MEMORANDUM OPINION

JOHN D. BATES, District Judge.

Defendant Gregory Loreng pleaded guilty to two counts of possession of child pornography in violation of 18 U.S.C. § 2252A(a)(5)(B), and, on May 1, 2013, the Court sentenced him to ninety-six months of imprisonment. The government now seeks restitution for two children it alleges were pictured in the images, known by the pseudonyms "Amy" and "Cindy." Loreng opposes the request. The issue of calculating losses for victims of child pornography crimes has generated many decisions in the last few years, and questions related to Amy's restitution requests in other cases are currently pending in the D.C. Circuit and before the Supreme Court. This Court, however, cannot wait for further authority to develop because Loreng is entitled to a final determination of restitution "not to exceed 90 days after sentencing," or by July 30, 2013. See 18 U.S.C. § 3664(d)(5). Accordingly, the Court tackles the issue now and finds that, on this record, no restitution is warranted.

BACKGROUND

Seeking restitution simultaneously with sentencing, the government filed its initial request for restitution on April 23, 2013, merely eight days before Loreng's sentencing hearing, and effectively leaving Loreng one business day to respond. See Sentencing Hr'g Tr. at 4:3-5 (May 1, 2013). Finding that this left inadequate time for Loreng to fully address the voluminous request and that the government failed to follow the procedures set out in 18 U.S.C. § 3664, the Court ruled that the amount of restitution could not be determined at sentencing. The Court set a schedule for supplemental briefing as well as a date for a restitution hearing, which was ultimately held on July 24, 2013.1

In discussing the need to delay the determination of restitution at the sentencing hearing, the Court also noted substantive problems in the government's belated request. The government recognized that the Court could only award restitution for the losses to Amy and Cindy caused by Loreng, but offered the Court limited guidance on how to calculate that amount. To calculate the amount of losses caused by Loreng, the government suggested dividing Amy's and Cindy's total losses by the number of defendants who have been ordered to pay restitution in all cases. The Court warned that it was "skeptical" that the approach "offers [a] principled basis for calculating how much of Cindy's and [Amy's] losses the defendant's acts proximately caused." Sentencing Hr'g Tr. at 6:18-22. The Court noted that if a formula is used, the total number of individuals who committed the crime may be the more appropriate denominator. See id. at 6:22-7:3 ("It is unclear why the losses caused by this defendant are related to the number of successful convictions to date. I don't see the correlation there. Instead, the victims' injuries seem more appropriately related to the number of times that the images have been viewed, whether or not the individuals viewing the images are already or will be successfully prosecuted."). The Court suggested direct evidence the government may provide, and instructed that, "[i]nsofar as the government is urging that the Court adopt some more general theory, ... it is incumbent upon the government to suggest a better formula for calculating damages caused by this defendant." Id. at 7:14-17. Finally, the Court asked the government to provide an "estimate of the number of individuals, whether or not they have been successfully prosecuted, who will access the images in the relevant time frame" just "in case" the Court is ultimately persuaded to adopt a formula based on the total number of viewers. Id. at 7:25, 8:7-9.

In support of its renewed request, the government has submitted a set of restitution materials for both Amy and Cindy. It provided a 2008 economic report, written when Amy was 19 years old, which itemizes Amy's projected total losses at $3,367,854, including post-2008 treatment and counseling expenses and lost earnings. See Amy Restitution Materials [Docket Entry 30-3] at 114 (Apr. 23, 2013).2 The restitution materials also contain a letter from Amy's attorney, her victim impact statement, and an expert psychological report from 2008, supplemented by reports of subsequent evaluations. In its updated request, the government seeks a restitution award of $19,355.48 for Amy, based on its proposed formula of dividing a victim's total losses by the number of defendants convicted for possessing or distributing her images. See Government's Supplemental Req. for Restitution for Amy [Docket Entry 42] at 9 (May 24, 2013) ("Supplemental Amy Req."). As for Cindy, the government provides an economic loss report from 2012, when Cindy was 24 years old, which estimates her losses at $1,185,332, a letter from Cindy's attorney, a victim impact statement, a psychological report, and a vocational assessment. The government seeks $28,222 for Cindy based on the same formula. See Government's Supplemental Req. for Restitution for Cindy [Docket Entry 43] at 9 (May 24, 2013) ("Supplemental Cindy Req."). The probation office concurs in the government's request.

The Amy materials describe the abuse Amy suffered at the hands of her uncle who raped and sexually exploited her when she was a young child to produce images for a child molester in Seattle. See Amy Restitution Materials at 3, 67. The materials address her continued suffering from the underlying abuse, her fear of the uncle who was recently released from prison, her trauma from the fact that the images are out there in the world and that her friends and others might accidentally see them, and the distress from the fact that individuals continue to view these images. A psychologist report explains that Amy "continues to suffer from the ongoing effects of her victimization from child abuse and from the continued use of her image by child pornography viewers, traders, and abusers." Id. at 93-94; see also id. at 67 ("My life and my feelings are worse now because the crime has never really stopped and will never really stop.").

