TACHA, Circuit Judge.
At approximately 3:00 a.m. on July 11, 1995, Defendant Michael Shinault entered a Food-4-Less grocery store in Wichita, Kansas. Armed with a semi-automatic pistol, he robbed the store of $250. About an hour later, the defendant committed a similar armed robbery of a Total gas station, netting about $40. The defendant was charged with two counts of violating the Hobbs Act, 18 U.S.C. § 1951 (interfering with interstate commerce by robbery), two counts of violating 18 U.S.C. § 924(c) (using or carrying a weapon during a crime of violence), and one count of violating 18 U.S.C. § 922(g)(1) (being a felon in possession of a firearm). A jury returned a guilty verdict on all counts. The defendant now appeals his conviction on several grounds, including contentions that the trial violated his constitutional protection against double jeopardy and that underrep-resentation of minority racial groups in the pool from which his jury was drawn violated his Sixth Amendment right to an impartial jury. We exercise jurisdiction under 18 U.S.C. § 1291 and affirm.
The defendant went to trial in the Wiehita-Hutehinson division of the District of Kansas. After voir dire, a jury with no alternates was sworn. At that point, one of the jurors noted that she had child-care responsibilities that would make it difficult for her to serve on the jury. The district court excused that juror and, without objection from either the government or the defense, swore in another juror. The jury found the defendant guilty of all the charged crimes. At the sentencing phase, the district court applied the Armed Career Criminal enhancement to the defendant’s sentence, based on his previous criminal history. The defendant’s term of imprisonment totaled 562 months.
The defendant appeals on the following grounds: (1) that the jury selection procedures in the District of Kansas denied him his Sixth Amendment right to a jury drawn from a fair cross-section of the community; (2) that the unusual jury selection procedure used in this case violated the Double Jeopardy Clause of the Fifth Amendment; (3) that the court’s instructions to the jury regarding his Hobbs Act crimes effectively removed one element of the crime from the jury’s consideration; (4) that the court based the Armed Career Criminal sentence enhancement on insufficient evidence; (5) that Congress did not have the power to enact the Hobbs Act; and (6) that the defendant’s convictions under the Hobbs Act and 18 U.S.C. § 924(c) violated the Double Jeopardy Clause by imposing multiple punishments on the defendant for the same conduct.
I. Jury Composition
The defendant first asserts that the jury selection system in the Wichita-Huteh-inson division of the District of Kansas violates the Sixth Amendment and the Jury Selection and Service Act of 1968, 28 U.S.C. §§ 1861, et seq., because it systematically excludes Asians, Blacks, and Hispanics from jury service. The Sixth Amendment grants criminal defendants the right to trial by an impartial jury. U.S. Const, amend. YI. A jury selection system violates that right if the system does not draw its jury members from a fair cross section of the community. See Taylor v. Louisiana, 419 U.S. 522, 530, 95 S.Ct. 692, 42 L.Ed.2d 690 (1975). Similarly, the Jury Act “ensure[s] that potential grand and petit jurors are selected at random from a representative cross section of the community and that all qualified citizens have the opportunity to be considered for service.” United States v. Bearden, 659 F.2d 590, 593 (5th Cir.1981), quoted in United States v. Contreras, 108 F.3d 1255, 1265 (10th Cir.), cert. denied, — U.S. -, 118 S.Ct. 116, 139 L.Ed.2d 68 (1997). Because the Jury Act’s fair cross section requirement parallels a defendant’s Sixth Amendment right to trial by an impartial jury, the defendant’s Jury Act challenge and his constitutional challenge are both evaluated under the Sixth Amendment standard. See United States v. Test, 550 [1271]*1271F.2d 577, 584-85 (10th Cir.1976) (en banc) (quoting Taylor, 419 U.S. at 528-30 & n. 11, 95 S.Ct. 692).
We review the district court’s factual determinations relevant to the defendant’s Sixth Amendment and Jury Act challenge for clear error, see United States v. Gault, 141 F.3d 1399, 1401 (10th Cir.1998), but we review de novo the court’s legal determination whether a prima facie violation of the fair cross-section requirement has occurred. See United States v. Sanchez-Lopez, 879 F.2d 541, 546 (9th Cir.1989).
