circuit Judges.
FLAUM, Circuit Judge.
Osyp Firishchak hid an ignominious past when he came to the United States in the wake of World War II. He represented to U.S. officials that his wartime activities comprised working on a Ukrainian cooperative. In fact, he served in the Ukrainian Auxiliary Police ("UAP"), an organization whose activities included aiding Nazis by forcibly rounding up Jews for deportation to concentration camps.
In 2005, a district court concluded that Firishchak lied to enter the country and obtain naturalization. The sanction was severe: Firishchak was stripped of his citizenship. We affirmed, United States v. Firishchak, 468 F.3d 1015 (7th Cir.2006) ("Firishchak II"), and this appeal concerns the fallout. The government initiated *307 removal proceedings. An Immigration Judge ("IJ") applied the doctrine of collateral estoppel, ruling that the findings in the 2005 case at once barred re-litigation of the underlying issues and dictated Firishchak's ouster from the country. The Board of Immigration Appeals ("BIA") agreed that collateral estoppel was both appropriate and appropriately applied. Firishchak has now filed a petition for review with us. For the reasons stated below, we deny the petition.

I. Background
We need not say much more than we have before about the underlying facts. See Parklane Hosiery Co., Inc. v. Shore, 439 U.S. 322, 326, 99 S.Ct. 645, 58 L.Ed.2d 552 (1979) (collateral estoppel serves the twin purposes of protecting litigants from re-litigating identical issues and protecting courts from re-deciding them). Most of what we need can be drawn from the district court's denaturalization decision, following a bench trial, in United States v. Firishchak, 426 F.Supp.2d 780 (N.D.Ill. 2005) ("Firishchak I"), aff'd 468 F.3d 1015 (7th Cir.2006).
In 1949, Firishchak filed an application for a visa under the Displaced Persons Act. See 62 Stat. 1009-14 (1948) ("DPA" or "Act"). The DPA created the Displaced Persons Commission. Under the Act, an "eligible displaced person" (generally a victim of, or one who fled, Nazi persecution) could obtain permanent residence in the United States. When Firishchak filed his application with the Commission, he indicated that, between 1941 and 1944, he was working on a Ukrainian cooperative. He procured a visa and, in 1954, was naturalized as an American citizen.
Firishchak's actual wartime activities varied markedly from his post-war representations. In fact, he spent several years working for the UAP in a city called L'viv. (The city lies in modern-day Ukraine, but was part of Poland at the beginning of World War II.) The UAP was a Nazi-controlled armed force that persecuted Jews during the war. The work included confining Jews to a ghetto near L'viv, forcibly removing Jews from the ghetto so they could be relocated to concentration camps, and arresting Jews who lacked proper paperwork or who failed to wear Star of David armbands. The UAP's members, playing their part in a particularly infamous round-up of Jews known as the "Great Operation," shot and killed Jews who resisted, fled, or attempted to hide.
Firishchak maintained during the proceedings in Firishchak I, as he does now, that he was not involved with the UAP. But considerable evidence indicated that he was lying, and the district court made unvarnished findings to that effect. The lie had consequences: the DPA's mechanism for obtaining permanent residence was extended only to "eligible displaced persons"a term that included victims of Nazi persecution, but left out oppressors as well as those who "willfully make a misrepresentation for the purpose of gaining admission into the United States." 62 Stat. at 1013.
Firishchak's lie poisoned his subsequent procurement of citizenship because the Immigration and Nationality Act ("INA") requires, as a prerequisite to nationalization, five years of continuous residence in the United States "after being lawfully admitted for permanent residence." 8 U.S.C. § 1427(a) (emphasis added). And the INA further provides that procuring citizenship "by concealment of a material fact or by willful misrepresentation" is a ground for revoking citizenship. 8 U.S.C. § 1451(a). Thus, by lying to obtain permanent resident status, Firishchak planted the seed for the revocation of his subsequently obtained *308 citizenship. See Fedorenko v. United States, 449 U.S. 490, 514, 101 S.Ct. 737, 66 L.Ed.2d 686 (1981) (concealment of war-time activities to obtain a visa under the DPA is grounds for revoking citizenship); United States v. Tittjung, 235 F.3d 330, 336 (7th Cir.2000) (a certificate of naturalization does not act as a blank slate where a visa was unlawfully obtained under the DPA). In addition, stripping Firishchak's citizenship was appropriate for two distinct though intertwined reasons the UAP was a movement hostile to the United States under the DPA, and the UAP assisted in Nazi persecution. Firishchak II, 468 F.3d at 1024-25.
