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*Probably?*

I’ve been wanting to write an article entitled “Oatmeal Raisin: The Cookie Nobody Loves.” Unfortunately, although this title captures, I am convinced, a deep truth, I could not find a way to link it to tax law. So instead of describing why, if you leave out lots of plates of different kinds of cookies and come back a little while later there are always more oatmeal raisin cookies left than any other kind, but if you come back an hour later, all the cookies, including the oatmeal raisin cookies, are gone (nobody loves ‘em, but they do like ‘em), this post will describe the piece I wrote instead: *Probably? Understanding Tax Law’s Uncertainty*.

As I described in an earlier post, flipping a coin is risky, because while we do not know *whether* it will come up heads, we do know the *probability* that it will come up heads (50%). The presidential election is uncertain, because we do not know whether John McCain will be elected president, *and* we do not know the probability that he will be elected president. A.J. Sutter pointed out in a comment to that post that the distinction between risk and uncertainty (that is, between known probabilities and unknown probabilities) ties into the debate about the correct interpretation of probability statements. As it happens, that debate is precisely *Probably?*‘s topic.

We might say that the probability that an event will occur is the number of times that event will occur over the long run out of the number of times that it could occur. So when we say that a coin has a 50% chance of coming up heads, we mean that if we flip the coin a lot of times–a million, say–about half of those flips will come up heads. And the more times we flip, the closer the percentage of heads will get to 50%. This is a frequentist interpretation of a probability statement.

But this interpretation doesn’t work if the event we’re talking about is not risky, but is, rather, uncertain. As others have noted, tax law is uncertain–that is, that we do not, and cannot, know the probability that a court will uphold a particular tax position. Tax advisors make these sorts of probability statements all the time, because a taxpayer faces lower penalties if he can get a tax advisor to give an opinion that there is a certain level of probability that the taxpayer’s position will eventually be upheld by a court. But if we don’t and can’t know this probability, what does it mean to say that there is a, say, 90% chance that a particular tax position will be upheld?

It means, I think, that the speaker *believes* that there is a 90% chance the tax position will be upheld. Or, put another way, the speaker would pay 90 cents to play a game in which he would get a dollar if the position were upheld and get nothing if it were struck down. This is what’s known as a “subjectivist” interpretation of a probability statement.

So, who cares? Well, *everyone* should care, of course!