This case presents two questions of general significance:
1. What is the meaning of the term “willfully” in former section 19405, subdivision (a)(1), of the Revenue and Taxation Code (now section 19705, subdivision (a)(1), of the same code; hereafter former section 19405(a)(1))?
2. Is the misdemeanor offense defined in former section 19401, subdivision (a), of the Revenue and Taxation Code (now section 19701, subdivision (a), of the same code; hereafter former section 19401(a)) an offense necessarily included within the offense defined in former section 19405(a)(1)?
The majority resolves the first issue by holding, in part I of its opinion, that a defendant acts “willfully,” as that term is used in former section *67919405(a)(1), only if the defendant voluntarily and intentionally violates a known legal duty. (Maj. opn., ante, at pp. 660, 666.) The majority resolves the second issue by holding, in part II of its opinion, that the misdemeanor offense defined in former section 19401(a) is an offense necessarily included within the offense defined in section 19405(a)(1). (Maj. opn., ante, at p. 670.) To reach the latter conclusion, the majority also holds that the felony offense defined in former section 19405(a)(1) requires, as one of its elements, that the information in the tax return, statement, or other document be actually false. (Maj. opn., ante, at pp. 667, 670.) I agree with each of these holdings.
But I disagree with most of the majority opinion’s part III, in which the majority applies these holdings to determine whether in this proceeding defendant Johnny Ardean Hagen was properly convicted of the felony offense defined in former section 19405(a)(1). Here, the majority concludes: (1) the trial court’s error in misdescribing for the jury the mental state required by former section 19405(a)(1) was harmless and does not require reversal of Hagen’s convictions (maj. opn., ante, at pp. 670-671); (2) the evidence at trial is sufficient to support a finding that defendant had the required mental state (id. at pp. 671-672); and (3) in light of the evidence, the trial court was not required to instruct the jury on the necessarily included misdemeanor offense defined in former section 19401(a) (maj. opn., ante, at pp. 672-673).
I agree that sufficient evidence was presented at trial to support a jury determination that defendant Johnny Hagen acted with the required mental state of willfulness. But the jury never made this determination because the erroneous jury instructions failed to present the issue for the jury’s resolution, and this error may not be dismissed as harmless on this record. I conclude also that the trial court’s instructions to the jury were erroneous not only, in misdescribing the mental element of the offense defined in former section 19405(a)(1) but also in failing to provide the jury with the option of convicting Hagen of the necessarily included offense defined in former section 19401(a). In my view, these errors require reversal of Hagen’s judgment of conviction and a remand for retrial.
I
Former section 19405(a)(1) states that a person commits a felony if that person “[wjillfully makes and subscribes any return, statement, or other document, that contains or is verified by a written declaration that it is made under the penalties of perjury, and that he or she does not believe to be true and correct as to every material matter.” (As amended by Stats. 1993, ch. *680826, § 6 and repealed by Stats. 1994, ch. 1243, § 58; see now § 19705, italics added.) The majority correctly construes the term “willfully” in former section 19405(a)(1) as meaning that in committing the proscribed act— making and subscribing a materially false tax return—the person voluntarily and intentionally violated a known legal duty.
In this case, the jury’s verdict convicting defendant Johnny Hagen of three counts of violating former section 19405(a)(1) was based on his failure to report as income, on three consecutive joint state income tax returns for himself and his wife, certain funds that his wife had embezzled from her employer. The jury returned these verdicts after the trial court, in its instructions to the jury, failed to correctly explain the meaning of “willfully” in former section 19405(a)(1). The trial court told the jury that “willfully” in this context means “with a purpose or willingness to commit the act or to make the omission in question.” Under the court’s instruction, the jury was not required to determine whether Hagen knew he had a legal duty, when preparing and executing each of the joint state income tax returns, to report embezzled funds as income. Under the court’s instruction, it was sufficient that Hagen intentionally signed and submitted a return that failed to include the embezzlement proceeds in the reported income.