The Jury Act requires, as a procedural matter, that a defendant’s motion challenging a district’s jury selection process contain “a sworn statement of facts which, if true, wohld constitute a substantial failure to comply with the [Act].” 28 U.S.C. § 1867(d). The defendant did not file such a sworn statement in this case, though he did file a motion with this court to supplement the record on appeal with such a statement. Even though the Tenth Circuit interprets the sworn statement requirement strictly, see Contreras, 108 F.3d at 1267, in this case, “it is unnecessary to address section 1867, because the merits dispute properly raised, briefed, and argued by the parties, and carefully considered by the district court, presents an unsurmountable barrier for the appellant,” United States v. Pion, 25 F.3d 18, 22 n. 3 (1st Cir.1994), regardless of the impact of Shinault’s alleged procedural shortcomings on either his statutory challenge or his constitutional challenge.
In substance, the Jury Act sets forth guidelines for selecting grand and petit juries in federal courts. See 28 U.S.C. § 1861. It requires that each judicial district devise a plan for randomly selecting jurors based on voter registration rolls or lists of actual voters. See id. § 1863(b)(2). The plan adopted by the District of Kansas provides for the random selection of prospective grand and petit jurors from the official lists of actual voters in each of the counties in -the six divisions in Kansas. See D. Kan. R. 38.1. The names of individuals selected from the actual voter lists are placed on a “Master Jury Wheel” for the division in which the individuals reside.' The clerk of the court draws names as needed from the divisional master wheel and mails a jury qualification form to the selected individuals. The form asks the potential jurors to identify their racial and ethnic background. All individuals who return the forms, are eligible for service, and are not excused from service, are placed on the “Qualified Jury Wheel.” One is ineligible to sit on a jury if he or she is not an American citizen, is not eighteen years old,' has not resided in the judicial district for at least one year, cannot speak or understand English, is physically or mentally incapable of serving, or is a felon. See 28 U.S.C. § 1865(b). Moreover, certain classes of persons, such as active military, personnel, are barred as exempt, and others, such as volunteer safety personnel, will be excused upon request. See id. § 1863(b)(5),(6). Once the qualified wheel has been stocked, jury veni-res are randomly selected from the qualified wheel; The defendant argues that this method of jury selection, particularly reliance on lists of actual voters, systematically excludes Asians, Blacks, and Hispanies from jury service in the Wichita-Hutchinson Division of the District of Kansas.
In order to establish a prima facie case that a jury selection system violates the Sixth Amendment fair cross section requirement, a defendant must demonstrate:
(1) that the group alleged to be excluded is a “distinctive” group in the community; (2) that the representation of this group in venires from which juries are selected is not fair and reasonable in relation to the number of such persons in the community; and (3) that this underrepresentation is due to systematic exclusion of the group in the jury-selection process.
Duren v. Missouri, 439 U.S. 357, 364, 99 S.Ct. 664, 58 L.Ed.2d 579 (1979). If the defendant proves a prima facie violation, the government then bears the burden of proving that attainment of a fair cross section is incompatible with' a significant state interest. See id. at 368, 99 S.Ct. 664.
The defendant identifies three groups that are allegedly unfairly represented in the District of Kansas’s jury system: Asians, Blacks, and Hispanies. The defendant need not belong to any of these groups in order to have standing to object to their exclusion from jury service. See Taylor, 419 U.S. at 526, 95 S.Ct. 692. The government concedes [1272]*1272that Asians, Blacks, and Hispanics are all distinctive groups.
A. Unfair Representation
1. The Relevant Statistics
The second element of the prima facie ease requires the defendant to show that representation of the distinctive groups on jury venires in the District of Kansas “is not fair and reasonable in relation to their numbers in the community.” Duren, 439 U.S. at 364, 99 S.Ct. 664. The defendant and the government disagree about how the three groups’ “numbers in the community” should be measured. The defendant compares the minorities’ percentages on the qualified wheel to the minorities’ percentages among the entire voting-age population in the Wichita-Hutchinson division. The government contends that the court should compare the minorities’ percentages on the qualified wheel to their percentages among that portion of the entire voting-age population that is eligible to sit on juries.