Cindy's materials explain that she was "repeatedly and systematically" sexually abused by her father from infancy until age 12. See Cindy Restitution Materials [Docket Entry 31-3] at 140 (Apr. 23, 2013). The psychologist report details her significant physical and mental health struggles, which began with the abuse and neglect she experience throughout her childhood, and which continue to be significantly affected by her complex relationship with and "conflicting" feelings for her father. Id. at 142-44, 147. They also detail the trauma of discovering, at age 15, that images of the abuse exist and have been disseminated on the internet. Although the materials focus on the effects of the abuse itself, the materials establish that Cindy's "struggle to manage the repercussion of her sexual abuse experience ha[s] been significantly affected by the ongoing actions of those individuals who distribute her pornographic images and those who use her images for deviant sexual excitement." Id. at 150. Further, the "know[ledge] that pornographic pictures of her as a child remain on the internet and continue to be available ... has an enduring negative impact on her emotional stability." Id. Cindy's materials indicate that she felt that "she was being abused again and again" when she received notifications of newly-discovered offenders, and that she has opted out of receiving such notices. Id.

ANALYSIS

The governing restitution statute, 18 U.S.C. § 2259, provides that "the court shall order restitution for any offense under this chapter," which includes child pornography offenses under 18 U.S.C. § 2252A. Section 2259 directs the Court to award "the full amount of the victim's losses." 18 U.S.C. § 2259(b)(1). Losses include costs of medical services, such as psychological care, occupational therapy, and lost income, as well as "any other losses suffered by the victim as a proximate result of the offense." 18 U.S.C. § 2259(b)(3). Interpreting this provision, the D.C. Circuit has held that "restitution awards under § 2259 are limited to harms the defendant proximately caused." See United States v. Monzel, 641 F.3d 528, 537 (D.C.Cir.2011). In determining the proper restitution award for each victim, the Court must hence determine "the amount of [each victim's] losses attributable to [defendant's] offense and order restitution equal to that amount." Id. at 540. "The burden is on the government to prove the amount of Amy's [and Cindy's] losses [defendant] caused." Id.; see also 18 U.S.C. § 3664(e) ("The burden of demonstrating the amount of the loss sustained by a victim as a result of the offense shall be on the attorney for the Government."). The Court resolves factual disputes "as to the proper amount" of restitution "by the preponderance of the evidence." 18 U.S.C. § 3664(e).

Although most federal courts have, like the D.C. Circuit, found a proximate cause requirement in the statute, these courts have differed in how the proximate cause test applies. Compare United States v. Benoit, 713 F.3d 1, 22 (10th Cir. 2013) ("[T]he district court apparently divided the total loss claimed by Vicky, $1,224,694.04, by 222, the number of restitution judgments Vicky had received at the time of the hearing. This implicit calculation does not meet the proximate cause standard we have announced on the record before us."), with United States v. Cantrelle, No. 11-542, slip op. at 19, 2013 WL 1624824 (E.D.Cal. Apr. 15, 2013) (on remand from the Ninth Circuit awarding Amy $17,307.44 and Vicky $2,881.05 by dividing the total award by the number of defendants convicted). Courts in this District may soon get additional guidance on the question, because a case presenting these issues is pending in the D.C. Circuit. See United States v. Monzel, No. 12-3093 (D.C.Cir.) ("Monzel II"). Moreover, the Supreme Court has granted certiorari on the underlying question — whether the statute contains a proximate cause requirement — and, if it adopts the proximate cause test, may provide some guidance on how to apply it. See Paroline v. United States, No. 12-8561.3 This Court has a statutory obligation to determine restitution now. See 18 U.S.C. § 3664(d)(5). Acting now without the benefit of authoritative guidance that may deem certain formulas or approaches sufficient as a matter of law, the Court will approach the task like any factual question, examining the record to determine whether the government met its burden to establish the amount of Amy's and Cindy's losses attributable to Loreng by a preponderance of the evidence.

I. Showing that Amy and Cindy Are Victims of Loreng's Acts

Restitution is paid to the "victim" of a crime of child sexual exploitation. See 18 U.S.C. § 2259(b)(1). A victim is "the individual harmed as a result of a commission of a crime under this chapter." 18 U.S.C. § 2259(c). As courts across the country have found, a child depicted in a pornographic image is a "victim" within the meaning of section 2259(c). Loreng argues that, in this case, the Court has no basis for finding that Amy and Cindy are in fact the children depicted in images that Loreng viewed, and hence that they are "victims" of his crime.