As the majority recognizes, the trial court’s instruction is erroneous because it misdescribes an element of the offense. As the majority also recognizes, this misdescription of an element of the offense is federal constitutional error subject to the harmless error standard that the United States Supreme Court enunciated in Chapman v. California (1967) 386 U.S. 18 [87 S.Ct. 824, 17 L.Ed.2d 705, 24 A.L.R.3d 1065], Under that standard, the essential inquiry “is not whether, in a trial that occurred without the error, a guilty verdict would surely have been rendered, but whether the guilty verdict actually rendered in this trial was surely unattributable to the error.” (Sullivan v. Louisiana (1993) 508 U.S. 275, 279 [113 S.Ct. 2078, 2081, 124 L.Ed.2d 182], original italics.)
As I have explained in separate opinions in previous cases, there are three common circumstances in which a reviewing court may conclude that a jury verdict is “surely unattributable to the error” in misdescribing an element of an offense. These circumstances are: “(1) when the jury has necessarily resolved the omitted factual question under other properly given instructions, (2) when some factual finding the jury has made is the functional equivalent of a finding on the omitted factual question (because no rational jury could find the fact actually found without also finding the omitted fact), and (3) when the defendant admitted or affirmatively conceded the omitted factual question.” (People v. Breverman (1998) 19 Cal.4th 142, 194 [77 Cal.Rptr.2d *681870, 960 P.2d 1094] (dis. opn. of Kennard, J.); see also People v. Flood (1998) 18 Cal.4th 470, 548, 550-554 [76 Cal.Rptr.2d 180, 957 P.2d 869] (dis. opn. of Kennard, J.).)
None of these circumstances is present here. No jury instruction correctly presented to the jury the question whether defendant Johnny Hagen knew, when reporting income on his state income tax returns, that he had a legal duty to include stolen funds that he or his wife had received. The jury did not make any factual finding that may properly be regarded as the functional equivalent of a finding that Hagen was aware of this legal duty. Nor did Hagen admit or affirmatively concede that he was aware of this legal duty at the relevant times.
To justify its harmless error conclusion, the majority first observes, accurately, that the court instructed the jury to find defendant Johnny Hagen guilty of the offense defined in former section 19405(a)(1) only if Hagen, when he signed and submitted the tax returns, “did not believe [the returns] to be true and correct as to every material matter.” The majority then reasons, correctly, that in light of this instruction, the jury’s guilty verdict necessarily includes a finding that Hagen did not believe the tax returns were true and correct as to every material matter. Finally, the majority asserts, incorrectly, that this implied finding necessarily implies a further finding that Hagen knew of his legal duty to report the embezzlement proceeds. (Maj. opn., ante, at pp. 670-671 [stating that “had the jury harbored reasonable doubt as to whether the Hagens knew of their reporting obligation, it would not have found beyond a reasonable doubt that they did not believe their returns to be true and correct as to every material matter”].) Stated another way, the majority apparently bases its conclusion that the instructional error was harmless on the proposition that a finding that Hagen did not believe the tax returns were true and correct as to every material matter is the functional equivalent of a finding that Hagen knew he had a legal duty to report embezzlement proceeds as income on his state tax returns.
That proposition is, as the majority elsewhere acknowledges, false: intentionally signing a tax return while lacking a belief that a tax return is true and correct as to every material matter is not functionally equivalent to voluntarily and intentionally violating a known legal duty. The majority correctly explains the relationship this way: “Lack of belief in the return’s correctness may not be precisely equivalent to knowledge of its falsity; the prosecutor in a given case might at least argue that a taxpayer who recklessly failed to discover the truth regarding information demanded on a return and who, for that reason, did not know the return to be false, nonetheless did not ‘believe [the return] to be true and correct.’ [Citation.] A taxpayer, moreover, *682might knowingly omit information from a tax return in the mistaken belief that he or she was not required to report that information. Such a taxpayer, arguably, would not believe the return to be entirely ‘true and correct.’’ ” (Maj. opn., ante, at p. 665, italics added.) Thus, the majority, to justify its conclusion that the instructional error was harmless, is forced to contradict its own reasoning.1
The most that can be said here is that the prosecution presented circumstantial evidence from which a reasonable juror could have inferred that defendant Johnny Hagen knew of his legal duty to include unlawfully obtained funds in his reported income. But this is not enough to establish that the instructional error was harmless. It is not enough because “[i]n the words of Justice Scalia, ‘misdescription of an element of the offense . . . deprives the jury of its factfinding role’ and thus is ‘not curable by overwhelming record evidence of guilt.’ (Carella v. California (1989) 491 U.S. 263, 270 [109 L.Ed.2d 218, 225, 105 S.Ct. 218] (conc. opn. of Scalia, J.).” (People v. Harris (1994) 9 Cal.4th 407, 457 [37 Cal.Rptr.2d 200, 886 P.2d 1193] (conc. & dis. opn. of Kennard, J.).)
