There is nobody who I'd trust to decide who is considered educated and more responsible and therefore who would get more votes. And the historical record on similar subjects is pretty bad.

I would also expect a feedback loop where people who can vote more vote to give more voting power to people like themselves.

(And I also find it odd that most people who contemplate such things assume they would be considered educated and more responsible. Imagine a world where, say, the socially responsible get more voting power, and that (for instance) thinking that there are innate differences between races or sexes disqualifies one from being socially responsible.)