For candidates it has to be a range variety of stuff including economics, sociology, politics, etc. Really when you're considering a candidate for the position of CEO of a large corporation, you're testing a candidate rather thoroughly, so why any idiot can become a president of the whole state?
For voters the only thing I can think of is the ablility to continue thinking critically under stress and the ability to sustain psychological pressure. Also the ability to recognize and analyze propaganda methods and tricks.