The government’s position has “intellectual merit.” United States v. Rioux, 97 F.3d 648, 657 (2d Cir.1996). The defendant’s method (comparing the minorities’ percentages on the qualified wheel to their percentage in the entire community) involves a comparison between a population that meets the eligibility requirements to a population of both eligible and ineligible people. See id. As the government contends, however, to accurately evaluate whether the District of Kansas’s use of actual voter lists violates the Sixth Amendment, we should compare the percentage of minorities in the qualified wheel to the percentage of minorities in the segment of the general population that is eligible to serve on juries. Otherwise, it will be difficult to ascertain whether a disparity is attributable to the district’s use of actual voter lists or to the general eligibility criteria. For instance, if the percentage of Asians on the qualified wheel were much smaller than the percentage of Asians in the general population, we would not know whether the disparity existed because of the district’s use of actual voter lists or simply because members of that group are ineligible for jury service at a higher rate than the general population (if, for example, many Asians were not United States citizens or did not speak English). To negate the possibility that the disparities result from the general eligibility requirements, we would have to compare the qualified wheel to the portion of the general population that is eligible to serve. See United States v. Esle, 743 F.2d 1465, 1479 n. 3 (11th Cir.1984) (Tjoflat, J., concurring). However, there is apparently no reliable measurement of that subset of the general population.
Thus, despite the shortcomings of the defendant’s statistical method, we find that his method of comparison was appropriate under the circumstances of this case. See Rioux, 97 F.3d at 657 (finding general figures acceptable where more detailed figures were not available). The defendant derived his population data from the most recent census, a practice that the Supreme Court has found adequate in the past. See Duren, 439 U.S. at 364-65 & nn. 22-24, 99 S.Ct. 664. We now turn to the defendant’s statistics and ask if they show that Asians, Blacks, or Hispanics are unfairly represented on juries in the Wichita-Hutchinson division of the District of Kansas.
2. The Statistical Showing
In determining whether a group has been underrepresented on jury venires, “courts generally rely on two methods of comparison: absolute disparity and comparative disparity.” Gault, 141 F.3d at 1401-02. Absolute disparity measures the difference between the percentage of a group in the general population and its percentage in the qualified wheel. For instance, if Asians constitute 10% of the general population and 5% of the qualified wheel, the absolute disparity is 5%. Comparative disparity measures the decreased likelihood that members of an underrepresented group will be called for jury service, in contrast to what their presence in the community suggests it should be. This figure is determined by dividing the absolute disparity of the group by that group’s percentage in the general population. In the example above, the comparative disparity is 50%: Asians are half as likely to be on venires as they would be if represented in proportion to their numbers in the community-
[1273]*1273In this ease, the relevant numbers are as follows:
Distinctive Group Asian Black Hispanic
Percentage of voting age population 1.27% 5.11% 2.92%
Percentage of qualified veniremen .51% 2.55% 1.50%
Absolute Disparity .76% 2.56% 1.42%
Comparative 59.84% ■ 50.09% 48.63% Dispai'ity
In this circuit, “absolute disparity ... is the starting place for all other modes of comparison.” United States v. Yazzie, 660 F.2d 422, 427 (10th Cir.1981). Here, the greatest absolute disparity is less than 3%, which, as the district court noted, is far less than the percentages that the Supreme Court has relied upon in its cases finding Sixth Amendment violations. See, e.g., Duren, 439 U.S. at 365-66, 99 S.Ct. 664 (39% absolute disparity); Jones v. Georgia, 389 U.S. 24, 88 S.Ct. 4, 19 L.Ed.2d 25 (1967) (14.7%). Courts generally are reluctant to find that the second element of a prima facie Sixth Amendment case has been satisfied when the absolute disparities are less than 10%. See United States v. Rioux, 930 F.Supp. 1558, 1570 (D.Conn.1995) (collecting cases). Furthermore, our circuit has found that absolute disparities of 4.29% and 7% failed to establish a prima facie violation. See Yazzie, 660 F.2d at 427 (4.29%); Gault, 141 F.3d at 1402-03 (7%).
The defendant urges us to focus on the comparative disparities rather than the absolute disparities because of the small size of the minority populations in Kansas. Indeed, small absolute disparity figures are less persuasive in a case such as this, where, because of the minorities’ small population, even the complete exclusion of the groups would result in absolute disparities of less than 6%. See United States v. Jackman, 46 F.3d 1240, 1247 (2d Cir.1995) (noting the weakness of absolute disparity analysis when dealing with small population).
