Dare you buy a Henry Moore on eBay? - Statistics can tell you what to avoid
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Dare you buy a Henry
Moore on eBay?
Statistics can tell you what to avoid
When the rarefied world of modern art sales meets the digital age,
almost anything is possible. You, too, can buy a Henry Moore on
eBay. But it is risky. The old, high-commission auction-houses have
rivals, but you will need statistics to guide you. Joseph Gastwirth
and Wesley Johnson tell you where the fakes may be lurking.
Henry Moore’s sculptures – huge works in bronze
or carved marble – are iconic. The public know them
from museums and public places. Less well known is
that Moore, the pre-eminent British sculptor of the
20th century, produced many smaller-scale sculptures,
drawings, etchings and lithographs, and that these
frequently come up for sale. One perhaps surprising
place to find them is on eBay. Guide prices there range
from £250 to tens of thousands of pounds. And such
eBay Henry Moores are not at all uncommon. On one
day in December 2010, no fewer than five were on offer,
from apparently separate sellers, and all described as
original.
The internet has provided consumers with new
and easy ways to purchase goods – and the commis-
sions charged by an internet auction host are a fraction
of those of the major art houses. But it has allowed
less scrupulous businesses and individuals to offer
poor-quality or mislabelled items. Ideally, before buying
works at auction one would have experts examine them,
Mother and Child II (1983) Cramer, Grant and Mitchinson (CGM) catalogue 672 as is done at the big auction-houses like Sotheby’s and
10 march2011 © 2011 The Royal Statistical Society
because they recently had surgery. The method authentic when it is not, objects that were
also needs at least two evaluators of classifica- described as “similar” to or “related” to Moore
tions or tests of success or failure. Furthermore, were excluded. We analysed only objects that
the evaluations should be independent of each were claimed to be actually by Henry Moore.
other. In the case of screening for DVT, one
test measures the level of antibodies while the
The data and statistical model
other is based on different technologies4.
Here we had our two subgroups – draw- The results of the study were summarized in
ings and sculpture, where questionable works two 2 × 2 tables reporting the matched pair
are common, versus lithographs and etchings, classifications for the two groups of artwork
where they are rarer. In order to obtain a suf- (Table 1). The drawings and sculpture data,
ficient and representative sample of Moore’s as we have said, were combined because the
work, almost all of the objects described as background information indicated that the
having been created by Henry Moore that ap- prevalence of non-genuine items of both types
peared on eBay during the period from March was similar. Furthermore, the fractions of
2005 to November 2007 (239 of them in all) these two items that both evaluators thought
were assessed. We needed not one but two dubious were similar. Table 1 shows, for each
independent evaluators: the first was Stephen group, the items that both evaluators thought
Gabriel, an expert on Moore, and the second questionable; that Stephen Gabriel thought
was one of the authors ( JLG). Both have had questionable but Gastwirth thought genuine;
a long-time interest in Moore’s art and have that Gabriel thought genuine but Gastwirth
Mother and Child VIII (1983) CGM catalogue 678
extensive libraries. A third collaborator, Dr H. thought questionable; and that both evaluators
Hikawa, downloaded the descriptions of each thought genuine.
item, which typically included a digital photo, Two things affect the numbers that ap-
Christie’s, but for items listed on eBay, which and provided the two evaluators with copies. pear in the tables: the actual prevalence of non-
come from all over the world, this is impracti- The files were e-mailed to the first evaluator, genuine objects in each of the two groups, and
cal. One of us ( JLG) has long been interested while the second evaluator was given a printed the accuracy of the evaluators. This is where
in art by Moore. After noticing on eBay a small version. To further ensure the independence having two independent evaluators is so vital:
sculpture, supposedly made by Henry Moore, of the evaluations, the two assessors did not they provide a mutual cross-reference. Suitably
that did not “look right” he checked with discuss any of the art for sale during this statistically treated, each can provide a stand-
friends at the Moore Foundation. period. Because a major objective of the study ard by which to judge the other. Furthermore,
They had received inquiries from buyers is to protect consumers against “misleading” the evaluators’ accuracy has two parts. The first
who have purchased works incorrectly attrib- descriptions, which suggest that an item is is their sensitivity. This is the probability that a
uted to Moore; so the question of estimating
the prevalence of counterfeit art work arose.
