It Had To Be That Way
AEW wrote that he did not understand how the distinction between risk and uncertainty relates to subjectivist and frequentist interpretations of probability. He gave this very good example:
Say I have two dice, one with dollar signs on 4 sides, and one with dollar signs on two sides. I put one in each hand (behind my back) and let you choose a hand. I take that die and say ‘I’m going to roll this, and if a dollar sign comes up, you win a dollar.’ What are the odds that you win a dollar? You could say that the probability is either 1/3 or 2/3, you don’t know. Or you could say the probability is 0.5. Does this count as uncertainty? It’s true that to say that the probability is 0.5 is subjective in the sense that someone who peeked behind my back would have a different belief of the probability. But it’s fully consistent with a frequentist interpretation of probability in that if we repeated the process ad infinitum, the frequency would approach 50%.
A couple of things. First, before the whole process starts, we are dealing with risk. If the hand is truly selected randomly, there is a 50% chance that there will be a 1/3 chance of a dollar sign, and a 50% chance that there will be a 2/3 chance of a dollar sign, so there is a 3/6 chance, or 50% chance, that I will roll a dollar sign. And true to a frequentist interpretation, if we repeat the whole thing (picking the hand, then rolling the die that was in that hand), the frequency of dollar signs will approach 50%.
But after we pick the hand, but before we roll the die that was in that hand, what are we dealing with? If we roll that die over and over, the frequency will not approach 50%. It will approach either 1/3 or 2/3. It sounds like we are operating under risk if we rephrase the game, “I am holding one die. There is a 50% chance that it has two dollar signs, and a 50% chance that it has four dollar signs.” But we are not just talking about an event in the future–the die actually already has either two dollar signs or four dollar signs. So if we looked at the die, we could get more information and get a “better” (i.e., more accurate) probability.
So, risk or uncertainty? I really struggle with this. Indeed, maybe it doesn’t even matter whether the die already has two or four dollar signs; maybe the distinction between the present and the future isn’t even relevant. Some people (me? haven’t decided yet) are complete determinists, and believe that if we had all information about everything, we would know exactly what would happen in the future. So in some sense, if we could get more information about things and get better probabilities, we don’t know the real probability of anything at all. (Indeed, to a pure determinist, the real probability of every event, given full information, would always be either 0% or 100%.)
But, even if everything is in some sense uncertain, the distinction is still useful. (I am allowed to say “useful” because I am not a philosopher; rather, I am interested in how we can use these ideas as we think about creating and shaping law.) Some things operate more like known probabilities, and some things operate more like unknown probabilities–that is, some things are more risky (e.g., coin flipping), and some things are more uncertain (e.g., presidential elections). And tax probability statements fall, I think, into the latter group.
(Side note: there’s a great example of determinism in action in the book The Eudaemonic Pie, which chronicles the successful attempt of some nerds to beat a roulette wheel. Basically, they realized that roulette balls fall where they do because of physical forces, so they studied roulette wheels and built a computer they could strap to their body that would allow them to input the relevant physical facts and predict where the ball would fall. They were successful. The most amazing thing is that this all happened in the 1970s, and they had to build all the computer equipment themselves, down to designing, drawing, and using acid to etch the circuits onto the PC boards. I cannot recommend this book highly enough. There is also a sequel of sorts, The Predictors, which details what these guys did next: started a wildly successful stock-picking business, of course! This is all nonfiction.)