The comparative disparities are larger: 48%, 50%, and almost 60%. While these numbers may be more indicative of a Sixth Amendment violation, they too are distorted by the small population of the different minority groups. “[T]he smaller the group is, the more the comparative disparity figure distorts .the proportional representation.” United States v. Hafen, 726 F.2d 21, 24 (1st Cir.1984); see United States v. Whitley, 491 F.2d 1248, 1249 (8th Cir.1974). “For example, in an area that had 500,000 whites and only one black eligible to serve as jurors, a random selection system that failed to place the single black on the master wheel would produce a 100 per- cent comparative disparity, even though an all-white jury would clearly form a'‘fair cross section’ of the community.” Hafen, 726 F.2d at 24. In this case, considering the small size of each' of the groups in relation to the larger community, it is not surprising that the comparative disparity numbers are large. It is equally unsurprising thát the group with the largest comparative disparity, Asians, has the- fewest members.
Although both statistical measurements have their weaknesses in this situation, there can be no doubt that the figures computed under either method do not demonstrate the type of “marked” or “gross” disparities that we have found necessary to establish that the representation of a group is not fair and reasonable in relation to their number in the community. See Gault, 141 F.3d at 1402-03 (quoting Test, 550 F.2d at 590). The second element of the Duren test not being satisfied, the defendant cannot make out a prima facie case that the District of Kansas’s selection procedure violates either the Sixth Amendment or the Jury Service and Selection Act of 1968. ■
II. Double Jeopardy
The district court empaneled and swore in a complete jury. Then, after being advised that one of the jurors had child-care responsibilities that would not allow her to serve, the court excused that juror, replaced her with another, and swore in the new juror. This unusual procedure raises a tangle of double jeopardy issues. We review two different lines of cases in .order to resolve those issues.
[1274]*1274A. The Terminating-Event Requirement
The Double Jeopardy Clause of the Fifth Amendment states that no person -shall be “twice put in jeopardy of life or limb.” U.S. Const, amend. V. The clause protects criminal defendants against having to endure the risk of conviction twice. Thus, the first relevant line of cases expresses the logical principle that the Double Jeopardy Clause does not apply to situations in which the defendant has been placed in jeopardy only once. These cases have their origin in Ball v. United States, 163 U.S. 662, 672, 16 S.Ct. 1192, 41 L.Ed. 300 (1896), in which the Supreme Court held that the Double Jeopardy Clause does not prevent a second trial when the defendant’s original conviction has been overturned on appeal. Ball rested on the notion that when a conviction is overturned, a new trial does not present the defendant with a new, or second risk of conviction. Ball “effectively formulated a concept of continuing jeopardy that has application where criminal proceedings against an accused have not run their full course.” Price v. Georgia, 398 U.S. 323, 326, 90 S.Ct. 1757, 26 L.Ed.2d 300 (1970). The continuing jeopardy principle achieved its fullest expression in Richardson v. United States, 468 U.S. 317, 325, 104 S.Ct. 3081, 82 L.Ed.2d 242 (1984), in which the defendant challenged the prosecution’s attempt to retry him after his original proceeding had ended in a mistrial because of a hung jury. The Supreme Court held “that the protection of the Double Jeopardy Clause by its terms applies only if there has been some event, such as an acquittal, which terminates the original jeopardy.” Id.; see also Justices of Boston Mun. Court v. Lydon, 466 U.S. 294, 309, 104 S.Ct. 1805, 80 L.Ed.2d 311 (1984) (rejecting the defendant’s double jeopardy argument because “he fails to identify any stage of the state proceedings that can be held to have terminated jeopardy”). The Court said that the declaration of a mistrial, in that instance, did not terminate his original jeopardy.
Only two other circuits have addressed the situation before us, the Ninth and the Sixth, and only the Ninth relied on the principle of continuing jeopardy to reject the defendant’s argument (we discuss the Sixth Circuit’s approach infra). In that case, a jury of twelve, with no alternates, was empaneled and sworn. See United States v. Trigg, 988 F.2d 1008, 1009 (9th Cir.1993). Before any testimony was given, the judge excused three jurors because of unavailability and replaced them with three jurors drawn from the veni-re. See id. The entire new jury was then sworn again. See id.
The Ninth Circuit concluded that the unusual procedure “cannot terminate jeopardy any more than a failure of a jury to reach a verdict.” Id. at 1010. The court held that “jeopardy does not terminate during the process of jury selection merely because sworn jurors are excused during the process of selecting alternates.” Id. The Tñgg court apparently interpreted Richardson to mean that there could be no terminating event for Double Jeopardy purposes if the original jury had not, at the least, made a decision on the merits of the case. See also Richardson, 468 U.S. at 327, 104 S.Ct. 3081 (Brennan, J., concurring in part and dissenting in part) (interpreting Richardson to mean that “only an actual judgment of acquittal, or an unre-versed conviction, would ‘terminate’ jeopardy and thereby bar retrial”).
