I find it very unlikely that this will happen, mostly due to a lack of sufficiently effective rationalists with an interest in taking over the world directly and the moral fiber to provide good government once they do so. But I think it would be awesome.
One of the standard methods of science-fiction world-building is to take a current trend and extrapolate it into the future, and see what comes out. One trend I've observed is that over the last century or so, people have kept coming up with clever new ways to find answers to important questions - that is, developing new methods of rationality.
So, given what we do currently know about the overall shape of such methods, from Godel's Incompleteness Theory to Kolmogorov Complexity to the various ways to get around Prisoner's Dilemmas... Then, at least in a general science-fictional world-building sense, what might we be able to guess or say about what rationalists will be like in, oh, 50-100 years?