The government describes one image it claims is of Amy and one image purportedly of Cindy, see Supplemental Amy Req. at 9-10; Supplemental Cindy Req. at 9. But it offers no record citation for these descriptions, nor does it offer any evidence to link those descriptions to the victims named. In other cases, the government has established that the individuals seeking restitution were depicted in the images found in the defendant's possession by submitting reports from the National Center for Missing and Exploited Children that examine the images collected from a certain defendant and identify them. See, e.g., United States v. Berk, 666 F.Supp.2d 182, 185 (D.Me.2009). The government here did not submit such a report by the time of the restitution hearing. Pressed as to this omission at the hearing, government counsel acknowledged that there was no evidence in the existing record to tie Loreng to images of Amy or Cindy. But government counsel noted that he has in his possession a National Center for Missing and Exploited Children report that would provide the needed link. He seeks to have the Court consider this report, along with an affidavit from a forensic investigator who viewed the images. Loreng objects to this eleventh-hour request, explaining that he would raise a number of objections if he had time to review the report.

The Court agrees that it is far too late to supplement the record with this key evidence. The government submitted its initial restitution request on April 23, 2013, without including this report. After the Court found this submission dilatory, and gave the government a chance to submit an expanded request, the government filed a supplemental request on May 24, 2013, again without this report. Loreng responded to this request on June 27, 2013, squarely raising the lack of evidence identifying the images. See Def.'s Response to Supplemental Restitution Req. [Docket Entry 46] at 6 (June 27, 2013) ("I. The Government Has Not Established that the Claimants Are in Fact the Individuals Depicted in the Images Possessed by Mr. Loreng."). Although on notice as to the defendant's evidentiary challenge to the "victim" determination, the government chose not to respond to Loreng's filing at all, and only during the July 24, 2013, restitution hearing — mere days before the statutory deadline for a final determination of restitution — sought, for the first time, to submit the needed report. This is far too late for the defendant to respond and for the Court to evaluate new evidence. The government had ample opportunity to provide evidence key to its request, and it has failed to take it. Because the Court declines to consider the report, the Court finds that there is no record evidence that Loreng possessed images of Amy and Cindy. The Court hence has no basis to find by a preponderance of the evidence that Amy and Cindy were victims of Loreng's acts. This alone suffices to deny the government's restitution request.

As will soon become apparent, this is just the first of several fatal failures in the government's evidentiary showing. For the ensuing discussion, however, the Court will assume that Amy and Cindy are "victim[s]" of Loreng's acts within the meaning of section 2259(c).

II. Other Evidentiary Problems as to Amy

The government argues that to measure the losses Loreng proximately caused, the Court should take a victim's total lifetime losses and divide that by the number of defendants convicted to date. Before the Court addresses the government's approach to calculating the amount of Amy's and Cindy's losses, the Court will consider two problems that preclude Amy's recovery even assuming that the government's formula for calculating the losses caused by Loreng is valid.

First, Loreng challenges the evidence of Amy's total lifetime loss, an economic report from 2008 (prepared for a 2009 case involving a different defendant), which estimates Amy's lifetime losses at $3,367,854. He makes two arguments against the report. First, he contends that the report is insufficient because it predates Loreng's May 2012 arrest. Not only, Loreng argues, does the timing mean that better evidence of Amy's projected losses is now available, but "the losses reported by Amy's experts (and the harm described by Amy in her victim impact statement) had already vested as of 2008" so they cannot be caused by Loreng. See Def.'s Resp. to Supplemental Restitution Req. at 11. The Court is unpersuaded that economic reports predating a defendant's conduct are always inadequate. To be sure, such a report may not be the best evidence obtainable, but the government's burden is simply the modest "preponderance of the evidence," and a report estimating future losses in 2008 may well meet this burden. Nor does the report estimate harm that was projected to occur independent of Loreng. Rather, it estimates projected harm, i.e., harm that is expected to occur from all the individuals who possess and distribute Amy's images, although it cannot yet identify these individuals by name. This is akin to a life insurance company projecting that 1,000 customers will die that year, so the total costs in policy payments will be $100,000,000. At the end of the year, $100,000 can be attributed to each deceased customer even though ex ante the company did not know which customers would die. The report then, like a life insurance policy, accounts for Loreng, although his acts are only linked with his name after his arrest.

Unlike Loreng's general arguments about economic reports that predate a defendant's arrest, his specific critique of Amy's economic report is on firm ground. Loreng points out that other record evidence, namely Amy's updated psychologist report, indicates that her progress has exceeded expectations; for instance, while the economic report's estimate of future counseling costs is based on the assumption that she will require weekly counseling sessions through age 81, the record now establishes that Amy's "life significantly stabilized" and she "has now phased down [her therapy sessions] to once a month." Amy Restitution Materials at 90. 106. Given specific evidence that the 2008 projections are no longer accurate, the government had to provide the Court with some basis for reducing the lifetime losses figure in light of these developments. Whether it needed to submit an updated expert report or just a brief supplement indicating how, if at all, Amy's progress should affect the Court's calculations of her lifetime losses, the government should have done something. It did not, leaving the Court to speculate about the actual total loss.