From our informal correspondence it Table 1. Assessments of genuineness of Henry Moore’s art offered on eBay from March 2005 to November
appeared that a much higher percentage of 20075
“drawings” or “small sculptures” were dubious
than was the case for signed etchings and Prints Evaluator 2
lithographs (prints). This last detail sug-
gested a statistical approach that we could Questionable Genuine Total
use to estimate the proportion of fake Henry
Moores – or “questionable works”, in the more Evaluator 1 Questionable 6 10 16
cautious language of the art world – that were Genuine 1 149 150
out there.
In medical and social science applications, Total 7 159 166
where even the best method of classification is
not a “gold standard”, the Hui–Walter method1
can be used to estimate the accuracy rates of Sculptures and drawings Evaluator 2
clinical tests2 and survey classifications3. That
Questionable Genuine Total
method requires one to study two subpopula-
tions, with a different prevalence of the trait Evaluator 1 Questionable 59 6 65
in each. The high prevalence group might be
individuals who had symptoms of deep vein Genuine 2 6 8
thrombosis (DVT) while the low prevalence
Total 61 12 73
group consists of individuals at risk of DVT
march2011 11
non-genuine object will be classified correctly interval gives 82% of them questionable. This the data9. The estimated correlation was 0.29,
– that they will spot a fake. The second part clearly means that government agencies con- which is insufficient to result in a serious bias
is their specificity, which is in some ways the cerned with consumer protection are justified in the prevalence estimates.
reverse – that they will know a genuine article in informing the public of potential authentic-
when they see one. These are very far from be- ity issues. In contrast, only 4.1% of the signed
ing the same thing. An evaluator who classified prints appear to be of doubtful authenticity. Implications for buyers of artwork
every item as genuine would have a very high The obvious first lesson is: if you are thinking
specificity, but a sensitivity of zero. of buying a Henry Moore on eBay, buy a print Clearly the results indicate that consumers
If one considers the classification of rather than a drawing or small sculpture. should not take for granted the authenticity of
objects in the framework of classical statistics, While a number of authors have raised works by Moore, and probably other major art-
where the null hypothesis is that the object is questions about the validity of the estimates ists, that are offered on eBay or other internet
genuine and the alternative is that it is not, the from latent class models such as the Hui– sellers, and that they should carefully compare
Type I error equals 1 minus specificity and the Walter7, most of the studies indicate that it is the digital photographs and related informa-
Type II error is 1 minus sensitivity. the estimates of sensitivity and specificity that tion provided by sellers with the correspond-
The Hui–Walter method takes the data are most affected by modest violations of its ing information in the major catalogues. This
of Table 1 and calculates probabilities of assumptions; the estimates of prevalence are also applies to Moore’s prints because several
genuineness for objects in each category and more sturdy. Furthermore, the greater the dif- that were classified as non-genuine were from
calculates also estimates of the accuracies of ference in the prevalence of the characteristic an unsigned version where a questionable
the evaluators. The virtue of the method is that in the two groups, the greater is the robustness signature was added. As in all observational
it gives information both about the evaluators of the prevalence estimate8 – and here our studies, there is a possibility that some impor-
and the evaluated. It assumes that the accuracy difference is indeed great: between fake rates tant covariates, such as provenance or prior
rates of each evaluator are the same for both of 91.5% in drawings and 4.1% in prints lies ownership of the item, were not available. It is
categories of art and that, conditional on the a difference of 87.4%. We may therefore place difficult to think, however, of a realistic covari-
true status of an object, the evaluations are some reliance on our conclusions. The key as- ate that could explain the very low prevalence
independent. Given that, it provides statistical sumption is that each evaluator has the same of genuine drawings and small sculptures. The
estimates of the specificity and the sensitivity of sensitivity and specificity for artworks of both very high proportion of dubious drawings and
each evaluator, and of the fraction of prints and types, and that they are independent. small sculptures by Moore offered on eBay
the fraction of drawings that are questionable. Although we took pains to ensure that indicates that prospective buyers of art by
The results, with their confidence intervals, are the evaluators worked independently, there other major artists, such as Picasso or Chagall,
given in Table 2. are two ways in which a modest degree of should also be very careful.
