                               In the

    United States Court of Appeals
                 For the Seventh Circuit
                     ____________________
No. 13-3198
UNITED STATES OF AMERICA,
                                                   Plaintiff-Appellee,

                                 v.

WILLIAM BEAVERS,
                                               Defendant-Appellant.
                     ____________________

         Appeal from the United States District Court for the
           Northern District of Illinois, Eastern Division.
              No. 12 CR 124 — James B. Zagel, Judge.
                     ____________________

       ARGUED APRIL 3, 2014 — DECIDED JUNE 30, 2014
                     ____________________

   Before POSNER, FLAUM, and ROVNER, Circuit Judges.
   FLAUM, Circuit Judge. William Beavers, a former Chicago
alderman and Cook County Commissioner, was convicted of
multiple counts of tax fraud. He appeals his conviction on
several grounds. Beavers challenges many of the district
court’s evidentiary rulings and jury instructions, and he also
contends that his right to a jury composed of a fair cross-
section of the community was violated. We affirm.
2                                                  No. 13-3198

                        I. Background
   William Beavers was a Chicago alderman from 1983 until
November 2006. In December 2006, he began serving as a
Cook County Commissioner. Beavers had three political
campaign committees: Citizens for Beavers, Friends of Wil-
liam Beavers, and the 7th Ward Democratic Organization.
He was the chairman of each campaign committee as well as
the only authorized signor for each committee’s bank ac-
count. There is no dispute that Beavers’ federal tax returns
from 2005 to 2008 exhibited various inaccuracies; the parties
disagree, however, as to whether these inaccuracies were
honest mistakes or deliberate misrepresentations.
     The first inaccuracy was Beavers’ underreporting of his
2005 income. Each of Beavers’ campaign committees was re-
quired to file semi-annual disclosure reports (called “D-2s”)
listing its expenditures. In its D-2 for the first half of 2005,
Citizens for Beavers reported a payment of $56,149 to Bea-
vers. This payment was legal under Illinois law. However,
Beavers had given his tax preparer a letter, addressed to the
IRS and signed by Beavers, stating that he had received only
$43,000 in campaign funds from Citizens for Beavers. Thus,
Beavers’ tax return listed $43,000—rather than $56,149—as
“additional income.”
    The second inaccuracy concerned Beavers’ undeclared
use of campaign funds to increase his pension annuity.
Shortly before Beavers left his position as a Chicago alder-
man in November 2006, the Municipal Employees Annuity
and Benefit Fund of Chicago informed Beavers about his op-
tions for his aldermanic pension. To take advantage of the
option that maximized his pension benefits, Beavers provid-
ed the Annuity Fund with a check for $68,763, which was
No. 13-3198                                                  3

drawn on the account of Citizens for Beavers. Beavers did
not report the $68,763 as income on his tax return for 2006,
nor did Citizens for Beavers report the expenditure on its
D-2s for 2006, 2007, or 2008. Additionally, when Beavers lat-
er applied to a bank for a personal loan, his financial state-
ments did not include the $68,763 as an outstanding loan
from his campaign. From the time he took the funds in No-
vember 2006 until April 2009, Beavers did not repay any of
the $68,763 to his campaign.
    The third inaccuracy concerned the monthly stipends
that Beavers took as a Cook County Commissioner. Cook
County paid its Commissioners not only an annual salary,
but also a monthly stipend of $1,200 from the Cook County
Contingency Account. Beavers cashed (or deposited in his
personal bank account) every monthly check from December
2006 through November 2008. Beavers informed the County
(through forms that he submitted) that he would claim these
$1,200 stipends as income. However, he did not report these
monthly checks on his tax returns for 2006, 2007, or 2008.
    The fourth problem was that, between 2006 and 2008,
Beavers wrote himself 100 checks totaling $226,300 from his
three campaign-committee accounts. At trial, the govern-
ment demonstrated that Beavers often wrote these checks in
order to finance his gambling trips to the Horseshoe Casino
in Hammond, Indiana. Beavers cashed 93 of the 100 checks
the day before, the day of, or the day after he used his “play-
er’s card” at the Horseshoe. An IRS agent who examined
these checks and the campaigns’ bank accounts testified that
Beavers often repaid his campaigns in some amount, but he
never repaid the full $226,300. The agent further testified
4                                                 No. 13-3198

that there were no loan agreements or formal documentation
for any of these “advances.”
   The fifth problem concerned Beavers’ efforts to obstruct
the IRS. The government says that the fact that Beavers
“made the 100 campaign checks payable to himself made it
more difficult to determine what he did with the proceeds.”
Beavers’ campaign-committees’ records said nothing of
gambling or personal use. Indeed, some check stubs had no
explanation of the check’s purpose, while others indicated
that checks were used for campaign-related expenses even
though the timing suggested that they were used to fund
Beavers’ gambling. Beavers and his campaign committees
did not document when he repaid the funds.
    In April 2009, federal agents approached Beavers and
said they wanted to interview him in connection with a
grand jury investigation into his unreported conversion of
campaign funds for personal use. Beavers then took several
corrective actions. One week after agents contacted him, he
filed amended tax returns for 2007 and 2008. He reported
nearly $20,000 in additional income for each year, explaining
that “[c]ampaign funds deemed reportable was [sic] inad-
vertently omitted from the original return.” The following
month, Beavers wrote a $68,000 check—drawn on the ac-
count of one of his campaign funds, Friends for Beavers—to
repay another campaign fund, Citizens for Beavers. (He later
wrote several checks from his personal account in an effort
to repay Friends for Beavers.) In fall 2010, the media report-
ed that a grand jury had issued a subpoena for Cook County
records about Beavers and the contingency-fund stipends.
Later, in April 2011, Beavers filed a second amended tax re-
turn for 2008 in which he reported an additional $11,000 in
No. 13-3198                                                   5

