They can, into political criminals. http://en.wikipedia.org/wiki/Viktor_Yanukovych#Criminal_conv... does not give a lot of detail but practically he was actually convicted of sexual assault. His occupation at 17 was assaulting women late at night by hitting them over the head and stealing their valuables, including overcoats, then leaving them bleeding in the snow.

I don't believe he rigged the second election, but he would not have to be in power to do it. Ukraine uses popular vote, and the original rigged election was simply done by falsifying voting records in a few regions where he had lots of local support.