I wouldn't go as far as geniocracy, but instead go for technocracy. it doesn't value compassion the same way geniocracy does, but if people that know what they are doing are in power (e.g. a foreign minister that actually understands teh framework of foreign countries, a health minister that actually completed a public health master/ MD, etc) then it should result in the most plausible decisions, that will lead to the least damage and the greates advantage in the long term. but then again that genius that no one could stand in class is not going to get elected xD
Well, terrorists probably came about because the infrastructure that could provide education in the countries with terrorists was repeatedly destroyed (Iraq, during the gulf war, gaza strip during intifada). If you for example compare those countries with let's say jordan or syria before it's downfall (the worst thing that ever happened to the arabic countries) these never gave birth to that many radicals.
The stupidity on the arabic side probably also comes about due to the huge amount of children they have (i mean every guy can marry 4 women, and 10-30 children are not uncommon, especially in more conservative families). with that many children it's hard to provide for them all, to educate them all and most of all it's near impossible for all of them to find proper work. At most two children can inheret a family business (if there is one) and the rest has to find jobs for themselves. However instead of turning to jobs they turn to radical groups that put the blame on the west.
Well, I think the ideal government structure would be something along the lines of the EU, just with more legislative power, and not as an alliance of states, but more as a united state. I mean it works pretty well for now^^ and the good thing is since the EU government is somewhat more international and the individual citizens don't care that much about the image of who is in the positions of power, you usually have someone competent doing the decisions (and if not, someone competent will drag the mistaken decision before the court)