income. This newly amended return included the explana-
tion that “[a]dvances for expenses by the employer were not
included on the W2 and were not accounted for on the origi-
nal return.”
    In 2012, the government charged Beavers with three
counts of violating 26 U.S.C. § 7206(1), which prohibits wil-
fully making a material false statement on a tax return, and
with one count of violating 26 U.S.C. § 7212(a), which pro-
hibits corruptly obstructing the IRS in its administration of
the tax laws. The jury convicted Beavers on all counts. Bea-
vers was sentenced to six months’ imprisonment and was
ordered to pay about $31,000 in restitution and a $10,000 fi-
ne. He appeals.
                        II. Discussion
   A. Evidentiary rulings
    Beavers raises several evidentiary challenges. He also ar-
gues that the district court’s rulings violated his constitu-
tional right to present a meaningful defense and impermis-
sibly burdened his right against self-incrimination. We typi-
cally review evidentiary rulings for an abuse of discretion,
but we review de novo whether an evidentiary ruling violat-
ed Beavers’ constitutional rights. United States v. Alayeto, 628
F.3d 917, 920–21 (7th Cir. 2010).
       i.   The evidence of Beavers’ remedial actions
   Beavers first argues that the district court erred by ex-
cluding evidence of his conduct after federal agents ap-
proached him—namely his amended tax returns and pay-
ments to reimburse his campaign committees. The govern-
ment moved in limine to exclude all of this evidence. Rely-
ing on Federal Rules of Evidence 401 and 403, the govern-
6                                                  No. 13-3198

ment argued that Beavers’ actions were not probative of his
state of mind at the time he filed the original returns, and
that the jury would be confused by the admission of evi-
dence of remedial actions. Beavers, on the other hand, ar-
gued that such evidence was probative of his good faith and
lack of intent to file fraudulent returns in the first place. He
also said that the fact that he repaid (with campaign funds)
the $68,763 that he used to increase his pension shows that
he considered the amount a loan, rather than income.
    The district court ruled that the evidence would be ad-
missible if Beavers could establish that each remedial action
was relevant to his state of mind at the time he filed the orig-
inal tax returns. Beavers ultimately elected not to testify, and
he did not otherwise succeed in establishing the required ev-
identiary foundation. Thus, the evidence of his remedial ac-
tions was not presented at trial. Beavers argues that (1) the
evidence of his remedial actions was relevant under Rule
401; (2) the district court’s conditional admission impermis-
sibly burdened Beavers’ Fifth Amendment right against self-
incrimination; and (3) the court’s rulings deprived him of his
constitutional right to present a meaningful defense.
    First, the district court conditioned the admission of evi-
dence of Beavers’ corrective actions upon a showing that
these actions had a connection to Beavers’ state of mind at
the time he filed his incorrect returns. The logic of the ruling
was that, in the absence of a foundation establishing this
link, the amended tax returns (and evidence of other reme-
dial actions) did not make it more likely that Beavers be-
lieved his original returns were accurate when he filed them.
   District judges making relevancy determinations in this
type of situation should proceed on a case-by-case basis. Cf.
No. 13-3198                                                      7

United States v. Tishberg, 854 F.2d 1070, 1073 (7th Cir. 1988)
(reasoning, in the sufficiency context, that the defendant’s
amended return “may demonstrate a good faith effort to
correct his previous mistakes,” but also noting that the re-
turn “does not negate the import of his previous action”).
Nevertheless, courts have repeatedly affirmed the exclusion
of evidence of remedial action taken after the taxpayer
knows he is under investigation. See United States v. McClain,
934 F.2d 822, 834–35 (7th Cir. 1991) (finding “no reason” to
disturb the district court’s ruling that defendant’s 1985 tax
return was not probative of his state of mind at the time he
filed his 1984 return, given his indictment in the intervening
year); United States v. Radtke, 415 F.3d 826, 840–41 (8th Cir.
2005); United States v. Ross, 626 F.2d 77, 81 (9th Cir. 1980); Post
v. United States, 407 F.2d 319, 325 (D.C. Cir. 1968); United
States v. Stoehr, 196 F.2d 276, 282 (3d Cir. 1952); see also United
States v. Philpot, 733 F.3d 734, 748 (7th Cir. 2013) (explaining,
in political corruption case, that defendant’s remedial “ac-
tions after his bonuses were reported in the press shed little
or no light on his state of mind two years earlier” when he
received those bonuses). A common thread in many of these
cases is that subsequent remedial actions may not be proba-
tive of the defendant’s prior state of mind because such ac-
tions are equally consistent with (1) promptly correcting a
genuine mistake and (2) trying to cover up a purposeful lie
in the hope of avoiding prosecution. Cf. Fed. R. Evid. 407
(barring evidence of subsequent remedial action to prove an
admission of fault).
    In any event, the district court did not exclude the evi-
dence entirely—it simply conditioned the evidence’s admis-
sion on some kind of showing of its relevance to Beavers’
state of mind at the time he filed his original returns several
8                                                     No. 13-3198