After we, in Firishchak II, affirmed the district court's decision, the government initiated removal proceedings. Removal was sought on the same grounds as the district court had relied on in revoking Firishchak's citizenship. See 8 U.S.C. § 1227(a)(1)(A) (an alien inadmissible at time of entry is deportable); id. § 1182(a)(3)(E)(i) (participants in Nazi persecution are ineligible for visas or entry); id. § 1227(a)(4)(D) (an alien who participated in Nazi persecution is deportable). The IJ ruled that the district court's denaturalization proceeding in Firishchak I was entitled to preclusive effect, concluding that all of the elements to establish removability were "fully litigated and necessarily decided" in the prior proceeding. Therefore, the IJ ordered that Firishchak be removed to the Ukraine. The BIA dismissed Firishchak's appeal, after which he filed a petition for review with us.

II. Discussion
Under the doctrine of collateral estoppel, also referred to as issue preclusion, "once an issue is actually and necessarily determined by a court of competent jurisdiction, that determination is conclusive in subsequent suits based on a different cause of action involving a party to the prior litigation." Montana v. United States, 440 U.S. 147, 153, 99 S.Ct. 970, 59 L.Ed.2d 210 (1979); see also Bobby v. Bies, ___ U.S. ___, 129 S.Ct. 2145, 2152, 173 L.Ed.2d 1173 (2009); Taylor v. Sturgell, 553 U.S. 880, 891, 128 S.Ct. 2161, 171 L.Ed.2d 155 (2008) (the preclusive effect of a prior federal court decision is a matter of federal common law). The organizing principle is that courts should respect "the first actual decision of a matter that has been actually litigated." 18 Wright, Miller & Cooper, FEDERAL PRACTICE AND PROCEDURE § 4416, at 386 (2d ed. 2002).
When the requirements for collateral estoppel[1] are met, we have held that it is proper to give preclusive effect to a denaturalization proceeding in a subsequent removal proceeding. Tittjung v. Reno, 199 F.3d 393, 397 n. 2 (7th Cir.1999) (applying collateral estoppel in this context is well established); Kairys v. I.N.S., 981 F.2d 937, 939 (7th Cir.1992) ("[T]he existence of principles that limit the scope of a doctrine does not make its application discretionary...."); Schellong v. I.N.S., 805 F.2d 655, 658-59 (7th Cir.1986) (noting the variety of contexts in which collateral estoppel has been appropriately applied and *309 concluding that the doctrine should apply to removal proceedings so long as "the doctrine's application will not be unjust").
Firishchak argues that collateral estoppel should not bar relitigation of the issues in his removal proceeding because he did not receive a full and fair opportunity to litigate in Firishchak I.[2] The ground is theoretically sound. "Redetermination of issues is warranted if there is reason to doubt the quality, extensiveness, or fairness of procedures followed in prior litigation." Montana, 440 U.S. at 164 n. 11, 99 S.Ct. 970; RESTATEMENT (SECOND) OF JUDGMENTS § 28(3) & comment d (1982). Specifically, Firishchak argues that he did not receive a full and fair opportunity to litigate because the judge in the denaturalization case (and the IJ) were not randomly assigned; because the judge in the denaturalization case acted more like a litigant than a judge; and because the judge in the denaturalization case incorrectly concluded that the government met its burden of proof. We take up each argument in turn.