I disagree also with the majority’s conclusion that the trial court did not have to instruct the jury on the misdemeanor offense defined in former section 19401(a) as an offense necessarily included within the offense charged (that is, violation of former section 19405(a)(1)) because “[t]he record here contains no substantial evidence of the lesser offense.” (Maj. opn., ante, at p. 672.) To find defendant Johnny Hagen guilty of the misdemeanor, the jury would have had to find beyond a reasonable doubt *683that he underreported income on his tax returns while at the same time entertaining a reasonable doubt that he acted willfully or without believing that the returns were accurate. (Ibid.) Unlike the majority, I conclude that a reasonable juror could make these findings on the evidence presented.
In a criminal prosecution for a tax offense containing the element of willfulness, the government has the burden of proving “that the law imposed a duty on the defendant, that the defendant knew of this duty, and that he voluntarily and intentionally violated that duty.” (Cheek v. United States (1991) 498 U.S. 192, 201 [111 S.Ct. 604, 610, 112 L.Ed.2d 617].) A defendant’s knowledge of the duty may be established by direct evidence of the defendant’s awareness of relevant tax statutes, regulations, court decisions, administrative rulings, or any contents of the tax return forms and accompanying instructions that state the applicable legal duty. (Id. at p. 202 [111 S.Ct. at pp. 610-611].) Alternatively, or additionally, the required knowledge may be established by circumstantial evidence, including evidence of a defendant’s “general educational background and expertise” (U.S. v. Fletcher (2d Cir. 1991) 928 F.2d 495, 501) and evidence that a defendant “deliberately closed his eyes to what would otherwise have been obvious to him” (U.S. v. Fingado (10th Cir. 1991) 934 F.2d 1163, 1166). Thus, if a defendant claims to have been innocently mistaken about a tax reporting duty, the prosecution may refute the claim with evidence that the ■ defendant “was aware of a high probability that his understanding of the tax laws was erroneous and consciously avoided obtaining actual knowledge of his obligations.” (Ibid.)
The record here contains no direct evidence that defendant Johnny Hagen was aware of tax statutes, regulations, court decisions, administrative rulings, or tax form instructions stating that illegally obtained funds were reportable as income for tax purposes. The evidence on this issue was entirely circumstantial. Hagen had been employed by the California Highway Patrol for over 20 years, but there was no evidence that his duties ever included investigation of tax offenses or that he had ever received any training in that area. On the contrary, it appears that he served as a patrol officer, not an investigator.
The record shows that the tax returns that formed the basis of Johnny Hagen’s convictions were prepared by a fellow California Highway Patrol officer, Richard Contreras, based upon documents and information that Hagen and his wife supplied to Contreras during an interview. There is no evidence that Contreras explained to them during the interview that illegally obtained funds were reportable income or that he explained the concept of reportable income in a way that would necessarily have included such funds. *684Contreras testified he asked Hagen and his wife to tell him “all the income that they received from various jobs or interest or dividends, other income, business income.” He could not remember the exact words he used. He usually asked his clients to tell him about “all income” or “any other income,” but he may have inquired about wages and “whatever other income outside of that that was earned in that particular year.” (Italics added.) They did not, of course, tell him they had received and spent funds Hagen’s wife had embezzled from her employer.
As a result of some highly publicized prosecutions, the requirement that illegally obtained funds be reported as income for tax purposes is widely known. (Cf. Bucy, Criminal Tax Fraud: The Downfall of Murderers, Madams and Thieves (1997) 29 Ariz. St. L.J. 639.) But this knowledge is not universal, and I do not consider it beyond the realm of reasonable possibility that a California Highway Patrol, officer who performed only patrol duties would be unaware of this duty. Likewise, defendant Johnny Hagen’s failure to discuss the question with a fellow officer who prepared his taxes may suggest, but does not conclusively demonstrate, that he was either aware of the duty to report embezzled funds or aware of a high probability that the embezzled funds were reportable income and consciously avoided obtaining actual knowledge of his obligation. It is reasonably possible that Hagen construed his fellow officer’s statements as meaning that reportable income included only certain gifts and funds that were lawfully earned, and not funds obtained unlawfully.