Although the confidence intervals for the dependence could arise. Some sellers may
accuracy rates overlap, they suggest that the offer multiple objects and, whether by design
Potential applications in legal cases
evaluators had similar but not identical rates of or ignorance, there is likely to be correlation
accuracy. The first evaluator, Stephen Gabriel, in the status of the items put on eBay by the After we began the project we became aware
was more sensitive, detecting more counterfeit same seller. Also, both evaluators probably of several legal decisions in cases where eBay
items, while the second, Joseph Gastwirth, had consulted many of the same definitive cata- was sued for assisting the sale of counterfeit
a slightly higher specificity, correctly classifying logues and books and might have compared products. All the suits involved possible viola-
legitimate items. What is more remarkable is the photograph on eBay with the same “refer- tions of intellectual property and trademark
the estimated prevalence of dubious drawings ence photo”. To check the potential sensitivity infringement, but the legal criteria used in
and sculptures: 91.5% of them are questionable. of the results to possible dependence, a model different nations are not uniform. Moreover,
Even taking the lower end of a 95% confidence allowing for such correlation was also fitted to eBay did have a process that allowed firms to
report counterfeit items. Statistical evidence
had a key role in many of the cases.
In the United States, eBay was found not
Table 2. Maximum likelihood estimates of the two prevalence parameters and accuracy rates of the two
evaluators. Maximum likelihood estimates were obtained using the EM algorithm with standard errors based to have contributed to trademark infringement
on the bootstrap using the program TAGS6 in Tiffany v. eBay10. Tiffany presented a survey
which claimed that about 75% of the items
labelled as its product were counterfeit, while
Parameter Mean 95% Confidence interval
only 5% were surely genuine11,12. The courts
Se1, sensitivity of evaluator 1 (Stephen Gabriel) 0.968 (0.877,0.992) decided that, even though eBay had general
Se2, sensitivity of evaluator 2 (Joseph Gastwirth) 0.913 (0.810,0.962) knowledge that counterfeit Tiffany silver jew-
Sp1, specificity of evaluator 1 0.941 (0.889,0.969) ellery was being sold, it was only required to
Sp2, specificity of evaluator 2 0.995 (0.939,0.999) take action if it had contemporary knowledge
of which particular listings were infringing or
Prev1, fraction of prints that are dubious 0.041 (0.018,0.089)
would infringe in the future. Furthermore, the
Prev2, fraction of sculptures and drawings that are dubious 0.915 (0.818,0.962)
trial court noted significant flaws in Tiffany’s
12 march2011
survey. It was not probability-based, so one amount (at least 30%) of Tiffany jewellery trademark infringement cases. The method
could not calculate a confidence interval for the was counterfeit, this only helped establish that we have used here might be adapted to help
fraction of non-genuine items. Furthermore, eBay had general knowledge that counterfeit monitor the authenticity of items offered for
the search used to identify the items that products were being sold on its site. sale on the internet.