B. The Right to a Particular Tribunal
Trigg and Richardson seem to provide an easy answer here. In equipoise with those cases, however, is the long-standing-principle that a defendant has a “valued right to have his trial completed by a particular tribunal.” Illinois v. Somerville, 410 U.S. 458, 466, 93 S.Ct. 1066, 35 L.Ed.2d 425 (1973) (quoting Wade v. Hunter, 336 U.S. 684, 689, 69 S.Ct. 834, 93 L.Ed. 974 (1949)). As soon as the jury is sworn, the defendant acquires a constitutional interest in having that jury see his case through to a conclusion. See United States v. Martin Linen Swpply Co., 430 U.S. 564, 569, 97 S.Ct. 1349, 51 L.Ed.2d 642 (1977). A proceeding judged by a tribunal other than the one originally selected “may be grossly unfair. It increases the financial and emotional burden on the accused, prolongs the period in which he is stigmatized by an unresolved accusation of wrongdoing, and may even enhance the risk that an innocent defendant may be convicted.” Arizona v. Washington, 434 U.S. 497, 503-04, 98 S.Ct. 824, 54 L.Ed.2d 717 (1978).
[1275]*1275The constitutional test derived from the defendant’s right to have a trial completed by a particular tribunal is well established. Once a particular jury is sworn, the prosecutor may not try the defendant before another jury without demonstrating a “manifest necessity” for the new proceeding with a new tribunal. See id. at 505-06, 98 S.Ct. 824. The manifest necessity standard “has been quoted over and over again to provide guidance in the decision of a wide variety of cases.” Id. at 506, 98 S.Ct. 824.
The cases protecting the right to a particular tribunal focus on the inception of the proceedings — that is, whether the jury was sworn — while Richardson asks whether there has been an end to those proceedings. We have noted the apparent inconsistency between Richardson and other strains of Double Jeopardy jurisprudence before. See United States v. Wood, 958 F.2d 963, 970 (10th Cir.1992) (noting that some of our cases are “inconsistent with the continuing jeopardy principle suggested in Richardson ”). The different orientations could be read to create a conflict in a case such as this. On the one hand, because jeopardy attached after the swearing of the first jury, and that original tribunal did not ultimately decide'the case, one might read the precedent to compel the government to prove a manifest necessity for trying the case before a new jury. The Sixth Circuit took this approach when faced with a situation similar to the one before us. It held that “[o]nce jeopardy attaches, prosecution of a defendant before a. jury other than the original jury ... is barred unless (1) there is a ‘manifest necessity’ for a mistrial or (2) the defendant either requests or consents to a mistrial.” Watkins v. Kassulke, 90 F.3d 138, 141 (6th Cir.1996).1
On the other hand, under Richardson a terminating event must occur before the Double Jeopardy Clause even comes into play. Richardson found that a mistrial by virtue of a hung jury did not terminate jeopardy. Accordingly, the Ninth Circuit read Richardson to require no manifest necessity analysis at all, on the basis that jury selection procedures are much less final than the hung jury at issue in Richardson. See Trigg, 988 F.2d at 1009-1011.
C. Resolving the Ttvo Principles
The precedent, however, does not conflict. Two points make this clear. First, it is mistaken to interpret Richardson to mean that nothing short of an acquittal or unreversed conviction implicates the Double Jeopardy Clause. Richardson used the doctrine of “continuing jeopardy” to find that a mistrial after a hung jury was not a terminating event, and therefore no double jeopardy violation occurred. The Richardson Court primarily relied, however, not on “continuing jeopardy” cases, but on the century and a half of jurisprudence that had already made clear that double jeopardy did not bar retrial in such a circumstance. Thus, the observation that “ ‘continuing jeopardy’ describes both a concept and a conclusion” is appropriate. Breed v. Jones, 421 U.S. 519, 534, 95 S.Ct. 1779, 44 L.Ed.2d 346 (1975). In Richardson, the Court used “continuing jeopardy” to describe a conclusion. The Court’s finding that jeopardy never terminated was, more than anything, a shorthand expression of a time-tested conclusion that the retrial procedure at issue did not violate the Double Jeopardy Clause. The Court did not revolutionize our understanding of “continuing jeopardy.”