Additionally, Loreng identifies a serious problem with the government's other key figure — the number of defendants convicted of possessing images of Amy. Here, the government contends the correct figure is 174. The sole support for this number is the government's representation based on its own review of the Department of Justice's database that tracks convictions. Although the Court would normally credit such a representation, Loreng notes that the government asserted that "[a]t present, the number of restitution orders payable to Amy is 179" in a brief filed with the D.C. Circuit on February 11, 2013. See Br. for the United States at 14 n. 6, United States v. Monzel, No. 12-3093 (D.C.Cir. Feb. 11, 2013). But restitution has not been requested, let alone awarded, for every defendant convicted of a crime involving Amy's image, so it is difficult to see how the number of restitution orders as of February of this year can be higher than the number of convictions this May. At the restitution hearing, government counsel was unable to explain this discrepancy. Adding to the Court's perplexity, the Fifth Circuit, relying on a report by the National Center for Missing and Exploited Children, noted that there have been "over 3,200 child pornography cases since 1998" involving images of Amy's abuse. In re Amy Unknown, 701 F.3d 749, 752 (5th Cir.2012) (en banc). Given these indications that something is awry, the Court would need more from the government to find that only 174 defendants have been convicted for crimes involving Amy's images.

III. Loreng's Acts As Proximate Cause of the Victims' Losses.

Turning to the heart of the parties' dispute, Loreng argues that the government has failed to establish that his acts proximately caused any of the victims' losses. He points out that the government has not provided any evidence that either Amy or Cindy were aware of his conduct. Indeed, the record indicates that Cindy has opted out of receiving notifications about individuals being prosecuted. See Cindy Restitution Materials at 150. He also notes that, unlike victims in similar cases, neither Amy nor Cindy have provided any statement to the Court saying they were aware of this defendant and that his acts caused them harm. See Ex. A to Joint Submission Regarding Restitution Owed to Vicky at 36, United States v. Kennedy, No. 08-354 (W.D.Wash. Sept. 14, 2012), ECF No. 184 (discussing such evidence submitted for Vicky, another child victim). And while Amy's psychologist report in this case refers to a specific individual, see Amy Restitution Materials at 91 (psychologist report stating that Amy is aware of "current defendant Robert Hedrick" and is "outrage[d]" at his viewing her picture given his "important role in the community"), it says nothing about Loreng.

On the other hand, courts — including the D.C. Circuit — have recognized that "possession of child pornography causes harm to the minors depicted." Monzel, 641 F.3d at 537; see also Ashcroft v. Free Speech Coal., 535 U.S. 234, 249, 122 S.Ct. 1389, 152 L.Ed.2d 403 (2002) ("[A]s a permanent record of a child's abuse, the continued circulation [of a pornographic image] would harm the child who had participated. Like a defamatory statement, each new publication of the speech would cause new injury to the child's reputation and emotional well-being."). The record here indicates that both victims are suffering losses due to the fact that their images are continuing to be viewed, aside from the losses they suffer due to the underlying abuse itself and due to the general distribution of the images. In her victim statement, for instance, Amy says that the continued viewing of her images is "like I am being abused over and over and over again" and "[t]he truth is, I am being exploited and used every day and every night somewhere in the world by someone." See Amy Restitution Materials at 67, 69. And Amy's psychologist report indicates that she "continues to suffer from the ongoing effects of her victimization from child abuse and from the continued use of her image by child pornography viewers, traders, and abusers." Id. at 93-94 (emphasis added). Cindy's psychologist report also indicates that she is "significantly affected by the ongoing actions" of those who "distribute ... and those who use her images for deviant sexual excitement." See Cindy Restitution Materials at 150 (emphasis added). Cindy explains that having photographs of her abuse "on the Internet, presently being viewed by others, it makes it even more impossible to keep [the sexual abuse] in [her] past and move on from it," id. at 166, and describes how traumatic she finds it that "people [she] do[es]n't know are fantasizing about [her] sexually, especially as a child who is supposed to be protected and innocent." Id. It hence appears that both Amy and Cindy suffer from the continued viewing of the images, and that any individual who views one of the images contributes, to some extent, to that suffering and the resulting losses.

The Court need not resolve here whether some defendant-specific evidence (which the government has not provided in this case) is required to establish proximate cause. Because the evidence establishes that the continued viewing of the images, in the aggregate, causes Amy and Cindy losses, and because each instance of child pornography possession causes a part of that loss, the Court will assume that Loreng proximately caused some loss to each victim.4

IV. Amount of Amy's and Cindy's Losses Caused by Loreng.

This brings the Court, at last, to the factual dispute on which the parties focus: the amount of losses caused by Loreng that the government has established. See Catharine M. Goodwin et al., Federal Criminal Restitution § 7:29 ("Even where the court finds that the requisite victim and causation standards for restitution are met, there is yet another, final, step to the analysis that has its own criteria to be met for criminal restitution. The court must ultimately determine whether it is possible to quantify, to any `reasonable certainty,' that portion of the overall harm to the victim that was caused by this defendant's conduct, in order to impose restitution."). Calculating the amount of a victim's losses proximately caused by a defendant's acts can be a challenging task, but a district court cannot deny restitution simply because identifying the correct amount is difficult. Monzel, 641 F.3d at 539-40. Mathematical precision is not required. To award any restitution, however, the Court must find that the government proved "the amount of the victim's loss with some reasonable certainty." Id. at 540 (alteration and internal quotation marks omitted). Where the government has failed to prove that a defendant caused any specific amount of losses with "reasonable certainty," the government has not met its burden, and the restitution award must be denied.