years earlier. Beavers did not make this showing. In fact, his
theory of defense is at odds with his argument that the re-
medial evidence was relevant. Beavers’ argument in defense
(which he maintains on appeal) was that all of the transfers
from his campaign committees were loans, not income.
Thus, evidence that Beavers declared some of the campaign-
fund transfers as income on his amended tax returns after he
was under investigation has little bearing on whether he
considered the transfers to be loans at the time he took the
funds. In sum, the district court’s sensible approach to the
remedial evidence was within its discretion.
    Beavers next argues that the district court’s handling of
this issue impermissibly burdened his Fifth Amendment
right against self-incrimination, see generally Griffin v. Califor-
nia, 380 U.S. 609 (1965), because it forced him either to testify
(in order to lay the appropriate foundation) or to forgo the
opportunity to get evidence before the jury. Beavers’ argu-
ment misunderstands the nature of this right, however.
Criminal defendants often face difficult choices in weighing
the costs and benefits of testifying. And the rules of evidence
sometimes prevent defendants from getting their story—or
evidence of their state of mind—before the jury in the par-
ticular manner they would prefer. Cf. U.S. ex rel. Harris v. Illi-
nois, 457 F.2d 191, 197–98 (7th Cir. 1972) (“The State presently
contends, and we agree, that a defendant in a criminal trial
may not introduce evidence in his defense without laying a
proper foundation therefor.”). For instance, the general rule
against hearsay, see Fed. R. Evid. 802, would typically pre-
vent a defendant from calling a friend to the stand to relay
an exculpatory statement the defendant said to her, in lieu of
the defendant testifying himself. Thus, the rule against hear-
say may burden the defendant’s right to testify in the same
No. 13-3198                                                   9

way Beavers argues that his right was burdened here, since
it puts him to the choice of taking the stand (and exposing
himself to potentially damaging cross-examination) or losing
the chance to get evidence before the jury. That sort of bur-
den is not impermissible, however; it is simply part of a larger
system in which “[t]he accused does not have an unfettered
right to offer testimony that is … inadmissible under stand-
ard rules of evidence.” Taylor v. Illinois, 484 U.S. 400, 410
(1988). We see no meaningful difference between the hearsay
situation and the burden Beavers faced here—both burdens
are ordinary, well-established, and permissible. Indeed, we
have previously approved the exclusion of purported state-
of-mind evidence offered by a defendant where the defend-
ant could have, but did not, supply the requisite foundation
of relevance through his own testimony. See United States v.
Scott, 660 F.2d 1145, 1165–67 (7th Cir. 1981). Accordingly, we
reject Beavers’ argument on this score.
       ii. Evidence of Cook County’s alleged obligation to
           report the $1,200 monthly stipends on Beavers’
           W-2s
    Beavers next argues that the district court improperly ex-
cluded evidence about Cook County’s alleged mistakes on
Beavers’ W-2s. Recall that, when Beavers was a Cook County
Commissioner, the county paid him not only a salary but al-
so a monthly stipend of $1,200. Beavers cashed or deposited
in his personal bank account every monthly check from De-
cember 2006 through November 2008. He informed the
county that he would claim these stipends as income, but he
did not report the $1,200 monthly stipends as income on his
2006, 2007, or 2008 tax returns. The county also did not in-
clude Beavers’ monthly stipends in Beavers’ W-2s.
10                                                   No. 13-3198

    Beavers’ tax expert, Barry Gershinzon, was prepared to
testify that in his opinion, the county should have known
that Beavers was taking these stipend payments as income
and should therefore have included these payments as in-
come on Beavers’ W-2s. As with the evidence of Beavers’ cor-
rective actions, the district court ruled that the evidence of
the county’s supposed obligation with respect to these sti-
pends was relevant (and thus admissible) only upon a show-
ing that Beavers knew of that obligation at the time he com-
pleted his tax returns and relied on his W-2s as an accurate
statement of his income. Beavers contends that, just as the
government was allowed to introduce circumstantial evi-
dence of his intent to lie to the IRS, so too should he have
been able to offer circumstantial evidence that his failure to
include these stipends on his tax returns was simply a mis-
take.
    Beavers’ argument is unconvincing. In an ordinary case,
it may well be that an individual can reasonably rely on a
W-2 from his employer as an accurate statement of his in-
come. In this case, however, the government explained at
oral argument—and Beavers did not dispute—that Beavers
received his 2007 and 2008 W-2s from the county before he
advised the county each year that he would take the $1,200
monthly stipends as income. This timeline strongly suggests
that Beavers could not have reasonably relied on a document
that he knew understated his income. (And even putting the
timeline aside, it is reasonable for a district court to rule that
a defendant in an “intent” case should not be able to take
advantage of a fact that helps his case if the defendant did
not actually know of the fact at the relevant time. See, e.g.,
United States v. Harris, 942 F.2d 1125, 1132 n.6 (7th Cir. 1991)
(noting that testimony on the ambiguity of tax law on which
No. 13-3198                                                 11