Second and more importantly, continuing jeopardy also “describes ... a concept." Breed v. Jones, 421 U.S. 519, 534, 95 S.Ct. [1276]*12761779, 44 L.Ed.2d 346 (1975) (emphasis added). All of the Supre ne Court’s double jeopardy cases, even those that seem to conflict with Richardson, “presuppose[ ] some identifiable point at which a first trial may be said to have ended.” Lydon, 466 U.S. at 315, 104 S.Ct. 1805 (Brennan, J., concurring in part and concurring in the judgment). The Court has. said, for instance, that the manifest necessity test should be used “when a criminal proceeding is terminated without finally resolving the merits.” Arizona v. Washington, 434 U.S. 497, 505, 98 S.Ct. 824, 54 L.Ed.2d 717 (1978) (emphasis added); see also Somerville, 410 U.S. at 471, 93 S.Ct. 1066 (referring to the district court’s decision to “abort ” the proceedings) (emphasis added). Thus, even those cases that do not explicitly rely on the doctrine of “continuing jeopardy,” implicitly recognize that the concept is pertinent when deciding double jeopardy questions. The relevant question in this case, then, is when does a defendant’s “continuing jeopardy” terminate?
In order to determine whether the original proceeding ever “terminated,” we look to the interests of the Double Jeopardy Clause. See Breed, 421 U.S. at 534, 95 S.Ct. 1779. “[T]he continuing jeopardy principle appears to rest on an amalgam of interests— e.g., fairness to society, lack of finality, and limited waiver, among others.” Price v. Georgia, 398 U.S. 323, 329 n. 4, 90 S.Ct. 1757, 26 L.Ed.2d 300 (1970).
The question of whether jeopardy has objectively “terminated” should be analyzed in terms of the policies of the Double Jeopardy Clause, namely its concern that repeated trials may subject a defendant to embarrassment, expense and ordeal and compel him to live.in a continuing state of anxiety and insecurity, as well as enhancing the possibility that even though innocent he may be found guilty. Jeopardy may be said to have terminated only when the posture of a trial in some objective sense leaves that defendant in such a position that resumption of proceedings would implicate those policies.
Lydon, 466 U.S. at 320, 104 S.Ct. 1805 (Brennan, J., concurring in part and concurring in the judgment) (emphasis added) (citations and internal quotation marks and alterations omitted); see also Lovato v. New Mexico, 242 U.S. 199, 201, 37 S.Ct. 107, 61 L.Ed. 244 (noting that mere irregularity of procedure does not implicate the Double Jeopardy Clause). Only if the trial before the new tribunal reasonably implicates the policies described above has the first proceeding terminated. Only then do we proceed to the manifest necessity analysis.
The procedure in this case did not threaten the defendant with any of the harms that the Double Jeopardy Clause was meant to prevent. The replacement of one juror before any witnesses had testified did not reasonably subject the defendant to “embarrassment, expense and ordeal,” or force him to live in a “continuing state of anxiety,” to any greater extent than that he would have experienced if the district court had sworn an alternate along with the original twelve jury members and thereby avoided the issue before us altogether. Furthermore, for us to hold that the trial terminated at such a preliminary stage, without any allegation that the replacement was attributable to prosecu-torial tactics, would frustrate “society’s interest in giving the prosecution one complete opportunity to convict those who have violated its laws.” Arizona v. Washington, 434 U.S. 497, 509, 98 S.Ct. 824, 54 L.Ed.2d 717 (1978).
The defendant cannot point to any event that terminated the original jeopardy. That being the case, his Double Jeopardy challenge cannot succeed.
III. United States v. Gaudin
The defendant argues next that, in conflict with the Supreme Court’s decision in United States v. Gaudin, 515 U.S. 506, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995), the jury instructions in this case removed one element of the Hobbs Act violation from the jury’s consideration. In Gaudin, the Supreme Court recognized that the “Constitution gives a criminal defendant the right to have a jury determine, beyond a reasonable doubt, his guilt of every element of the crime with which he is charged.” Id. at 522-23, 115 S.Ct. 2310. The jury’s constitutional responsibility to determine whether the defendant is guilty of each element includes not only finding facts, but also applying the facts to [1277]*1277legal principles. See id. at 512-13, 115 S.Ct. 2310.