were purchased and examined by two Tiffany In France, however, a study that was
experts included non-silver jewellery as well submitted by Christian Dior and Luis Vuitton
Potential refinements and
as the silver items that were at issue in the estimated that 90% of items allegedly made by
improvements to the study design
case. The sample sizes (186 in 2004 and 139 these designers were not genuine. This study
in 2005) were less than those specified by the was accepted by the court. This estimate is Our work can be regarded as a proof of prin-
survey designer. One reason for this shortfall surprisingly similar to the 91.5% prevalence ciple: it is possible to obtain reasonable esti-
was that Tiffany was unable to purchase some estimate for non-genuine Henry Moore mates of the prevalence of counterfeit items
of the items that were supposed to be in their drawings and small sculptures in our study. even when the evaluators do not examine the
sample. It was quite likely that those “missing Partly on this basis, eBay was found liable for pieces individually. During the time the data
items” had a higher probability of being genu- contributing to trademark infringement. were collected, the evaluators observed that
ine than those that they were able to acquire, Although surveys have been used to some particular art objects came up repeat-
as knowledgeable individual buyers were also estimate the proportion of potential consum- edly, and that items from some particular
bidding for the genuine pieces but not for ers who are “confused” – a polite word for sellers, especially those who sold many items,
the fakes. Finally, Tiffany did not participate “deceived” – as to the source of a product were more likely not to be authentic. The
in eBay’s monitoring programme during this because of the design or packaging or are approach could be improved by incorporat-
time, so that items that could have been re- misled by advertising, statisticians may not ing knowledge that is gained during a first
moved from the site were not. Although eBay’s fully appreciate the potential for using sta- phase, either about the type of items that are
statistical expert agreed that a substantial tistical surveys and studies similar to ours in non-genuine or sellers of those products, into
Two Women Seated on Beach (1984) CGM catalogue 719
march2011 13a second phase study. That study might be a
probability-based buying programme that is
focused on a smaller group of likely sellers of
problematic objects.
When it is possible to obtain a third in-
dependent evaluation the latent class approach
does not require two subpopulations and has
been successfully used to evaluate screening
tests and estimate the prevalence of disease in
animals. The three-evaluator version is well
suited to estimating the prevalence of counter-
feit jewellery, as a second subpopulation with a
low prevalence of fakes might not exist.
One possible limitation of the method is
that an infringing seller might purchase one
expensive handbag, say, make counterfeit ver-
sions, but put a picture of the genuine bag on
the internet. Presumably, a disappointed pur-
chaser would complain to eBay, which would
inform the company about a particular seller
of infringing items. Trademark holders and
consumer protection agencies might still find
a broad-based study or survey that provided
a statistically reliable estimate of the fraction
of counterfeit products sold by internet sites
useful both in legal cases and to inform policy-
makers and the public of the magnitude of the
problem.
References
1. Hui, S. L. and Walter, S. D. (1980) Esti-
mating the error rates of diagnostic tests. Biometrics,
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2. Pepe, M. and Janes, H. (2007) Insights into
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Biostatistics, 8, 474–484. Two Reclining Figures in Yellow and Green (1967) CGM catalogue 74
3. Sinclair, M. D. and Gastwirth, J. L. (1996)
On procedures for evaluating the effectiveness of
reinterview survey methods: application to labor
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(1997) Diagnostic test comparisons in patients Properties of the Hui and Walter and related meth- liability after Tiffany v. eBay. Berkeley Technology
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Hikawa, H. (2011) Estimating the fraction of 9. Dendukuri, N. and Joseph, L. (2001) Economics at the George Washington University,
“non-genuine” artwork by Henry Moore on eBay: Bayesian approaches to modeling the conditional Washington, DC, and Wesley Johnson is Professor of
application of latent class screening test methodol- dependence between multiple diagnostic tests. Statistics at the University of California at Irvine.
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174 (in press). 10. 576 F. Supp. 2d 463 (S.D.N.Y. 2008) and
Acknowledgements
6. Pouillot, R., Gerbier, G. and Gardner, I. 600 F. 3d 93 (2d. Cir. 2010). Grateful thanks are due to the Henry Moore Founda-
A. (2002) “TAGS”, a program for the evaluation 11. Goldwasser, K. (2010) Knock it off: An tion (www.henry-moore.org) for their generosity in
of test accuracy in the absence of a gold standard. analysis of trademark counterfeit goods regulation providing digital images of the artwork. A fuller, more
Preventive Veterinary Medicine, 53, 67–71. in the United States, France and Belgium. Cardozo technical version is to appear in the Journal of the
7. Spencer, B. (2010) When do latent class Journal of International and Comparative Law, 18, Royal Statistical Society, Series A.
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