A. Random Assignment
Firishchak maintains that the judges who have heard his casethe IJ in the removal proceeding and the district court in Firishchak Iwere not randomly assigned. The non-random assignment, Firishchak intimates, deprived him of due process. Factual and legal problems hamstring the argument. First, Firishchak offers no reason to doubt that the judge in the denaturalization casethe case we focus on, as that is the case whose collateral-estoppel effect we considerwas randomly assigned. Instead, he offers only the possibility, as an epistemological matter, that the Northern District of Illinois might have abandoned its standard, decades-long randomized case assignment system. Without a reason to be suspicious, the argument fails on its own terms. See N.D. Ill. Local Rule 40.1(a) (random case assignment, with exceptions spelled out in the local rules). Although a party asserting collateral estoppel bears the burden of establishing that the earlier opportunity to litigate was full and fair, Kulavic v. Chicago & Ill. Midland Ry. Co., 1 F.3d 507, 517 n. 6 (7th Cir.1993), that does not mean that the estoppel proponent must preemptively address every way in which a proceeding could hypothetically have been rendered unfair. The government did not have to show that the judge was randomly assigned any more than it had to establish that the president's nomination of the judge had been confirmed by the Senate. See also Nguyen v. United States, 539 U.S. 69, 80-82, 123 S.Ct. 2130, 156 L.Ed.2d 64 (2003) (vacating the judgment of an improperly constituted court).
Of course, the inadequate legal basis for Firishchak's argument is just as important as the missing factual underpinnings. A non-randomly assigned judge, without more, simply does not make for a due process violation, and Firishchak does not explain why the analysis should work differently in the context of collateral estoppel. The Fifth Amendment's due process clause guarantees the right to an impartial decisionmaker, e.g., Concrete Pipe & Prods. of Cal., Inc. v. Constr. Laborers Pension Trust for S. Cal., 508 *310 U.S. 602, 617, 113 S.Ct. 2264, 124 L.Ed.2d 539 (1993), but not to a particular judge, United States v. Braasch, 505 F.2d 139, 147 (7th Cir.1974). And in United States v. Keane, 522 F.2d 534, 557 (7th Cir.1975), we adopted the reasoning of a district court which ruled that an individual does not have a due-process right to a randomly assigned judge. See United States v. Keane, 375 F.Supp. 1201, 1204 (N.D.Ill. 1974). In Tyson v. Trigg, 50 F.3d 436, 439-42 (7th Cir.1995), we upheld the constitutionality of a case assignment system that permitted prosecutors to play an active role in selecting trial judges, although we described the system as "unsightly." Other courts to have considered the question agree that due process does not demand random assignment of judges. Cruz v. Abbate, 812 F.2d 571, 574 (9th Cir.1987) (assignments need not be random and can be made for any reason, so long as it is not made in a biased manner "or [with] the desire to influence the outcome of the proceedings"); United States v. Osum, 943 F.2d 1394, 1400-1401 & n. 3 (5th Cir.1991) (suggesting that no enforceable right prevents a court from ignoring local rules in an effort to steer a case to a given judge); see also 28 U.S.C. § 137 (leaving it to individual courts to determine how they divide their business); 28 U.S.C. § 1407(a), (b) (assignment to particular judges by the panel on multidistrict litigation); Bd. of Sch. Dirs. of the City of Milwaukee v. State of Wisconsin, 102 F.R.D. 596, 598 (E.D.Wis.1984) (related pending cases may be transferred to a single judge); United States v. Isaacs, 493 F.2d 1124, 1168 (7th Cir.1974) (panel of non-Seventh Circuit judges constituted by the Chief Justice of the United States after mass recusal).
In sum, there is nothing in the assignment of the judge in this case, factually or legally, indicating that Firishchak was deprived of due process. The parties do not suggest another basis, different from the constitutional standards, for concluding that non-random assignment necessarily bars the application of collateral estoppel.[3]

B. Lack of Impartiality
Firishchak next suggests that he did not receive a full and fair opportunity to litigate because the judge's opinion reveals a lack of impartiality. Although he cites no legal authority, the argument is on sounder legal footing than his non-random-assignment argument. E.g., Edwards v. Balisok, 520 U.S. 641, 647, 117 S.Ct. 1584, 137 L.Ed.2d 906 (1997) (suppression of evidence of innocence by prison hearing officer violates due process). A biased judge would give us reason to doubt the fairness of the earlier proceeding, cf. Castilho de Oliveira v. Holder, 564 F.3d 892, 899-900 & n. 4 (7th Cir.2009) (asylum applicant was denied a meaningful opportunity to be heard, under the regulatory scheme, based on "the tone of the IJ's cross-examination," as well as its frequent interruptions, inappropriate questions and comments, and failure to engage with the record evidence), which might make the application of collateral estoppel improper.