Considering all of the relevant circumstantial evidence, a reasonable juror could have inferred that defendant Johnny Hagen knew he had a legal obligation to report all income, including theft proceeds, but the circumstantial evidence was not so strong or overwhelming as to make this inference inescapable or to preclude a reasonable juror from rejecting the inference and giving Hagen the benefit of a reasonable doubt. Thus, the state of the evidence at trial was such that a reasonable juror could have found Hagen guilty of the lesser but not the greater offense. This being so, the trial court through its instructions should have given the jury the option of convicting Hagen on the lesser offense.2
*685II
In this case, the jury that found defendant Johnny Hagen guilty of violating section 19405(a)(1) was never asked to determine whether Hagen voluntarily and intentionally violated a known legal duty when he executed the false tax returns. Although the evidence at trial was sufficient to permit a reasonable juror to infer that he did, the federal Constitution, as authoritatively construed by the United States Supreme Court, does not permit a reviewing court to substitute its assessment of the strength of the evidence for a missing jury determination on an ultimate fact necessary for a criminal conviction. Accordingly, I would reverse the judgment of the Court of Appeal and remand the matter to that court with directions to reverse Hagen’s convictions so that his guilt or innocence of the charged offense might be determined by a properly instructed jury. In the alternative, if the prosecution so elected, Hagen’s convictions should be reduced to the necessarily included misdemeanor offense defined in former section 19401(a). (See Pen. Code, § 1260; In re Brown (1998) 17 Cal.4th 873, 891-892 [72 Cal.Rptr.2d 698, 952 P.2d 715].)
The petitions of both respondent and appellants for a rehearing were denied January 20, 1999. Kennard, J., was of the opinion that the petition of appellants should be granted.
In a footnote (maj. opn., ante, at p. 671, fn. 10), the majority insists there is no contradiction. The majority claims that “[n]o contradiction exists between the statement that two elements of an offense are, in general, not identical or coextensive, and the statement that on the facts of a particular case the jury could not reasonably find one without finding the other.” But the majority never explains, so far as I can determine, what specific evidence in the trial of this case takes it out of the general rule that a finding of one mental element (lack of belief that the return is true and correct) does not compel a finding of the other (voluntary and intentional violation of a known legal duty). Specifically, the majority identifies no evidence that would preclude a reasonable juror from finding both that Johnny Hagen lacked a belief that his federal tax returns were entirely true and correct (because he knew he had not included the illegally obtained funds when listing his income) and that Johnny Hagen did not intentionally violate a known legal duty (because he did not know that he had a legal duty to report illegally obtained funds).
The only evidence the majority mentions in this connection is the testimony of the Hagens’ tax preparer, Richard Contreras, that he asked Johnny and Patricia Hagen about “other income” and that they failed to mention the illegally obtained funds. But Johnny Hagen’s failure to discuss these funds with a fellow California Highway Patrol officer is readily explainable by an unwillingness to risk criminal prosecution for the misapropriation; it does not necessarily imply knowledge of the legal duty to report the misappropriated funds as income on federal tax returns.
In a footnote (maj. opn., ante, at p. 673, fn. 11), the majority states that it “would have been pure speculation” for a jury to conclude that Johnny Hagen “knew about the money but believed he was not required to report it because it was illegally obtained.” This conclusion would require speculation, according to the majority, because of “the lack of any evidence suggesting Johnny failed to report the stolen funds because of ignorance or mistake as to the tax law.” (Ibid.) The main flaw in the majority’s reasoning is its assumption that Johnny Hagen had the burden of coming forward with affirmative evidence of his own ignorance of the relevant legal duty. Because knowledge of the legal duty was an element of the offense, *685it was the prosecution’s burden to prove Johnny had that knowledge. Thus, to obtain a favorable verdict Johnny did not need to persuade the jury that he entertained the mistaken belief; he needed only to raise a reasonable doubt in the jurors’ minds that he had the required knowledge of the legal duty to report illegally obtained funds as income on federal tax returns. Given the inconclusive state of the prosecution’s evidence on this issue, a reasonable and properly instructed juror might have entertained such a reasonable doubt.