Regarding your first point, this quote by Gian-Carlo Rota perhaps says what I want to say best:
"Most people, even some scientists, think that mathematics applies because you learn Theorem Three and Theorem Three somehow explains the laws of nature. This does not happen even in science fiction novels; it is pure fantasy. The results of mathematics are seldom directly applied; it is the definitions that are really useful. Once you learn the concept of a differential equation, you see differential equations all over, no matter what you do. This you cannot see unless you take a course in abstract differential equations. What applies is the cultural background you get from a course in differential equation, not the specific theorems. If you want to learn French, you have to live the life of France, not just memorize thousands of words. If you want to apply differential equations, you have to live the life of differential equations. When you live this life, you can go back to molecular biology with a new set of eyes that will see things you could not otherwise see."
Regarding your second point, I think one of the principles behind democracy is that even if each individual voter is not an expert, their collective decisions (ideally) will be similar to those of 'experts'. Think of Boosting in AI - you can often combine many weak learners to form a strong learner. So it is reasonable to expect politicians to be more qualified (restricted to policy making, of course) than the voters.
Regarding your first point, this quote by Gian-Carlo Rota perhaps says what I want to say best:
"Most people, even some scientists, think that mathematics applies because you learn Theorem Three and Theorem Three somehow explains the laws of nature. This does not happen even in science fiction novels; it is pure fantasy. The results of mathematics are seldom directly applied; it is the definitions that are really useful. Once you learn the concept of a differential equation, you see differential equations all over, no matter what you do. This you cannot see unless you take a course in abstract differential equations. What applies is the cultural background you get from a course in differential equation, not the specific theorems. If you want to learn French, you have to live the life of France, not just memorize thousands of words. If you want to apply differential equations, you have to live the life of differential equations. When you live this life, you can go back to molecular biology with a new set of eyes that will see things you could not otherwise see."
Regarding your second point, I think one of the principles behind democracy is that even if each individual voter is not an expert, their collective decisions (ideally) will be similar to those of 'experts'. Think of Boosting in AI - you can often combine many weak learners to form a strong learner. So it is reasonable to expect politicians to be more qualified (restricted to policy making, of course) than the voters.