The argument, however, founders on the merits. According to Firishchak, the district court's memorandum opinion, following a bench trial, "reads like the closing argument of a criminal prosecutor." We disagree. Firishchak highlights the district court's conclusion that the former "lied on the stand" as revealed by his demeanor and mannerisms. That was a *311 finding, more descriptive than reproachful, and does not approach the sort of abusive language that would give us pause.[4]Compare Liteky v. United States, 510 U.S. 540, 555-56, 114 S.Ct. 1147, 127 L.Ed.2d 474 (1994) ("[J]udicial remarks during the course of a trial that are critical or disapproving of, or even hostile to, counsel, the parties, or their cases, ordinarily do not support a bias or partiality challenge."), with Berger v. United States, 255 U.S. 22, 29, 41 S.Ct. 230, 65 L.Ed. 481 (1921) (trial judge said of German-Americans, "Your hearts are reeking with disloyalty"); see also In re United States, 614 F.3d 661, 666 (7th Cir.2010) (record revealed "unreasonable fury" toward government lawyers); Castilho de Oliveira, 564 F.3d at 899-900 & n. 4; United States v. Giorgi, 840 F.2d 1022, 1035 (1st Cir.1988) (to establish partiality, a litigant must do more than point to the mere fact of an adverse ruling or credibility determination). In this case, we do not agree that the language used by the judge evinces partiality. Here, while giving comprehensive and thoughtful treatment to the evidence and arguments, the court used stern language. Liteky, 510 U.S. at 555, 114 S.Ct. 1147. It is not a case in which the use of inflammatory language saps us of confidence that a party received a fair shake. See United States v. Figueroa, 622 F.3d 739, 743-44 (7th Cir.2010) (remanding a case for resentencing where a "litany of inflammatory remarks undermined anything else that the court said during the hearing").
Firishchak also complains that the district court used the word "we" when it was speaking for itselfe.g., "we find that he was a member of the UAP." Firishchak I, 426 F.Supp.2d at 784 (emphasis added). Apparently the suggestion is that the district court tipped its hand that it was allied with the government. To be sure, the practice of using the word "we" when writing in the first-person singulara nosism commonly referred to as the "royal we" is on the wane. THE NEW FOWLER'S MODERN ENGLISH USAGE 835 (R.W. Burchfield ed., 3d ed. 1996); H.W. Fowler, A DICTIONARY OF MODERN ENGLISH USAGE 689 (2d ed. 1965) (noting that we may mean "this newspaper, or this nation, or several other things" but discouraging its use where "collective anonymity ... is out of place"). Some view the practice by district judges critically. See Federal Judicial Center, JUDICIAL WRITING MANUAL 22 (1991) (characterizing the convention as "pompous"); but see THE CHICAGO MANUAL OF STYLE § 5.51, at 160 (15th ed. 2003) (suggesting that the practice may "draw in the reader" by making the prose less personal). There is, in any event, no prohibition against the royal we and its use does not support Firishchak's suggestion that the district court treated him unfairly.
Other evidence of partiality can be dispensed with quickly. Firishchak contends that the district court interrupted one witness's examination 19 times. He failed to include examples, either in an appendix as *312 the rules require, see FRAP 30(a); Cir. R. 30(a),(b), or even in citations to the voluminous, 727-page administrative record that the government filed. The matter has been waived, as we decline to further comb the record. Consolidation Coal Co. v. Dir., Office of Workers' Comp. Programs, 294 F.3d 885, 895-96 (7th Cir.2002) (waiver of matter as to which the record was devoid of underlying documentation); Linrud v. Linrud, 552 N.W.2d 342, 345 (N.D. 1996) ("Judges are not ferrets."). Arguments related to other incidents, such as the allegation that the judge actively assisted the government in admitting evidence, have been waived for the same reason. Finally, Firishchak re-raises some objections that we reviewed and rejected in Firishchak II; these arguments have not gained merit with time, and we need not discuss them further.