defendant did not actually rely would be irrelevant if the de-
fendant’s subjective belief were at issue).) Nonetheless, here
too the court did not exclude this evidence, but instead con-
ditioned its admission upon a showing of its relevance to
Beavers’ knowledge and reliance. This ruling was well with-
in the court’s “considerable discretion.” United States v. Mar-
shall, 75 F.3d 1097, 1109 (7th Cir. 1996) (citation omitted).
      iii. Right to present a meaningful defense
    Finally, Beavers contends that the district court’s eviden-
tiary rulings deprived him of his constitutional right to pre-
sent a meaningful defense. “Whether rooted directly in the
Due Process Clause of the Fourteenth Amendment or in the
Compulsory Process or Confrontation clauses of the Sixth
Amendment, the Constitution guarantees criminal defend-
ants a meaningful opportunity to present a complete de-
fense.” Crane v. Kentucky, 476 U.S. 683, 690 (1986) (citations
and internal quotation marks omitted)). But while the Con-
stitution “prohibits the exclusion of defense evidence under
rules that serve no legitimate purpose or that are dispropor-
tionate to the ends that they are asserted to promote,”
Holmes v. S. Carolina, 547 U.S. 319, 326 (2006), the Constitu-
tion does not require the admission of irrelevant evidence
(or other types of evidence whose relevance is outweighed
by other important considerations), see Crane, 476 U.S. at
689–90; Delaware v. Van Arsdall, 475 U.S. 673, 679 (1986). As
established above, the district court’s repeated invocation of
the relevance rule was reasonable and amply supported by
precedent. We therefore find no infringement of Beavers’
right to present a meaningful defense.
12                                                   No. 13-3198



     B. The district court’s handling of Beavers’ tax expert
    Beavers next argues that the district court erred in multi-
ple respects in its handling of his tax expert (and sole wit-
ness), Barry Gershinzon. First, Beavers contends that the
court permitted the government to conduct an overly exten-
sive voir dire of Gershinzon, when the court should have ac-
cepted Beavers’ written disclosure as sufficient. Second, Bea-
vers argues that the court improperly limited Gershinzon’s
testimony—most importantly, his opinion as to whether the
checks from Beavers’ campaign fund were loans—because
the court determined that Gershinzon was unreliable. Third,
Beavers maintains that the court erred by instructing the jury
to partly disregard Gershinzon’s opinion. We review the dis-
trict court’s actions for an abuse of discretion. See United
States v. Lee, 502 F.3d 691, 698 (7th Cir. 2007); United States v.
Koopmans, 757 F.2d 901, 906 (7th Cir. 1985).
         i. Background
     We will provide more detailed information below, but a
brief summary of the overall proceedings may be useful. Be-
fore trial, the defense repeatedly provided insufficiently de-
tailed summaries of Gershinzon’s opinions as well as the ba-
ses for his views. These summaries provided lists of general
topics and noted that the defense tax expert would opine
that Beavers complied with the tax code, but did not disclose
further required information. These insufficient disclosures
led the court to allow the government to conduct a voir dire
examination of Gershinzon. In the voir dire, Gershinzon tes-
tified that in his opinion, the $68,763 check from Beavers’
campaign committee to his pension fund was a loan, not in-
No. 13-3198                                                   13

come to Beavers. He also explained that in his opinion, the
100 campaign checks to Beavers were loans and advances.
Gershinzon explained that, in reaching both conclusions, he
relied heavily on Beavers’ statements that he (Beavers) con-
sidered the transactions to be loans. The district court ruled
that Gershinzon could not base his expert opinions on what
Beavers had told him about his (Beavers’) state of mind at
the time of the charged offenses.
    Gershinzon then testified before the jury, where he ini-
tially offered his opinions about whether the pension pay-
ment and 100 checks were loans. However, when Ger-
shinzon’s testimony then veered into topics that were argua-
bly irrelevant, the district court ordered a second voir dire
examination—conducted outside the jury’s presence—to de-
termine the relevance of those statements.
    At this second voir dire, Gershinzon testified that Bea-
vers’ W-2 from Cook County incorrectly omitted the $1,200
monthly stipend from his gross income. He also testified that
he believed Beavers’ W-2 from the City of Chicago was in-
correct because it did not reflect the $68,763 campaign check
to the pension fund “as a reduction of taxable wages.” When
questioned by the government as to whether Beavers’
$68,763 contribution to the pension was “voluntary”—an is-
sue that had tax implications—Gershinzon said the payment
was not mandatory, but he did not feel comfortable opining
whether it was “voluntary” on Beavers’ part.
    At the end of this voir dire, the district court said that it
was “deeply concerned” about Gershinzon’s reliability. The
court noted that Gershinzon could not testify about the basis
for his conclusions without reliance on Beavers’ statements
to him about Beavers’ subjective intent. The court also stated
14                                                No. 13-3198

