Imagine that you had to give a probability density to each probability estimate you could make of Obama winning in 2012 being the correct one. You’d end up with something looking like a bell curve over probabilities
Bell curves prefer to live on unbounded intervals! It would be less jarring, (and less convenient for you?), if he ended up with something looking like a uniform distribution over probabilities.
It’s equally convenient, since the mean doesn’t care about the shape. I don’t think it’s particularly jarring—just imagine it going to 0 at the edges.
The reason you’ll probably end up with something like a bell curve is a practical one—the central limit theorem. For complicated problems, you very often get what looks something like a bell curve. Hardly watertight, but I’d bet decent amounts of money that it is true in this case, so why not use it to add a little color to the description?
Bell curves prefer to live on unbounded intervals! It would be less jarring, (and less convenient for you?), if he ended up with something looking like a uniform distribution over probabilities.
It’s equally convenient, since the mean doesn’t care about the shape. I don’t think it’s particularly jarring—just imagine it going to 0 at the edges.
The reason you’ll probably end up with something like a bell curve is a practical one—the central limit theorem. For complicated problems, you very often get what looks something like a bell curve. Hardly watertight, but I’d bet decent amounts of money that it is true in this case, so why not use it to add a little color to the description?