[caption id="" align="alignright" width="454"] Value of Bert Cooper's Rothko, 1960's and Today[/caption]

We have talked before about error in art, and the two types of errors that can occur--false positives and false negatives. At the time, we discussed this problem from the perspective of scholars and museums. Today, we consider the problem from the perspective of buyers. How much should you pay for a famous painting such as a Rothko?

In statistics and decision sciences, to answer this question we must decide on a "loss function"--what do you lose if you over- or under-estimate the true value? For an art buyer, undervaluing the painting is actually an advantage. Overvaluing it, on the other hand, can lead to significant losses, so we would penalize that more in our loss function.

Consider this example from Jay Livingston:

Maybe Shamus can find some solace in a Times story that ran the same day about a Manhattan art gallery that had been selling expensive forgeries.  I know that in art, quality and value are two very different things.  Still, I had to stop and wonder when I read about

Domenico and Eleanore De Sole, who in 2004 paid $8.3 million for a painting attributed to Mark Rothko that they now say is a worthless fake. One day a painting is worth $8.3 million; the next day, the same painting – same quality, same capacity to give aesthetic pleasure or do whatever it is that art does – is “worthless.”*  Art forgery also makes me wonder about the buyer’s motive.  If the buyer wanted only to have and to gaze upon something beautiful, something with artistic merit, then a fake Rothko is no different than a real Rothko.  It seems more likely that what the buyer wants is to own something valuable – i.e., something that costs a lot. Displaying your brokerage account statements is just too crude and obvious.  What the high-end art market offers is a kind of money laundering. Objects that are rare and therefore expensive, like a real Rothko, transform money into something more acceptable – personal qualities like good taste, refinement, and sophistication.

Andrew Gelman responds:

I’m in sympathy with Livingston’s general point—I too am happy to mock people who happen to have more money than I do—and Rothko’s art has always seemed pretty pointless to me. I mean, sure, it can look fine on the wall, but it hardly seems like something special to me.

But I think Livingston’s going too far, in that he’s forgetting the natural human desire not to get ripped off.

If stories of art rip-offs become more common, we can expect the price paid for (even real) paintings to go down. This will not be because their underlying value--aesthetically, as a piggy bank, or as a way of showing off--has decreased, but because buyers have adjusted their loss function to account for the probability of forgery.