
    ESTATE OF James A. ELKINS, Jr., Deceased; Margaret Elise Joseph, and Leslie Keith Sasser, Independent Executors, Petitioners-Appellants, v. COMMISSIONER OF INTERNAL REVENUE, Respondent-Appellee.
    No. 13-60472.
    United States Court of Appeals, Fifth Circuit.
    Sept. 15, 2014.
    
      Harry Max Reasoner, Esq., Juliana Denise Hunter, Jeremy Charles Marwell, Stacey Neumann Vu, Esq., Vinson & El-kins, L.L.P., Houston, TX, Donald Frederick Wood, Vinson & Elkins, L.L.P., Austin, TX, for Petitioners-Appellants.
    Arthur Thomas Catterall, Jonathan S. Cohen, Kathryn Keneally, U.S. Department of Justice, William J. Wilkins, Internal Revenue Service, Washington, DC, for Respondent-Appellee.
    Before STEWART, Chief Judge, and WIENER and COSTA, Circuit Judges.
   WIENER, Circuit Judge:

Petitioners-Appellants Margaret Elise Joseph and Leslie Keith Sasser (“Petitioners”), as Independent Executors of the Estate of their deceased father, James A. Elkins, Jr. (“Decedent”), petitioned the United States Tax Court (“Tax Court”) to review and eventually eliminate the federal estate tax deficiency assessed against the Estate by Respondent-Appellee, the Commissioner of Internal Revenue (“the Commissioner”). That deficiency resulted solely from the Commissioner’s disallowance of the “fractional-ownership discount” applied by the Estate in determining the taxable values of Decedent’s pro rata shares of the jointly stipulated fair market values (“FMV”) of 64 original works of modern and contemporary art in which the Decedent owned only fractional interests at his death.

In the Tax Court, the Commissioner steadfastly maintained that absolutely no fractional-ownership discount was allowable. This presumably accounts for his failure to adduce any affirmative evidence—either factual or expert opinion— as to the quantum of such discounts in the event they were found applicable by the court.

The Tax Court rejected the Commissioner’s zero-discount position, but also rejected the quantums of the various fractional-ownership discounts adduced by the Estate through the reports, exhibits, and testimony of its three expert witnesses— the only substantive evidence of discount quantum presented to the court. Instead, the Tax Court concluded that a “nominal” fractional-ownership discount of 10 percent should apply across the board to Decedent’s ratable share of the stipulated FMV of each of the works of art; this despite the absence of any record evidence whatsoever on which to base the quantum of its self-labeled nominal discount.

We agree in large part with the Tax Court’s underlying analysis and discrete factual determinations, including its rejection of the Commissioner’s zero-discount position (which holding we affirm). We disagree, however, with the ultimate step in the court’s analysis that led it not only to reject the quantums of the Estate’s proffered fractional-ownership discounts but also to adopt and apply one of its own without any supporting evidence. We therefore affirm in part, reverse in part, and render judgment in favor of Petitioners, holding that the taxable values of Decedent’s fractional interests in the works of art are the net amounts reflected for each on Exhibit B of the Tax Court’s opinion. This, in turn, produces an aggregate refund owed to the Estate of $14,359,508.21, plus statutory interest.

I. FACTS AND PROCEEDINGS

A. Issue on Appeal

Despite the size and complexity of Decedent’s estate and the millions of dollars of federal estate tax that it returned and paid, the single question presented in this appeal is narrow, straightforward, and easily posed:

Given the parties’ stipulation of the FMV of each of the works of art in which Decedent owned fractional interests at his death, is the Estate taxable on Decedent’s undiscounted pro rata share of those FMVs, as the Commissioner contended on audit and throughout the Tax Court proceedings, or is it taxable only on those values reduced by fractional-ownership discounts of either (1) a uniform 10 percent each, as held by the Tax Court, or (2) the various percentages that the Estate advanced through the testimony and reports of its expert witnesses?

