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, centered somewhere around "Obama has a 70% (or something) chance of winning." Then to make a decision based on that distribution using normal decision theory, you would average over the possible results of an action, weighted by the probability. But this is equivalent to taking the mean of your bell curve - no matter how wide or narrow the bell curve, all that matters to your (standard decision theory) decision is the location of the mean.

Less evidence is like a wider bell curve, more evidence like a sharper one. But as long as the mean stays the same, the average result of each decision stays the same, so your decision will also be the same.

So there are two kinds of precision here: the precision of the mean probability given your current (incomplete) information, which can be arbitrarily high, and the precision with which you estimate the true answer, which is the width of the bell curve. So when you say "precision," there is a possible confusion. Your first post was about the "how precise can these probabilities be," which was the first (and boring, since it's so high) kind of precision, while this post seems to be talking about the second kind, the kind that is more useful because it reflects how much evidence you have.