Because there aren't any. Although I would not use the word "sane" here, I would use the word "capable", as in capable of running a political unit the size of a country. The inconvenient truth that nobody wants to acknowledge is that there are no human beings capable of doing that. Countries are simply too big and too complicated. (This is actually true IMO for units much smaller than countries, but countries is the current level of discussion.) The problem is not to find someone who can govern a country sanely; the problem is to figure out how to organize ourselves and coexist given that nobody is capable of governing a country sanely.
Because bringing it to a halt would take precision work and even then it probably wouldn't be stable. Iterative systems oscillate. It's what they do.
Moreover, a lot of the suggestions about "how to solve it" are in fact what people are trying to do very hard, and are themselves part of the system. The obvious solutions are what are taking us in the current direction. The fact that they are obvious is why you can actually plot the cyclic progression of civilizations with some reliability. It's an interesting field of study.
(BTW, buckle up. We're almost certainly in for a period of substantial uncertainty based on those modes. But, also, you are not your government or social system. Whatever abuse those things may be in for doesn't mean that you won't come out of it. Also, while I'd say high technology shows little evidence of having eliminated the cycles up to this point, I do consider it a wild card personally. Doom is not guaranteed.)
See also http://www.livescience.com/22109-cycles-violence-2020.html , which also has some very Google-able keywords.
Bear in mind that it's a field of active research, and I'm giving those more as starting points I plucked out from Google hits than necessarily endorsing those exact theories. Personally I would only defend a somewhat weaker idea, that the future isn't somehow entirely random, but that we can indeed look to theories like this for some understanding of the next few decades, modulo the technology wildcard. Or at least a much better understanding than just thinking it's all whims of fate and everything's on the table equally. I said some reliability on purpose... it's not totally reliable, but you can still do much better than nothing.
The institutions that used to provide alternatives political voices have been co-opted. So who are they going to vote for?
See Die Linke (The Left party) in Germany taking over territory perhaps once held by the SPD (Socialdemocratic party).
So the accusations are not so much that `these voters belong to us'. But: no self-respecting party should form a coalition with these dictators ever.
That taboo has been broken on the state level in East German a long time ago. But it still holds some power on the federal level, and in West German states.
The voting systems make that hard. Eg for the US any one who wants to win the primaries has to pander to their extreme base.
Moving to range voting would help a bit http://www.rangevoting.org/
This cycle is completely about the ruling elite wanting the same crooked game to keep playing, and the voting public saying "You know what? Fuck you".
Yes, the Dems couldn't pull it off with Sanders, but it appears the republicans actually picked, perhaps not an anti-establishment candidate, but at least a non-establishment candidate.