This entire appeal thus begins and ends with the question of the taxable value of Decedent’s fractional interests in those 64 items of non-business, tangible, personal property that were jointly owned in varying percentages by Decedent and his three adult children at the instant of his death. And, the answer to that one question begins and ends with the proper administration of the ubiquitous willing buyer/willing seller test for fair market value: “Fair market value is defined as ‘the price at which the property would change hands between a willing buyer and a willing seller, neither being under any compulsion to buy or sell and both having reasonable knowledge of relevant facts.’ ”

B. Background

Over the course of their marriage, the Texas-domiciled Decedent and his wife acquired property, both real and personal, essentially all of which fell into the community that existed between them and thus was owned equally by the spouses. Among their many and varied acquisitions were race horses, real estate, interests in closely held businesses, and the said 64 works of art. Their interests in each of those works were retained for the remainder of their respective lifetimes, and that art was displayed in their home or office, or those of their adult children, or, occasionally, at an art gallery, museum, or other public place, albeit not as one cohesive collection or assemblage.

Decedent and his wife each created an inter vivos Grantor Retained Income Trust (“GRIT”) that held title to their respective half interests in three of the 64 works (the “GRIT Art”). After the death of his wife during the terms of the GRITs, and for the remainder of his lifetime, Decedent continued to own his 50 percent interest in those three pieces. His three children received his late wife’s 50 percent interest, 16.667 percent each.

By virtue of a bequest to him from his wife of her 50 percent interest in each of the remaining works and his subsequent disclaimer of a 26.945 percent interest in each, Decedent owned at his death an aggregate 73.055 percent interest in each of those 61 pieces (the “Disclaimer Art”), comprising his original 50 percent and the 23.055 percent interest from his wife’s bequest that remained after deducting the 26.945 percent interest that Decedent disclaimed. That disclaimed interest passed equally to their three children, as their mother’s successor legatees, 8.98167 percent each, and was owned by them at his death.

From time to time following the death of his wife, Decedent and his children voluntarily subjected their respective interests in the works of art to various restraints on possession, partition, and alienation. For example, Decedent’s three children leased their combined 50 percent interests in two of the three pieces of GRIT Art to Decedent, thereby ensuring his uninterrupted possession of those two works. That lease, which was still in effect at Decedent’s death, specified, inter alia, that no co-owner could dispose of his or her interest in a leased work unless joined by all co-owners. The lease also provided that none could transfer or assign his or her “rights, duties and obligations” under the lease without the prior consent of all.

Similarly, Decedent and his children encumbered all 61 items of Disclaimer Art with a “Cotenants Agreement.” Among other things, it spelled out each co-owner’s right of possession for a specified number of days during any 12 month period. More pertinent to this appeal, that agreement prohibited the sale of an interest in any work by a co-owner without the prior consent of all. The one piece of GRIT Art that had not been subjected to the children’s lease to Decedent was eventually added to the list of works covered by the Cotenants Agreement.

C. Proceedings Prior to Tax Court Litigation

Decedent died testate in February 2006. His will was probated in Harris County, Texas, and his three children qualified as co-executors. The Decedent’s Estate Tax Return, Form 706, was filed the following May, reporting a tax liability in excess of $102 million. It listed, among other assets, fractional interests in various items of real and personal property, including his 73.005 percent interest in the Disclaimer Art and his 50 percent interest in the GRIT Art.

Following its audit of the estate tax return, the Internal Revenue Service (“IRS”) accepted net values that remained after deducting various fractional-ownership discounts on essentially every property, real and personal, in which Decedent owned a fractional interest, with but one exception: the 64 works of art. The IRS refused to allow any discount against the Decedent’s pro rata share-his fractional— ownership interest—-of the stipulated FMVs of these works. The IRS assessed an estate tax deficiency of $9,068,266.