To establish a victim's losses caused by one defendant who viewed an image, the government has two approaches at its disposal: provide direct evidence of the amount of losses caused by the defendant, or provide a reasonable estimate by reasoning backward from the total losses the victim suffered. The government here chose to rely on the second route only. In its supplemental requests for Amy and Cindy, it reasons that the Court should begin with a victim's total provable losses, including those already compensated by other defendants. The Court should then divide that total by the number of defendants to date found criminally responsible for offenses involving the victim's image. The government justifies this denominator by arguing that it distributes a victim's losses among the most culpable and readily definable population of offenders, ensuring that she receives a steady stream of payments without exposing an individual defendant to excessive liability. After using the formula to arrive at a baseline award, the government suggests that the Court can consider an array of factors, such as whether the defendant distributed the image, stalked the victim, or had a large number of images, to determine any upward (but apparently not downward) adjustment. The government does not request an adjustment in this case. See Supplemental Amy Request at 7-9; Supplemental Cindy Request at 7-9.

The government's formula (about which the Court already expressed hesitation at the sentencing hearing) is subject to a thorough attack in Loreng's response. But the government did not file a reply to address these concerns, nor did it make a dent in Loreng's reasoning at the restitution hearing. The proposed formula suffers from two flaws: it begins with the total amount of Amy's and Cindy's losses, instead of the portion of Amy's and Cindy's losses caused only by continued viewing of the images, and it employs an arbitrary method of apportioning the total among those who contribute to it.

Amy's and Cindy's total losses are "an aggregation of the acts of the person who committed and filmed her assault, those who distributed and redistributed her images, and those who possessed those images." United States v. Burgess, 684 F.3d 445, 460 (4th Cir.2012). The record here reveals the impact of all these acts. Amy's and Cindy's victim statements describe harm from the underlying abuse. See also Monzel, 641 F.3d at 538 ("[Amy] would have suffered tremendously from her sexual abuse regardless of what [this defendant] did."). The record as to Cindy, in particular, focuses overwhelmingly on the losses from the severe trauma of the abuse itself and her relationship with her father who perpetrated that abuse. And both Amy and Cindy suffer from the images' distribution. Amy's statement attributes substantial harm to the fear that her friends or others will accidentally see the photos, i.e., to the fact that the photos have been distributed and continue to circulate, as distinct from the fact that they are continuing to be viewed. See Amy Restitution Materials at 68 ("I am worried that when my friends are on the internet they are going to come across my pictures and it fills me with shame and embarrassment."); see also Cindy Restitution Materials at 150 (Cindy's "know[ledge] that pornographic pictures of her as a child remain on the internet and continue to be available ... has an enduring negative impact on her emotional stability" (emphasis added)). Hence, it is evident that, although continued viewing of the images adds to the victims' losses, beginning with all the victims' losses, including those from the abuse and the initial distribution of the images is the wrong starting point here — Loreng's acts and his existence as a potential viewer of the images played no part in the victim's abuse or the images' distribution.5 By seeking to divide the full losses evenly among a universe of defendants, the government ignores the role of the abusers and initial distributors, the very people who are most culpable and who most directly caused Amy's and Cindy's losses.6

The Court cannot correct this overbreadth for the government because the record contains no basis for ascertaining the proportion of the losses ascribable to the images' viewing rather than the abuse and the initial distribution that put the images out into the world. In other cases, the government has offered evidence on this question, such as a doctor's expert report that, "[b]ased upon my evaluation of this child, at least 50% of her physical, emotional and psychological damages as I have outlined in this case are directly due to the fact that others continue to download, trade and possess images of her abuse." United States v. Olivieri, No. 09-743, 2012 WL 1118763, at *9 (D.N.J. Apr. 3, 2012). But here, the government presented no such evidence. The Court thus has no basis to separate out losses due to Amy's or Cindy's initial abuse (let alone those from initial or continued distribution of the images) from losses due to the fact that images are being viewed.

The government's showing also fails at the apportionment stage. Assuming (counterfactually) that the total loss figure the government uses as a numerator is the total loss attributable to the continued viewing of the images, the government must still establish the portion of that loss caused specifically by Loreng. The government's formula divides the total losses by the number of defendants convicted at the time of the request, and then considers factors, such as distribution, stalking, or possession of numerous images, to depart upward from that baseline.