that Gershinzon could not “follow the rules” and was not
“careful with his assumptions.” As an example, the court cit-
ed Gershinzon’s testimony that many of his clients do not
understand their W-2s, but said that Gershinzon did not
consider the possibility that a former alderman and Cook
County Commissioner could “get a detailed explanation
from high ranking City and County officials as to what was
in his W-2 and how it was arrived at.”
   The court ultimately struck Gershinzon’s conclusions
about whether the transactions were loans, but it still al-
lowed the jury to consider Gershinzon’s testimony with re-
spect to the objective characteristics Gershinzon would look
for in determining whether a transfer was a loan, an ad-
vance, or income.
       ii. The first voir dire of Gershinzon
   Beavers argues that the court should have accepted his
written disclosures as sufficient and that the court thus erred
in permitting the government to conduct an extensive voir
dire of Gershinzon before trial. Federal Rule of Criminal
Procedure 16 required Beavers to provide the government
with a written summary of any expert testimony that he in-
tended to use as evidence at trial. Fed. R. Crim. Pro.
16(b)(1)(C). This summary must “describe the witness’s
opinions, the bases and reasons for those opinions, and the
witness’s qualifications.” Id.
   Before trial, the defense repeatedly gave the government
insufficiently detailed summaries. These summaries provid-
ed a general list of examination topics (e.g., “general ac-
counting principles,” “general tax reporting and bookkeep-
ing”) and one letter noted—in one sentence—that Ger-
No. 13-3198                                                   15

shinzon would testify that in his opinion Beavers complied
with the tax code. The summaries did not provide any more
specific information about Gershinzon’s opinions or the ba-
ses therefore. We agree with the district court that the sum-
maries were “sketchy on details” and that the voir dire was
an appropriate remedy. In fact, Beavers arguably chose that
course. (During a break in the voir dire, defense counsel
said, “Your Honor gave us a choice of either submitting
documents or voir dire. I think we chose – we chose the voir
dire… .”) And in any event, Beavers must—but cannot—
show prejudice from the court’s decision to allow the voir
dire, see United States v. White, 582 F.3d 787, 804 (7th Cir.
2009), because he was not entitled to surprise the govern-
ment with ill-defined expert testimony, see United States v.
Hoffecker, 530 F.3d 137, 185 (3d Cir. 2008) (noting that Rule 16
seeks “to minimize surprise that often results from unex-
pected expert testimony, reduce the need for continuances,
and to provide the opponent with a fair opportunity to test
the merit of the expert’s testimony through focused cross-
examination.” (quoting Rule 16 Advisory Committee Notes
(1993 Amendment))). We therefore reject Beavers’ argument
that the court abused its discretion on this score.
      iii. Limits on Gershinzon’s testimony
    Beavers next disputes the district court’s various limita-
tions on Gershinzon’s testimony. “We review a district
court’s decision to admit or exclude expert testimony for
abuse of discretion,” keeping in mind that screening evi-
dence “is a function squarely within the purview of the trial
judge.” Lapsley v. Xtek, Inc., 689 F.3d 802, 809 (7th Cir. 2012).
We can conceptualize some of the limitations as state-of-
16                                                 No. 13-3198

mind limitations, others as relevance limitations, and still
others as reliability limitations.
    We begin with state-of-mind limitations. First, the district
court ruled that Gershinzon could not base his expert opin-
ions on what Beavers had told him about his (Beavers’) state
of mind at the time of the charged offenses. This limitation
was proper. Otherwise, Beavers could have gotten highly se-
lective and favorable statements of his before the jury with-
out having to face cross-examination. Later, the district court
also ruled that Gershinzon could not testify as to whether he
(Gershinzon) believed the 100 checks were loans. The court
reasoned that such testimony would violate Rule 704(b) of
the Federal Rules of Evidence, which prohibits expert wit-
nesses in a criminal case from opining as to whether the de-
fendant had the mental state necessary for the charged
crime. As the judge explained, “[t]he relevant state of mind
is whether defendant intended to treat withdrawals from his
campaign coffers as income or as loans. The expert cannot
state an opinion on this issue.” For Gershinzon to have ad-
dressed this issue would have been the equivalent of opining
on whether Beavers had the “willfulness” necessary for a tax
offense. See United States v. Windfelder, 790 F.2d 576, 582 (7th
Cir. 1986). We accordingly find no abuse of discretion in this
limitation.
    Next, the relevance limitations prohibited Gershinzon
from testifying about issues that were not relevant absent
testimony or other evidence connecting them to Beavers’
state of mind at the time of the charged offenses. For exam-
ple, the court barred Gershinzon from offering his opinion
that Cook County erred by omitting the $1,200 monthly sti-
pend payments to Beavers. As explained above, this testi-
No. 13-3198                                                 17