D. Tax Court Proceedings

The Estate filed the instant action in Tax Court in July 2010, addressing the single substantive issue of the taxable values of Decedent’s fractional interest in the 64 items of art. By the time of the trial in September 2011, the parties had narrowed a number of issues by joint stipulations. During that one-day trial, six witnesses testified, five of whom were tendered as experts, three by the Estate and two by the Commissioner. The lone non-expert witness was Mrs. Leslie Keith Sasser, Decedent’s daughter and co-executor.

The gist of Mrs. Sasser’s responses to questions on direct, on cross, and from the court, was that she and the other Elkins heirs are strongly attached to the art work, largely sentimentally; that they do not view those works as business assets, primarily because they simply do not need the money; and that they are determined to retain the art for life, ie., they would never be sellers. In response to hypothetical questions from the court, Mrs. Sasser did respond—also hypothetically—that she and presumably the other Elkins heirs might be buyers of Decedent’s interest from a hypothetical willing buyer of that interest, but only if assured by an expert or experts that the price was fair:

THE COURT: Well, would you be willing to pay a pro rata portion ... of the fair market value of the whole piece of art, of each of the ones that you liked, to get that [ ] percent interest that somebody else had?
THE WITNESS: I would be willing to pay if somebody told me that it was a fair price to get that, and I can’t say what is fair.... If somebody who knew the art market assured me that was a fair price, then, yes, I would.
THE COURT: Such as [the Estate’s expert]?
THE WITNESS: Yes, if he assured me that it was a fair price, I would buy it back.

The Estate’s three remaining witnesses were tendered as experts in various aspects of the art’s values and were “received” as such by the court: David Nash as an expert in the art market, the merchantability of art, and the valuation of art; longtime Texas lawyer William T. Miller as an expert on the nature, procedure, time, and costs of actions of partition and enforcement of restraints on alienation litigated on the basis of Texas law; and Mark L. Mitchell as an expert on the valuation of fractional interests in property. The result of the combined, interrelated, and interdependent testimony and reports of these experts was that a proper application of the willing buyer/willing seller test would produce prices for the Decedent’s undivided interests in the works of art substantially below his pro rata share of their respective FMVs. They concluded that any hypothetical willing buyer would demand significant fractional-ownership discounts in the face of becoming a co-owner with the Elkins descendants, given their financial strength and sophistication, their legal restraints on alienation and partition, and their determination never to sell their interests in the art.

By contrast, the Commissioner adduced no expert testimony or other evidence to establish alternative quantums of fractional-ownership discounts, sticking instead to his no-discount position. He did proffer two experts as rebuttal witnesses. The Tax Court “received” one of them, Ms. Karen Hanus-McManus, as an expert appraiser of modern and contemporary art, and the other, Mr. John R. Cahill, as an expert on “art transactions,” but rejected his opinion as “not germane to the issues in this case.” Ms. Hanus-McManus’s testimony is best summarized by her stated conclusion that “there is no recognized market for partial interests] in works of modern art and contemporary art within the secondary markets, with the galleries, and with private dealers.” She would not state, however, that there had never been, or never could be, sales of undivided interests in such art; only that there was no established or “recognized” market for such fractional interests.

The Tax Court issued its opinion in March 2013. Applying the “fictitious willing buyer/willing seller” test to determine the taxable value of Decedent’s undivided interests in the various works of art, the Tax Court ultimately held that such interests are indeed subject to fractional-ownership discounts, but that the price on which the fictitious buyer and seller would finally agree would be the jointly stipulated values reduced by a “nominal” discount of 10 percent only.

II. ANALYSIS

A. Standard of Review

We review appeals from the Tax Court under the same standards which we review appeals from the district courts: de novo for purely legal conclusions; clear error for findings of fact. “Clear error exists if we are left with a definite and firm conviction that a mistake has been made.” We review mixed questions of fact and law de novo. We have long held that “determination of fair market value is a mixed question of fact and law.” As noted in the Estate’s appellate brief, de novo review is appropriate here because “there is a pure question of law imbedded in the valuation calculus.”