The government's proposed formula makes no sense as a measure of harm caused by this defendant, which is independent from the number of successful convictions to date. See Sentencing Hr'g Tr. at 6:22-7:3 ("[COURT:] It is unclear why the losses caused by this defendant are related to the number of successful convictions to date. I don't see the correlation there. Instead, the victims' injuries seem more appropriately related to the number of times that the images have been viewed, whether or not the individuals viewing the images are already or will be successfully prosecuted."). The record as to both Amy and Cindy indicates that it is the fact that an image is viewed, rather than the fact that a defendant is apprehended and convicted, that causes the harm. This is especially evident for Cindy, who has opted not to receive notifications when an individual is arrested. Indeed, there are record indications that the losses from a viewer who remains at large, one who may stalk the victim or abuse other children, are higher than from a viewer who is apprehended and convicted. See Amy Restitution Materials at 73 (describing Amy's fear that individuals will use her images to "groom" other children into these acts); Cindy Restitution Materials at 3 (same); Amy Restitution Materials at 92 (expressing fear that people "on the street" will "recognize" her); Cindy Restitution Materials at 150 ("Every man that possesses these pictures represents another person ready to abuse her, a person willing to abuse her today. Given this reality, she does not know how she can ever feel safe.").

The only distinction between viewers convicted and those who remain at large that supports giving less weight to the latter is the feasibility of entering a restitution order against a non-apprehended person. But this difference says nothing about causation; it simply makes it more likely that Amy and Cindy will recover their total losses from all wrongdoers. And the very holding of Monzel is that Amy and Cindy are entitled to their total losses caused by a particular defendant, i.e., to their losses as Loreng's victims rather than their losses as victims of other offenders' acts. See 641 F.3d at 537. That Amy and Cindy are unlikely to recover losses from unconvicted viewers hence cannot be a reason to find Loreng liable for a greater restitution award by estimating that he caused a greater share of the harm. Rather, a principled formula for discerning the portion of the loss defendant caused would be to divide the total loss (past, present, and future) resulting from the continued viewing of the images by the number of individuals (apprehended or not) who engaged or will engage in the act of viewing an image.

Moreover, even assuming (again counterfactually) that a compensation-based approach instead of a causation-based approach were appropriate, the government's specific formula — which turns on the number of defendants who have been convicted as of the date of the restitution request — leads to arbitrary awards. The first person to be convicted is liable for the full amount of the losses, the second for half that amount, and so on. Even after many individuals have been convicted, the formula yields arbitrary results. Supposing the total losses are $1,000,000, the 100th person to be convicted would be liable for $10,000 — presumably on the reasoning that $10,000 * 100 would compensate the victim fully. But the 101st person would be liable for $9,901 ($1,000,000/101). The $9,901 figure is meaningless — if the first hundred defendants paid their restitution award, the victim would already be more than fully compensated. Indeed, under the government's proposed formula, the first defendant pays all (100% of the losses), the second pays half (for total restitution awards of 150% of total losses), the third pays one third (for total restitution awards of 183.3% of total losses), and so on. The formula hence varies hugely based on the point in time restitution is sought, awards arbitrarily more than total losses, and results in wildly different figures divorced from a defendant's culpability or his effect on the victim. But see Monzel, 641 F.3d at 540 ("[T]he district court must rely upon some principled method for determining the harm Monzel proximately caused." (emphasis added)).

The government's answer to all these problems is to argue that the "formula" is a baseline, and the Court can take into account factors to deviate upward from the starting point. But that simply kicks the can down the road — the government has provided no principled method for taking into account these factors to "adjust" the baseline loss derived from the formula. And it is hardly a defense of the formula to say that when the results become too arbitrary to stomach, the Court can deviate; the examples of its wildly disparate results illustrate that the formula lacks any theoretical mooring, whether as a method for determining the ultimate reward or the baseline figure.

The government's showing in this case rests entirely on a deeply problematic formula, one that the Court warned the government may fail as a principled measure of restitution. See Sentencing Hr'g Tr. at 6:18-24. What is even more stark, perhaps, is what the government chose not to do. The government has not provided direct evidence of losses caused by Loreng's acts, for instance evidence that either Amy or Cindy were aware of those acts and required an additional counseling session or missed a day of work as a result. See Berk, 666 F.Supp.2d at 191-92 ("If, for example, an expert had originally opined that `Amy' or `Vicky' would need monthly counseling sessions and, upon learning of [defendant's] possession of her images, she would instead need weekly sessions, then the Court could order restitution for this additional loss. In fact, if there was evidence that the Victims had to attend even one additional counseling session due to [defendant's] actions, then restitution may have been appropriate. If, after being notified of [defendant's] offense, one of the Victims had to miss a day of work, then restitution may have been appropriate.").