mony was irrelevant absent evidence that Beavers knew of
and relied on the county’s alleged obligation. Similarly, the
defense sought to ask Gershinzon about a form that Beavers
received from the pension fund in early 2008, as part of the
defense’s attempt to show that Beavers’ $68,763 pension
payment was not income. The court prohibited Gershinzon
from testifying about this form because Beavers received it
in 2008, so it was irrelevant to Beavers’ state of mind in 2007
when he filed his 2006 tax return. The court’s relevance limi-
tations were therefore appropriate. (And where Gershinzon’s
testimony was relevant, the court permitted it. For instance,
Gershinzon testified about accounting principles; about the
purpose of certain tax forms; about how tax professionals
disagree on the proper tax treatment of certain transactions;
about the differences between income, loans, and advances;
and about which records he would consider in determining
whether a transfer was income, a loan, or an advance.)
    We turn now to the court’s reliability limitations. Recall,
the court’s determination as to Gershinzon’s reliability ulti-
mately resulted in the court’s finding Gershinzon unreliable
and instructing the jury to partly disregard Gershinzon’s tes-
timony—including, importantly, his opinions as to whether
the $68,763 pension payment and the 100 checks were loans
or income.
   The court found Gershinzon unreliable for multiple rea-
sons. Crucially, the court found that Gershinzon “[wa]s not
careful with his assumptions,” and those “assumptions have
overtaken at least the minimum neutrality an expert is sup-
posed to have.” As noted above, one assumption was that,
because many of Gershinzon’s clients do not understand
their W-2s, it apparently followed that a high-ranking public
18                                                No. 13-3198

official (with access to advisors) was in the same position.
The court also criticized Gershinzon’s assumptions because
Gershinzon relied on his conversations with Beavers in
forming assumptions and ultimately conclusions about the
proper tax treatment of the transactions at issue in this case.
For instance, in concluding that the $68,763 pension pay-
ment was a loan, Gershinzon relied in substantial part on
Beavers’ statement to Gershinzon that Beavers considered it
a loan. Similarly, in opining that the 100 campaign checks to
Beavers were loans and advances, Gershinzon also relied on
Beavers’ statements to him. Even though the court had in-
structed Gershinzon not to rely on Beavers’ statements, Ger-
shinzon explicitly referenced those statements, indicating to
the court that Gershinzon could not get Beavers’ statements
“out of his [own] mind… . He can’t follow the rules.” Ger-
shinzon was also unable to point to portions of the tax code
to support his assertions about the tax treatment of various
payments, including the pension-fund payment. Thus,
stripped of Beavers’ statements, Gershinzon’s most im-
portant opinions lacked meaningful support.
    Gershinzon also was unable to answer basic questions
about the topic of his testimony. Specifically, during the sec-
ond voir dire, the government asked Gershinzon about the
basis for his opinion that the City of Chicago should have
deducted Beavers’ lump-sum pension payment from his
gross income for 2006. Gershinzon acknowledged that Bea-
vers’ pension payment was not mandatory, but was unable
to say whether it was “voluntary,” because he could not tes-
tify to Beavers’ state of mind. The prosecutor clarified that
this was not a state-of-mind question; rather, a letter gave
Beavers three options, and Beavers selected the option that
maximized his pension benefits. Nonetheless, Gershinzon
No. 13-3198                                                         19

would not say that Beavers’ choice was “voluntary.” After
considerable back-and-forth between the prosecutor and
Gershinzon, the court eventually said, “[a] step which is not
compelled is a step which is voluntary.”
    We “give the district court wide latitude in performing its
gatekeeping function and determining both how to measure
the reliability of expert testimony and whether the testimony
itself is reliable.” Bielskis v. Louisville Ladder, Inc., 663 F.3d 887,
894 (7th Cir. 2011). In light of the foregoing analysis—which
indicates that Beavers’ expert relied on irrelevant considera-
tions, made questionable assumptions, and may have lacked
expertise about certain germane subjects (including relevant
portions of the tax code)—we find that the district court
properly exercised its discretion. Moreover, the court still
allowed Gershinzon to testify as to the objective characteris-
tics he would look for in determining whether a particular
transfer was income, a loan, or an advance. As a result, Ger-
shinzon’s analytical methodology was presented to the jury,
even if his particular conclusions were not.
       iv. Jury instruction about Gershinzon’s conclusions
    As noted, after Gershinzon testified, the district court in-
structed the jury to disregard his opinions as to whether the
relevant transactions were loans, advances, or income. How-
ever, the court also instructed the jury that it could consider
Gershinzon’s testimony about his methodology in determin-
ing whether a particular transfer is a loan versus income.
Beavers argues that the court’s wording was inappropriate
because it included a reference to the government expert’s
testimony; according to Beavers, this instruction “direct[ed]
the jury to disregard the defense expert but to consider the
government’s expert.” Contrary to Beavers’ argument, the
20                                                    No. 13-3198