B. Framework

1. No Special Deference

Preliminarily, we note two factors that do not come into play in today’s review. First, the Tax Court neither expressed nor implied credibility concerns with any witness, lay or expert, so there are no credibility calls to which we owe special deference. Second, the willing buyer/willing seller test of fair market value truly is ubiquitous: It is not peculiar to federal tax issues. Rather, it is universally employed in myriad legal contexts: civil and criminal; tort and contracts; administrative and insurance. We therefore owe no enhanced deference to the Tax Court’s application of that test.

2. Burden of Proof

As we affirm the Tax Court’s ruling that percentages of fractional-ownership discount are applicable, we need not consider whether it applied the correct burden of proof to reach that conclusion. The second part of today’s inquiry—the correct percentages of fractional-ownership discounts to be applied—presents a somewhat thornier question, at least theoretically. The Tax Court failed to require the Commissioner to bear that burden of proof, even though 26 U.S.C. § 7491 mandates that when, as here, the petitioning taxpayer adduces sufficient evidence to establish the material facts—in this case, the amounts of the discounts—the Commissioner has the burden of refuting such facts and proving different ones. Yet he chose not to adduce any evidence of discount quantum whatsoever, sticking instead to his no-discount position. By contrast, the Estate adduced a plethora of credible and highly probative evidence in support of both the applicability of such discounts vel non and the precise percentages of the discount to be applied to each separate item, as summarized in detail on Exhibit B of the Tax Court’s opinion. Under a proper administration of § 7491’s burden of proof rule, this case should have ended at that point with a judgment for the Estate. But, as shall be seen, the court’s failure to assign the burden of proof of quantum to the Commissioner, although error, makes no difference in the end.

3. Preponderance of the Evidence

After rejecting the Commissioner’s no-discount position, the Tax Court announced that the issue of the burden of proof was not important because it would proceed to determine the appropriate quantum of the discounts based on a preponderance of the evidence. In most trials, “[a] determination of where the preponderance lies requires a measuring and weighing of all the evidence, pro and con.” But, when, as here, the only evidence on an issue is that presented by but one party—and by the one that did not have the burden of proof, at that—there is no “preponderance”: It takes two to tango. As with its misapplication of the burden of proof, however, the Tax Court’s error in announcing its use of the preponderance standard to determine the amounts of the discounts ultimately makes no difference. This is because, having put all of his eggs in the one, no-discount basket at trial, the Commissioner cannot be heard on appeal to question the quantity, quality, or sufficiency of the evidence adduced by the Estate to prove the quantum of the fractional-ownership discounts to be applied. Likewise, given the total absence of substantive evidence from the Commissioner on the issue of quantum, the Tax Court should have accepted and applied the uncontradicted quantums of the partial-ownership discounts that the Estate proved with much more than substantial evidence.

4. Merits

Just as it was obvious to the Tax Court that the Commissioner had no viable basis for rigidly insisting that no fractional-ownership discount was applicable, it should have been equally obvious that, in the absence of any evidentiary basis whatsoever, there is no viable factual or legal support for the court’s own nominal 10 percent discount. This is particularly ironical when viewed in the light of the Tax Court’s correct distinction of this case from, among others, Estate of Scull v. Commissioner, 67 T.C.M. (CCH) 2953 (1994), and Stone v. United States, No. 06-0259, 2007 WL 2318974, at *3 (N.D.Cal. Aug. 10, 2007). The courts in both of those cases awarded nominal discounts, but, as the Tax Court noted, they were only awarded “because of a lack of proof [by the taxpayer] that any greater discount was warranted.” But the exact opposite situation is present here: The Estate, as taxpayer, presented all of the discount evidence, and a surfeit at that, further eschewing the propriety of a nominal discount.