Nor has the government provided affirmative evidence of harm from the viewing of a single image as a general matter, such as a statement from Amy or Cindy providing her subjective assessment of the effect the viewing of a single image has on her, or in the form of an expert report by a clinical psychologist who, based on an evaluation of Amy or Cindy, or on his general familiarity with victims of child pornography, could provide an estimate of the average loss caused by one viewer to the victim depicted in the image.7

Declining to provide direct evidence, the government chose to rely on a formula for estimating the loss Loreng caused by reasoning back from the total losses. But in doing so, it ignored the concerns the Court raised at the sentencing hearing about a denominator based on defendants convicted rather than all individuals who committed the act. See Sentencing Hr'g Tr. at 6:22-7:3. And it declined, despite the Court's request, id. at 7:14-17, to provide "a better formula." And, again ignoring the Court's express request at the sentencing hearing, id. at 7:25, 8:7-9, it failed to provide an estimate of the total number of individuals who can be expected to view Amy's and Cindy's images.

Because all the Court has is an unprincipled formula, the Court lacks a non-speculative basis for awarding restitution. Indeed, it appears that the government has not expanded the record (aside from adding supplemental psychologist reports that say nothing on the amount question) from the Amy restitution request that the D.C. Circuit considered in Monzel. On that record, the D.C. Circuit stated that the government "made no showing as to the amount of Amy's losses traceable to [the defendant]," Monzel, 641 F.3d at 537, and — noting that "there is relatively little in the present record to guide [the district court's] decisionmaking" — encouraged the "government [to] do more [on remand] to aid the district court." Id. at 540. Yet the government failed to improve on its scant Monzel showing here. "Without more specific evidence, any award of restitution would be an arbitrary calculation based on speculation and guess work, at best." United States v. Solsbury, 727 F.Supp.2d 789, 796 (D.N.D.2010); see also United States v. Mahone, 453 F.3d 68, 74 (1st Cir.2006) ("an award cannot be woven solely from the gossamer strands of speculation and surmise" (internal quotation marks omitted)); United States v. Chow, 760 F.Supp.2d 335, 344 (S.D.N.Y.2010) ("[T]he rule of reasonableness does not permit courts to impose a random restitution amount.").

As the above discussion indicates, however, the Court's findings about the government's showing in this case do not mean that a restitution request for a possessor of child pornography can never succeed. The government had many options — some of which it has successfully pursued in other cases. It could have presented direct evidence of these victims' losses specific to Loreng, or it could have presented affirmative evidence of the loss these victims or an average victim will experience from the viewing of the victim's image. Or, the government could have relied on a formula to reason backwards from total loss. But to use the latter approach, the government would have had to provide an estimate of the total lifetime losses for Amy and Cindy attributable to the viewing of child pornography as distinct from the underlying abuse and the general distribution of the images. It could have done this via, for instance, an expert report like the one submitted in Olivieri, No. 09-743, 2012 WL 1118763, at *9. The government would also have had to provide evidence from which the Court could estimate the total number of individuals who contribute to this total, i.e., the approximate number of people expected to view the images over time. While that number cannot be quantified with precision, a reasonable estimate could be made by working with the National Center for Missing and Exploited Children. See In re Amy Unknown, 701 F.3d at 752 (noting that the Center "reports that it has found at least 35,000 images of Amy's abuse among the evidence in over 3,200 child pornography cases since 1998"). The Court would then have determined Loreng's contribution to the total viewing-based loss by dividing Amy's and Cindy's lifetime losses attributable to viewing by the total number of individuals expected to view the images. Finally, the government could have suggested an alternative formula that would be a principled measure of the losses caused by Loreng, and provided the evidence needed under that approach.8

This, then, raises the question of why the government did not do more. It may be that a more record-based approach would lead to a restitution award for a single viewing that is a very low figure, a figure that is unsatisfying, and perhaps one that seems erroneously low given the gravity of the underlying crime. Suppose for instance the following record was presented. An economic loss report establishes that Amy's total lifetime losses are $10,000,000. Expert testimony by a psychiatrist who evaluated Amy establishes that half of the losses are attributable to the effects of the underlying abuse, and $5,000,000 is attributable to the distribution of the images on the internet. Expert testimony further indicates that half of those losses, or $2,500,000, is attributable to Amy feeling continued exploitation from the actual viewing of the images, rather than the fact that the images continue to circulate. Finally, suppose that the National Center for Missing and Exploited Children estimated that Amy's images are likely to be viewed 10,000 times. On such a record, the loss attributable to one viewer of one image would be $2,500,000/10,000, or $250 — the total loss from all the viewings divided by the number of viewings. (The loss caused by Amy's abuser, by contrast, would be $10,000,000, and the loss caused by the initial distributor would be $5,000,000.) Indeed, faced with this hypothetical, government counsel conceded at the restitution hearing that, on such a record, $250 would be the correct restitution award for an individual viewer. See Restitution Hr'g Tr. at 18:9-10, 19:8-10 (July 24, 2013). Yet there is reason to think here that this hypothetical may over estimate Amy's losses from one viewer — the total lifetime loss figure is higher in the hypothetical than in the economic loss report; and although the record contains no evidence as to the total number of viewers of the images, there is reason to think the number may be even higher than 10,000. See In re Amy Unknown, 701 F.3d at 752.9

