Alvin Goldman has criticized the idea that, when evaluating the opinions of experts who disagree, a novice should “go by the numbers”. Although Goldman is right that this is often a bad idea, his argument involves an appeal to a principle, which I call the non-independence principle, which is not in general true. Goldman's formal argument for this principle depends on an illegitimate assumption, and the examples he uses to make it seem intuitively plausible are not convincing. The failure of this principle has significant implications, not only for the issue Goldman is directly addressing, but also for the epistemology of rumors, and for our understanding of the value of epistemic independence. I conclude by using the economics literature on information cascades to highlight an important truth which Goldman's principle gestures toward, and by mounting a qualified defense of the practice of going by the numbers.