At oral argument, appellate counsel for the Commissioner insisted that the Tax Court’s sole reason for rejecting the discounts determined by the Estate’s experts was their failure to include, or assign sufficient weight to, the Elkins heirs’ strong emotional (“psychic”) attachment to the family’s works of art. Counsel claimed that the court faulted those experts for not concluding that, in and of itself, such psychic attachment would guarantee the hypothetical willing buyer a virtually undis-counted purchase price for the Decedent’s fractional interests, regardless of those heirs’ strong legal and financial positions as putative hostile co-owners with such a hypothetical willing buyer. According to Commissioner’s counsel, this is what led the Tax Court to reject the expert’s discounts out of hand. We disagree with counsel’s cherry picking of the Tax Court’s analysis. But even if counsel’s reading of the Tax Court’s reasoning were correct, it would not absolve that court of clear error.

We have again reviewed the entire transcript of the testimony of the Estate’s experts and their written reports, and we are satisfied beyond cavil that they considered and correctly weighed all factors and characteristics of the Elkins heirs when determining how much a hypothetical willing buyer would pay for Decedent’s fractional interests and thus become a co-owner with them. Those experts took into account both the pros and the cons: the children’s financial astuteness and their net worths; their hypothetical desire to acquire Decedent’s fractional interests if a hypothetical willing buyer should acquire them first, but also their uncontradicted testimony that they would do so only for a “fair price,” as determined by experts (presumably those who testified for them); their legal and financial ability to prevent any hypothetical willing buyer from quickly “flipping” his fractional interests in the art to third parties, particularly given the heirs’ contractual restraints on alienation and partition, as well as their predictable determination to rid themselves of unrelated co-owners regardless of how much time it might take. In sum, we do not read the Tax Court to have rejected the importance of all aspects of the children’s legal relationships to the art other than their “psychic” interests.

We repeat for emphasis that the Estate’s uncontradicted, unimpeached, and eminently credible evidence in support of its proffered fractional-ownership discounts is not just a “preponderance” of such evidence; it is the only such evidence. Nowhere is there any evidentiary support for the Tax Court’s unsubstantiated declaration that “a 10% discount would enable a hypothetical buyer to assure himself or herself of a reasonable profit on a resale of those interests to the Elkins children.” Besides the error in logic of presuming that the hypothetical willing buyer must turn right around and sell his fractional purchases to those heirs, we cannot escape the conclusion that, under the facts of this case and the way the parties tried it, such a determination constitutes reversible error under any standard of review.

5. Correct Quantum of Fractional-Ownership Discounts

In turning to the question of the appropriate quantum of discount, the Tax Court acknowledged that (1) only the Estate’s experts thoroughly analyzed the extent of the discount, (2) the relevant testimony of the Commissioner’s expert Ms. Hanus-Me-Manus boiled down to the single fact that there is no “recognized” market for fractional interests in art, and (3) the several co-owners’ agreements that regulated and restricted alienation, partition, and possession of essentially all of the art are distinguishable from such arrangements among persons engaged in arm’s length, for-profit, art transactions. We agree. In fact, this increases the level of our comfort in concluding that nothing in the testimony of the Commissioner’s experts, in his appellate brief, or in his appellate counsel’s oral argument, detracts from or calls into question the Estate’s unilateral discount evidence.

It is principally within the last few pages of its opinion that the Tax Court’s reversible error lies. While continuing to advocate the willing buyer/willing seller test that controls this case, the Tax Court inexplicably veers off course, focusing almost exclusively on its perception of the role of “the Elkins children” as owners of the remaining fractional interests in the works of art and giving short shrift to the time and expense that a successful willing buyer would face in litigating the restraints on alienation and possession and otherwise outwaiting those particular co-owners. Moreover, the Elkins heirs are neither hypothetical willing buyers nor hypothetical willing sellers, any more than the Estate is deemed to be the hypothetical willing seller.