Considering the challenges of proceeding without a formula and the risk that a formula may result in extremely low awards, some courts have noted that 18 U.S.C. § 2259 is unworkable. See, e.g., United States v. Kennedy, 643 F.3d 1251, 1266 (9th Cir.2011) ("The underlying problem is the structure established by § 2259: it is a poor fit for these types of offenses."). But workability may not be the problem. As discussed above, there are a number of routes the government could have chosen in this case, and many costly pieces of evidence, such as expert reports by a psychologist, can be reused for many defendants. Still, although a restitution award against child pornography possessors is available and practically attainable, an accurate award may be unsatisfying.

The likelihood of ending up at a low figure may reflect a more fundamental difficulty with seeking to compensate victims of these horrible crimes by the possessors of images. See Berk, 666 F.Supp.2d at 190 (noting that "victims and the Government have only recently begun seeking restitution from the end-users or possessors of child pornography" rather than those who committed the abuse or produced the images). While viewing child pornography is a grave crime that warrants severe punishment — a gravity that Loreng's ninety-six month sentence reflects in this case — it may turn out that the viewing of a single image where tens of thousands are circulating does not (without more) cause significant loss to the victim.10 Insofar as section 2259 seeks to award a victim the losses caused by a defendant, fully compensating her for that loss (her loss as Loreng's victim, rather than as a victim of other people's acts), it does work, even though a given loss figure may be small.

Section 2259 fails, however, to comport with the desire to compensate a victim for the full scope of the horrific abuse she suffered and the continued violations she experiences due to the acts of others. This result does not indicate that this Court has gone astray in interpreting section 2259's requirements, but, rather, reflects the difficulty of not having all the individuals responsible for Amy's or Cindy's losses before the Court. Indeed, when section 2259 is considered as to all the individuals collectively responsible for Amy's or Cindy's losses, it leads to expected results. The abuser himself proximately caused the full amount of the losses; individuals who initially distributed the images proximately caused all the losses not attributable to the abuse itself. Operating against the full universe of wrongdoers, then, section 2259 supports restitution awards that more than cover a victim's total losses.

To be sure, awarding the full amount of losses against a handful of individuals and then awarding much smaller totals against later distributors and even tinier totals against possessors may be troubling from the perspective of actual compensation — many perpetrators will never be caught and many others will be insolvent, so a victim is unlikely to be awarded a significant portion of these restitution awards and to recover on the ones that are entered. Congress may well wish to avoid this result, for instance by providing for statutory damages of a fixed amount per image. Many courts have called on Congress to do just that. See Burgess, 684 F.3d at 460 ("[W]e add our voice to the Ninth Circuit in Kennedy in requesting that Congress reevaluate the structure of the restitution statute in light of the challenges presented by the calculations of loss to victims in the internet age."); see also Kennedy, 643 F.3d at 1266. But this possibility does not mean that section 2259 is broken or — more saliently — that courts have erred by failing to divine an ideal formula for determining an accurate and satisfying award; it may just mean that losses caused by the possession of a single image are low, and that society wants these offenders to pay for somewhat more than the losses they caused. Such a judgment, in turn, is a quintessentially legislative one that must be made by Congress, not this Court.11

While the Court emphatically rejects the government's approach to calculating the amount of losses caused by one viewer, a word should be said about the defendant's approach as well. At the restitution hearing, Loreng's counsel rejected the aggregate loss model, i.e., any calculation based on a formula. Instead, Loreng would require in each case a victim statement reflecting knowledge of the particular defendant, a psychological report evaluating a victim's response to each defendant, an economic report produced after the defendant's acts, and an expert report from a statistician that takes into account a multitude of factors, including each defendant's offender characteristics. See Restitution Hr'g Tr. 37:1-24. Creating this array of evidence for each defendant would cost many times more than any restitution that would be recovered from an occasional viewer of the images. Demanding all this evidence would hence make section 2259 restitution requests entirely impractical where the expected restitution award is small, effectively preventing section 2259 from applying to possession and even some distribution cases. As explained above, the Court doubts that anything this costly and unworkable is required. The government needs better evidence to meet its burden, and any formula must reflect losses caused, but the government does not need to reinvent the wheel in each case.

CONCLUSION

Regardless of what a perfect record would reveal in this case, the fact remains that the record here is anything but perfect. The government has failed to make a showing as to critical questions. It has failed to establish that Loreng viewed or even possessed an image of either Amy or Cindy; it has failed to support the total economic loss figure for Amy; and it has failed to establish the number of defendants convicted for possessing or distributing Amy's images. For both Amy and Cindy, the government has provided evidence that falls far short of "reasonable certainty" as to the amount of their losses from Loreng's conduct. The government failed to meet its burden through and through — and not for lack of warning by the Court. Accordingly, the Court must award no restitution in this case.