C. Evidence and Findings in Firishchak I

Firishchak argues at length that the evidence in the denaturalization case was insufficient and that the district court ignored the applicable burden of proof. As Firishchak's brief maintains, "This case was always and still is all about the gross insufficiency of the evidence under the applicable burden of proof." We respectfully disagree: Firishchak's argument amounts to a contention that collateral estoppel should not apply because the first case was wrongly decided. The possibility that a prior action could result in the wrong outcome is a reason, as a matter of first principles, why one may not want courts to recognize the doctrine at all. Wright, Miller, & Cooper, supra, § 4416, at 398 (noting that the "dangers of issue preclusion are as apparent as its virtues"). Yet, whenever principles compete with one anotherfairness versus finality, certainty versus economythere are no right answers, only better ones. Courts recognize and apply collateral estoppel; Firishchak's efforts to relitigate the merits of the denaturalization case is precisely what the doctrine prevents.

III. Conclusion
The bookends of Osyp Firishchak's life have involved deportation, on different sides of the Atlantic Ocean, on different sides of the process, and by profoundly different means. When the government learned that Firishchak had been allowed to enjoy the benefits of American citizenship only as a result of a lie, our laws and justice system afforded him both the benefit of the doubt and a fair opportunity to be heard. The contention that he was denied a full and fair opportunity to litigate in the denaturalization case is not supported by the record. Therefore, collateral estoppel in the removal proceeding was both appropriate and appropriately applied. His petition for review is DENIED.
NOTES
[1]  Formulations vary, but for our purposes five conditions must be present for collateral estoppel to apply to a given issue: (1) Firishchak must have been afforded a full and fair opportunity to litigate in the denaturalization case; (2) the issue in the denaturalization case and in the removal proceeding had to have been identical; (3) the contested issue in the removal case must have been the same as, and necessarily decided in, the denaturalization case; (4) the issue must have been necessary to the judgment in the denaturalization case; and (5) Firishchak must have been a party in the denaturalization case. Schellong v. I.N.S., 805 F.2d 655, 658 (7th Cir.1986). Almost all of Firishchak's arguments relate to the first requirementa full and fair opportunity to litigate.
[2]  Firishchak makes an additional argument that collateral estoppel is inappropriate because the issues in the denaturalization case and the removal proceeding were not the same, because there was no finding that Firishchak misrepresented facts in the earlier proceeding. The argument, however, is waived because it was not advanced in his opening brief. United States v. Lupton, 620 F.3d 790, 807 (7th Cir.2010). In any event, the district court specifically determined in the denaturalization case that Firishchak had misrepresented facts, not just omitted them on the visa application.
[3]  Firishchak's additional argument that collateral estoppel is inappropriate because the IJ was not randomly assigned is a non sequitur, at least as he has presented the matter: we are deciding whether to give preclusive effect to the denaturalization case, not the removal proceeding, and our review of the former is de novo.
[4]  The same conclusion applies to Firishchak's argument that the district court adopted portions of the government's proposed findings verbatim. Firishchak does not say how much was adopted or provide citations, so the argument is waived, but the district court's engagement with the evidence in Firishchak I indicates that the argument lacks merit. See Anderson v. City of Bessemer City, N.C., 470 U.S. 564, 572-73, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985) (concluding that there was no reason to "doubt that the findings issued by the District Court represent the judge's own considered conclusions" where adoption of one side's findings was not "uncritical[ ]"); Metavante Corp. v. Emigrant Sav. Bank, 619 F.3d 748, 759 (7th Cir.2010) (district court gave "adequate" treatment to the case where record indicated that "the court read the findings that it adopted and carefully considered them").