We acknowledge, of course—as did the Estate’s experts—that a hypothetical willing buyer would be aware of and take into account all aspects of the remaining fractional interests in the art that the Elkins heirs owned, not just the likelihood of their hypothetical desire to acquire the Decedent’s fractional interests in the art from any successful hypothetical buyer thereof. An objective reading of the entirety of those experts’ written reports and their testimony at trial demonstrates beyond question that the heirs’ financial strengths, their out-of-hand rejection of the idea of ever selling their interests, and the time and money that the legal restraints in their arsenal would cost a willing buyer, combine to minimize any effect to the contrary that their “psychic” attachment to the art might otherwise have on the discounts that apply here. To repeat, Mrs. Sasser testified that if, hypothetically, she and her siblings were to purchase such interests, it would only be after first determining from experts that any price was fair and reasonable. And the experts consulted would likely be those persons whom the Tax Court accepted at trial; experts whose ultimate values were based on their substantial discounts below FMV.

Furthermore, like the absence of an established market, the subjective characteristics of the Decedent’s descendants as the owners of the remaining fractional interests would likely cut the other way: A potential willing buyer would undoubtedly insist that his potential willing seller further discount the sales price to account for the virtual impossibility of making an immediate “flip” of the art. Such a fully informed willing buyer would be well aware that, by virtue of becoming a co-owner with the sophisticated, determined, and financially independent Elkins heirs, he could not possibly make such a quick resale—absent a deep discount, that is. And, the situation is only exacerbated by the effect of the various restrictions on partition, alienation, and possession that survived the death of the Decedent.

III. CONCLUSION

We conclude our review by examining the entire record to see if we can determine the correct quantums of the fractional-ownership discounts and thereby avoid remand. When we do so, we conclude that the discounts determined by the Estate’s experts are not just the only ones proved in court; they are eminently correct. We are never comfortable in disagreeing with, much less reversing, a jurist of the experience, reputation, and respect enjoyed by the Tax Court judge whose work product we are called on to review today. Yet, our review of the court’s extensive explication of this case and its ultimate conclusion that the proper discount is 10 percent, leaves us with the “definite and firm conviction that a mistake has been made.”

At bottom, we find nothing in this record or in the Tax Court’s opinion that would justify any conclusion other than that the Estate is entitled to a final determination of the estate tax owed that produces a tax refund calculated on the basis of the fractional-ownership discounts and net taxable FMVs set forth on Exhibit B to the court’s opinion. The record on appeal is sufficient for us to render a final judgment and dispose of the sole issue in this case without prolonging it by remand at the cost of more time and money to the parties. Accordingly, we (1) affirm the Tax Court’s rejection of the Commissioner’s insistence that no fractional-ownership discount may be applied in determining the taxable values of Decedent’s undivided interests in the subject art work; (2) affirm the Tax Court’s holding that the Estate is entitled to apply a fractional-ownership discount to the Decedent’s ratable share of the stipulated FMV of each of the 64 works of art; (3) reverse the Tax Court’s holding that the appropriate fractional-ownership discount is a nominal 10 percent, uniformly applied to each work of art, regardless of distinguishing features; (4) hold that the correct quantums of the fractional-ownership discounts applicable to the Decedent’s pro rata share of the stipulated FMVs of the various works of art are those determined by the Estate’s experts and itemized on Exhibit B to the Tax Court’s opinion; and (5) render judgment in favor of the Estate for a refund of taxes overpaid in the amount of $14,359,508.21, plus statutory interest in a sum to be agreed on by the parties, based on the timing of the payment of that refund to the Estate, all as jointly stipulated to us by the parties.

AFFIRMED in part; REVERSED in part; and RENDERED. 
      
      . The Estate had applied a fractional-ownership discount of 44.75 percent uniformly to the Decedent's interest in each work of art when preparing the estate tax return, Form 706. It did so based on the appraisal of Sotheby's, Inc. and the report of Deloitte L.L.P. As the IRS disallowed that discount, however, the Estate treated it as a fail-back position in the Tax Court and adduced expert testimony of discrete discounts for the various works.
     