In Gaudin, the government charged the defendant with making false statements on a loan document in violation of 18 U.S.C. § 1001. See id. at 507, 115 S.Ct. 2310. Although the crime required a finding that the alleged statements were material to the federal agencies insuring the loan, the court did not submit the issue of materiality to the jury. See id. at 508, 115 S.Ct. 2310. The court said to the jury: “You are instructed that the statements charged in the indictment are material statements.” Id. The Supreme Court found that the district court’s practice violated the defendant’s right to have the jury determine his guilt of each element of the crime. See id. at 522-23, 115 S.Ct. 2310.
In this case, the defendant was charged with, among other things, violating the Hobbs Act, a statute that makes it a crime to obstruct interstate commerce by robbery. See 18 U.S.C. § 1951. One element of that offense is interference with interstate commerce. See Stirone v. United States, 361 U.S. 212, 218, 80 S.Ct. 270, 4 L.Ed.2d 252 (1960). The court here submitted the interstate commerce element to the jury, instructing them as follows:
The defendant need not have intended or anticipated an effect on interstate commerce. You may find the effect is a natural consequence of his actions. If you find the defendant intended to take certain actions, that is, he did the acts charged in the Indictment in order to obtain property, and you find those actions have either caused, or would probably cause, an effect on interstate commerce, then you may find the requirements of this element have been satisfied.
If you decide there was any effect at all on interstate commerce, then that is enough to satisfy this element. The effect can be minimal. For example, if a successful robbery of money would prevent the use of those funds to purchase articles which travel through interstate commerce, that would be a sufficient effect on interstate commerce.
Jury Instruction # 15. Aceoi'ding to the defendant, the italicized portion of this instruction dictated to the jury how they should apply the law to the facts of this case and, therefore, violated the Gaudin rule. ■
The defendant’s case is unlike Gaudin in at least one important respect. In Gaudin, the court did not submit the materiality element to the jury. Two other circuits appear to have held that the Gaudin rule is limited to cases in which the element at issue was not submitted to the jury. See United States v. Castleberry, 116 F.3d 1384, 1389 (11th Cir.), cert. denied, — U.S. -, 118 S.Ct. 341, 139 L.Ed.2d 265 (1997); United States v. Parker, 104 F.3d 72, 73 (5th Cir.) (en banc), cert. denied, — U.S. -, 117 S.Ct. 1720, 137 L.Ed.2d 842; id. at 73-75 (DeMoss, J., dissenting). ' We need not decide here whether, as the defendant argues, the rule in Gau,-din extends to a case in which the element was submitted but in such a way as to effectively dictate the jury’s application of the law to the facts because, even if Gaudin could reach so far, the instruction here did not effectively remove the issue from the jury’s consideration.
The court did not tell the jury that if they believed the government’s evidence, they had to find the interstate commerce element satisfied. Instead, the court merely concluded its definition of interstate commerce by giving an example. That example did not tie a legal result to the particular facts of the defendant’s case. The defendant goes too far, in reading Gaudin to prohibit attempts to clarify the law for jurors, especially on such an unfamiliar subject as interstate commerce.
IV. Armed Career Criminal Enhancement
The defendant also challenges his sentence enhancement for being an Armed Career Criminal pursuant to 18 U.S.C. § 924(e) and section 4B1.4. of the Sentencing Guidelines. When reviewing sentence enhancements under the sentencing guidelines, we accept the factual findings of the district court unless they are clearly erroneous. See United States v. Farnsworth, 92 F.3d 1001, 1009 (10th Cir.), cert. denied, — U.S. -, 117 S.Ct. 596, 136 L.Ed.2d 524 (1996). At sentencing, the district court may rely on facts stated in the presentence report unless the defendant has objected to them. See [1278]*1278United States v. O’Dell, 965 F.2d 937, 938 (10th Cir.1992). When a defendant objects to a fact in a presentence report, the government must prove that fact at a sentencing hearing by a preponderance of the evidence. United States v. Easterling, 921 F.2d 1073, 1078 (10th Cir.1990).