instruction expressly told the jurors that they could “consid-
er Mr. Gershinzon’s testimony, as well as the testimony of
the government’s [expert] witness, David Weiner, regarding
facts and circumstances relevant in deciding whether a par-
ticular check is a loan, advance, or income.” Beavers’ argu-
ment is therefore unpersuasive, and the court’s instruction
was well within its discretion.
     C. Jury instruction about the definition of a loan
    Next, Beavers contends that the district court incorrectly
instructed the jury on the definition of a “loan.” We review
the legal accuracy of a jury instruction de novo, but we eval-
uate the particular phrasing for abuse of discretion. United
States v. Dickerson, 705 F.3d 683, 688 (7th Cir. 2013).
     Beavers wanted the following instruction:
     When a taxpayer receives a loan, he incurs an obliga-
     tion to repay that loan at some future date. Because of
     this obligation, the loan proceeds do not qualify as in-
     come to the taxpayer. When he fulfills the obligation,
     the repayment of the loan likewise has no effect on his
     tax liability.
Beavers’ proposed instruction quotes the Supreme Court’s
language in a tax case, C.I.R. v. Tufts, 461 U.S. 300, 307 (1983).
The district court instead gave the following instruction,
which the government proposed:
     When a taxpayer receives a loan, he incurs an obliga-
     tion to repay that loan. Because of that obligation to
     repay, loan proceeds do not constitute income. The
     transfer of money from one party to another consti-
     tutes a loan only if, at the time of the transfer, the par-
     ties to the transaction intend that the person who re-
No. 13-3198                                                    21

   ceives the money actually will be obligated to repay
   it.
   In determining whether the defendant has received
   particular funds as a loan or as income, you should
   consider all of the facts and circumstances surround-
   ing the defendant’s receipt of the funds.
Both instructions are correct statements of the law. Both con-
vey that loan proceeds are not income because the taxpayer
has incurred a genuine obligation to repay the loan.
    Nonetheless, Beavers argues that the district court’s in-
struction was erroneous for two reasons. First, he says that
the court was wrong to include the word “actually” in in-
structing the jury that a transfer of money is a loan only if
“the person who receives the money actually will be obligat-
ed to repay it.” (emphasis added). Beavers states that the
word “actually” is “superfluous” because an obligation to
repay a loan means an actual obligation to repay that loan.
Appellant Br., 28. But superfluity is not error. By pointing out
that an obligation is an actual obligation, Beavers concedes
that the court’s statement of the law is correct. The court’s
inclusion of an additional (perhaps unnecessary) term for
emphasis does not transform a correct statement of the law
into an incorrect one, and it falls well within the court’s dis-
cretion. Relatedly, Beavers argues that the court’s defining a
loan as an “actual obligation” implied that the parties’ sub-
jective intent to repay is not enough, and that some tangible
obligation (like a promissory note) is required. But the in-
struction simply does not say that. Rather, it conveys that the
recipient must actually intend to repay, which is legally ac-
curate and consistent with case law. See, e.g., Tufts, 461 U.S. at
307 (using the phrase “true loan”); Crowley v. C.I.R., 962 F.2d
22                                                   No. 13-3198

1077, 1082 (1st Cir. 1992) (using “bona fide loan”); Frierdich v.
C.I.R., 925 F.2d 180, 185–86 (7th Cir. 1991) (using both “true
loan” and “bona fide loan”); Moore v. United States, 412 F.2d
974, 978 (5th Cir. 1969) (using “bona fide loan”).
    Second, Beavers argues that the district court erred by in-
structing the jury that something is a loan only if the parties
intend it as such at the time of the transfer. Beavers raised this
objection after the instruction was given, so we review his
claim only for plain error. See United States v. Natale, 719 F.3d
719, 729 (7th Cir. 2013). We will reverse only if there was an
obvious error that affected Beavers’ substantial rights,
and that error seriously affects the fairness or integrity of ju-
dicial proceedings. United States v. Marcus, 560 U.S. 258, 262
(2010). In this case, it is not “obvious” that any error has oc-
curred, especially because the instruction was probably cor-
rect. See, e.g., Geftman v. C.I.R., 154 F.3d 61, 68 (3d Cir. 1998)
(“For ‘disbursements to constitute true loans there must
have been, at the time the funds were transferred, an uncon-
ditional obligation on the part of the transferee to repay the
money, and an unconditional intention on the part of the
transferor to secure repayment.’”) (quoting Haag v. C.I.R., 88
T.C. 604, 615–16 (T.C. 1987), aff’d, 855 F.2d 855 (8th Cir. 1988)
(table)); Todd v. C.I.R., 101 T.C.M. (CCH) 1603 (T.C. 2011)
(“[T]he Court gives the promissory note little weight. This
factor indicates the parties did not intend to establish a debt-
or-creditor relationship at the time the funds were ad-
vanced.”), aff’d, 486 Fed. App’x 423 (5th Cir. 2012). We there-
fore reject all of Beavers’ challenges to the jury instruction
about the definition of a loan.
No. 13-3198                                                   23