      
      . The Estate and the Commissioner have jointly stipulated this amount as the tax refund that would be due under these circumstances and have further stipulated that they will confer and calculate the proper amount of statutory interest owed if the stipulated refund is ultimately determined to be due and owing.
     
      
      . Anthony v. United States, 520 F.3d 374, 377 (5th Cir.2008) (citing Treas. Reg. § 20.2031-1(b)).
     
      
      . Decedent’s son, who was one of the three co-executors, died unexpectedly in June 2010, after which his two sisters, Petitioners herein, continued to serve as the Independent Executors of Decedent’s estate.
     
      
      . The Commissioner and the Estate eventually stipulated undiscounted FMVs totaling $24,580,650 for the Disclaimer Art and $10,600,000 for the GRIT Art, differing slightly from the appraisal of $23,530,650 for the Disclaimer Art and $9,600,000 for the GRIT Art previously received by the Estate.
     
      
      .The Estate’s petition included additional refund claims that turn on the valuation of the art work, including a greater charitable deduction produced by that valuation and deductions for greater fees and cost of administration than originally projected. Such claims are ancillary to and controlled by the ultimate determination of the taxable value of the art.
     
      
      . The Commissioner appears to have ignored, or been unaware of, the venerable lesson of Judge Learned Hand’s opinion in Cohan: In essence, make as close an approximation as you can, but never use a zero. See Cohan v. Comm’r, 39 F.2d 540, 543-44 (2d Cir.1930).
     
      
      . Emphasis supplied.
     
      
      . Estate of Elkins v. Comm’r, 140 T.C. 86, 2013 WL 892399 (2013).
     
      
      . Green v. Comm’r, 507 F.3d 857, 866 (5th Cir.2007).
     
      
      . United States v. Roussel, 705 F.3d 184, 195 (5th Cir.2013) (citing United States v. Griffin, 324 F.3d 330, 365 (5th Cir.2003)).
     
      
      . Succession of McCord v. Comm'r, 461 F.3d 614, 626 (5th Cir.2006).
     
      
      . Estate of Dunn v. Comm’r, 301 F.3d 339, 348 (5th Cir.2002).
     
      
      . Adams v. United States, 218 F.3d 383, 385-86 (5th Cir.2000).
     
      
      . United States v. Rides, 639 F.2d 1305, 1309 (5th Cir. Unit B Mar. 1981).
     
      
      . Blade’s Law Dictionary defines "preponderance of the evidence” as: "The greater weight of the evidence, not necessarily established by the greater number of witnesses testifying to a fact but by evidence that has the most convincing force; superior eviden-tiary weight that, though not sufficient to free the mind wholly from all reasonable doubt, is still sufficient to incline a fair and impartial mind to one side of the issue rather than the other.” See Blade’s Law Dictionary 1301 (9th ed.2009).
     
      
      .For the first time on appeal, the Commissioner attempts to address the quantum of the fractional-ownership discounts as supporting the Tax Court’s 10 percent discount. It is well settled, however, that we do not consider contentions raised for the first time on appeal. Crawford Prof'l Drugs, Inc. v. CVS Caremark Corp., 748 F.3d 249, 267 (5th Cir.2014).
     
      
      . Indeed, the testimony of Ms. Hanus-Mc-Manus that there is no recognized or established market for undivided interests in art lends support to a greater discount. The absence of an established market would be a factor that a willing buyer would consider as calling for a deeper discount of fractional interests in art. Such absence does not, however, mean that willing buyers and willing sellers of fractional interests in art do not exist and cannot find one another through means other than an established market, e.g., eBay, art galleries, art dealers’ networks, conventions, social networking, and the like.
     
      
      . Green v. Comm'r, 507 F.3d 857, 866 (5th Cir.2007).
     