A criminal defendant is subject to the Armed Career Criminal enhancement if he is convicted of violating 18 U.S.C. § 922(g) and has at least three prior convictions for “violent felonies” or “serious drug offenses.” See U.S. Sentenci0ng Guidelines Manual § 4B1.4 commentary; 18 U.S.C. § 924(e)(2) (defining “violent felony” and “serious drug offense”). The presentence report recommended that Mr. Shinault be sentenced as an Armed Career Criminal. The defendant objected on the grounds that two of three convictions forming the basis for the Armed Career Criminal enhancement—those listed in paragraphs 53 and 54 of the presentence report—charged a person other, than Mr. Shinault. The charging documents in those convictions named Richard L. Bumphus as the perpetrator for one crime and Michael Washington for the other.
At the sentencing hearing, the man who prepared the presentence report, Jim Fritz, a probation officer from the U.S. Probation Department, testified that Mr. Shinault was in fact the person convicted of the crimes listed in paragraphs 53 and 54 of the presen-tence report. Mr. Fritz testified first that court documents pertaining to the prior convictions noted that Richard L. Bumphus and Michael Washington were aliases of Mr. Shi-nault. Second, Mr. Fritz testified that he also referenced Mr. Shinault’s FBI “rap sheet,” which listed him as the perpetrator of the two previous crimes. Mr. Fritz confirmed that the FBI does not enter a conviction on a person’s , record without first comparing fingerprint samples to ensure that the updated record is accurate. According to Fritz’s testimony, the FBI had matched Mr. Shinault’s fingerprints with those of the defendants in the previous cases. The district court made its findings on the basis of this evidence, and we cannot say that it clearly erred in doing so.
The defendant asserts that the district court also clearly erred in finding that the third prior conviction was established even though the government presented no information relating to it at the sentencing hearing. The defendant, however, did not object to the presentence report on the ground that the third conviction was inaccurate; the defendant only contended that he was not the person convicted of the crimes identified in paragraphs 53 and 54. “Failure to object to a fact in a presentence report, or failure to object at the hearing, acts as an admission of fact.” United States v. Deninno, 29 F.3d 572, 580 (10th Cir.1994). Thus, the district court was justified in relying on the presentence report for proof of the first conviction.
V. Commerce Clause and Multiple Punishment Challenges
The defendant raises two final arguments that this court has previously addressed and rejected. First, the defendant contends that Congress lacked the constitutional authority under the Commerce Clause to enact the Hobbs Act. We have held, however, that “[b]ecause the Hobbs Act regulates activities that in aggregate have a substantial effect on interstate commerce,” the Act is a “permissible exercise of the authority granted to Congress under the Commerce Clause.” United States v. Bolton, 68 F.3d 396, 399 (10th Cir.1995), cert. denied, 516 U.S. 1137, 116 S.Ct. 966, 133 L.Ed.2d 887 (1996); see also United States v. Romero, 122 F.3d 1334, 1340 (10th. Cir.1997), cert. denied, — U.S. -, 118 S.Ct. 1310, 140 L.Ed.2d 474 (1998).
The defendant also argues that his convictions violate his Fifth Amendment rights. For each of the defendant’s acts of robbery, the jury convicted him of violating both the Hobbs Act (committing a robbery affecting interstate commerce) and 18 U.S.C. § 924(c) (using or carrying a weapon during a crime of violence). The crime of violence supporting the defendant’s section 924(c) conviction was the Hobbs Act violation. The defendant contends that his convictions under both the Hobbs Act and section 924(c) violated the double jeopardy protection against receiving multiple punishment for the same conduct. See Blockburger v. United [1279]*1279States, 284 U.S. 299, 52 S.Ct. 180, 76 L.Ed. 306 (1932). We have previously rejected this double jeopardy challenge, however, because “Congress may impose multiple punishment for the same conduct without violating the Double Jeopardy Clause if it clearly expresses its intent to do so,” and Congress did so in section 924(c). United States v. Overstreet, 40 F.3d 1090, 1093, 1095 (10th Cir.1994).
Conclusion
We hold (1) that the jury selection procedures in the Wichita-Hutchinson division of the District of Kansas did not deny the defendant the right to a jury drawn from a fair cross-section of the community, (2) that the unusual jury selection procedure used in this case did not violate the defendant’s right not to be tried twice for the same offense, (3) that the court did not take an element of the crime away from the jury’s consideration, (4) that the court did not clearly err in making its factual determinations related to the Armed Career Criminal sentence enhancement, (5) that Congress did not exceed its constitutional authority under the Commerce Clause in passing the Hobbs Act, and (6) that the defendant’s convictions under the Hobbs Act and 18 U.S.C. § 924(c) do not amount to multiple punishments for the same conduct. We AFFIRM.