   D. Fair cross-section claim
    Finally, Beavers alleges that his right to a jury made up of
a fair cross-section of the community was violated because
none of the fifty prospective jurors were African-American
males. Beavers raises both a statutory claim, based on the
Jury Selection and Service Act of 1968, 28 U.S.C. §§ 1861, et
seq., and a constitutional challenge based on the Sixth
Amendment.
       i.   Background
    The panel of potential jurors in this case was drawn pur-
suant to the Plan for Random Selection of Jurors of the Unit-
ed States District Court for the Northern District of Illinois in
effect at the time of trial. The panel was comprised of ap-
proximately fifty potential jurors, four of whom were Afri-
can-American females. Three of the four African-American
prospective jurors were seated, two as jurors, and one as an
alternate. The fourth was excused for cause because she
worked as a tax preparer for H&R Block. After jury selection
commenced, Beavers objected to the fact that no African-
American men were included, and argued that this violated
Batson v. Kentucky, 476 U.S. 79 (1986). Beavers requested that
the panel be dismissed and replaced with a new one or, al-
ternatively, that the panel be supplemented with additional
prospective jurors. The district court declined both requests.
It noted that the relevant question was how the panel was
assembled by the jury office, and said that if Beavers wished
to make an argument about that office’s methodology, he
could investigate the issue.
24                                                No. 13-3198

    Beavers made no further requests for relief at the time;
the jury was empaneled and the trial commenced. After his
conviction, Beavers raised the fair cross-section issue again
in his post-trial motions, arguing that the absence of African-
American males in the panel was the product of “systematic
exclusion.” The district court denied Beavers’ motion on the
grounds that (1) it was untimely; (2) no claim or evidence of
error in the administration of the plan was presented; (3) Af-
rican-American males are not a recognized distinctive group;
and (4) there was no evidence that the composition of the
venire was brought about by any illegality or unfairness.
      ii.   Statutory claim
     The Jury Selection and Service Act provides, “No citizen
shall be excluded from service as a grand or petit juror in the
district courts of the United States on account of race, color,
religion, sex, national origin, or economic status.” 28 U.S.C.
§ 1862. A statutory challenge must be made by motion “be-
fore the voir dire examination begins, or within seven days
after the defendant discovered or could have discovered, by
the exercise of diligence, the grounds therefor, whichever is
earlier.” 28 U.S.C § 1867(a). The motion must also contain “a
sworn statement of facts which, if true, would constitute a
substantial failure to comply with the provisions of this ti-
tle....” 28 U.S.C § 1867(d). This is “the exclusive means” by
which a violation of the Act may be raised. 28 U.S.C.
§ 1867(e).
   It is undisputed that Beavers did not file a motion before
the voir dire examination began, which is the relevant mo-
ment in this case. Instead, Beavers orally objected during the
voir dire examination. He also did not provide the required
“sworn statement of facts.” 28 U.S.C § 1867(d). Thus, he
No. 13-3198                                                    25

waived any statutory challenge. See United States v. Phillips,
239 F.3d 829, 841 (7th Cir. 2001) (“Defendants’ failure to
make a motion in a timely manner and failure to provide ev-
idence, other than oral observations as to the lack of statisti-
cal proportionality, precluded a statutory challenge.”) (cita-
tions omitted).
      iii.   Constitutional claim
    Beavers next raises a constitutional challenge to the com-
position of the jury pool, which we review de novo. United
States v. Neighbors, 590 F.3d 485, 491 (7th Cir. 2009). “The
Sixth Amendment secures to criminal defendants the right to
be tried by an impartial jury drawn from sources reflecting a
fair cross section of the community.” Berghuis v. Smith, 130
S. Ct. 1382, 1387 (2010). To make a prima facie showing that
the fair cross-section requirement has been violated, a de-
fendant must show that: (1) the group allegedly excluded is
a distinctive group in the community, (2) 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) this underrepresentation is due to
systematic exclusion of the group in the jury selection pro-
cess. Duren v. Missouri, 439 U.S. 357, 364 (1979); Neighbors,
590 F.3d at 491.
    Beavers did not develop an argument in his opening brief
as to why African-American men constitute a distinctive
group in the community. Women are a distinctive group, see,
e.g., Duren, 439 U.S. at 364, as are African Americans, see, e.g.,
Neighbors, 590 F.3d at 491. But the parties have cited no cases,
and we have found none, addressing whether African-
American men constitute a distinctive group under Duren.
We have clearly set out the standards by which we decide
26                                                 No. 13-3198

whether a group is “distinctive” for Duren cross-section
claims, see United States v. Raszkiewicz, 169 F.3d 459, 463 (7th
Cir. 1999), but Beavers did not conduct that analysis or even
cite that case until his reply brief.
    Beavers waived this issue because he did not address this
question of first impression in detail in his opening brief. See
Mahaffey v. Ramos, 588 F.3d 1142, 1146 (7th Cir. 2009) (“Per-
functory, undeveloped arguments without discussion or cita-
tion to pertinent legal authority are waived.”). His approach
prevented the opposing party from having the opportunity
in its brief to respond and fully air the arguments on the
other side. We express no view on the merits of Beavers’
waived argument.
    We also find that if Beavers sought to make a separate
argument under the Equal Protection Clause, he waived this
argument as well. His brief on appeal seems to argue that
the district court committed an equal protection violation in
handling jury selection as it did, because around the time of
Beavers’ trial, another judge in the same district ordered a
new panel when the original jury pool contained only one
African-American male. However, Beavers did not develop
his legal theory and cited no cases in support of it. Again,
this constitutes waiver. E.g., United States v. Holm, 326 F.3d
872, 877 (7th Cir. 2003).
                       III. Conclusion
     We AFFIRM William Beavers’ conviction.
