Bryan Caplan asks: "How would the world change if everyone shared your factual beliefs?" He adds: "In the hypothetical, values remain unchanged."
However, one of my factual beliefs is that our values are responsive to reason, so that others would ultimately share my values if only they thought a bit more carefully about it. (Or vice versa, in cases where I am the mistaken one. But naturally I don't believe that this is so in any particular case!) Part of sharing all my factual beliefs is to believe that you would - on further reflection - share my values.
But there's something incoherent about believing something that you think you would reject on further reflection. The latter meta-belief implies that your original belief is unjustified. And as soon as you appreciate that fact, you can no longer hold the belief. (To believe something is to judge that it's true; you can't do that if you've just judged that it's probably false, or at least that you have no grounds for thinking it true.)
So, anyone who shared all my factual beliefs would be rationally compelled to also share my normative beliefs (values)!