The closest system to actual democracy that there is, is direct democracy. However I would make 2 additional rules to introducing the new system, but first the pros and cons of it.
Pros:
Trust in the government and politicians is declining steadily, things aren't getting better with the current system.
Cons:
As you've seen, modern politics are mostly about the tyranny of a minority. (((special interests))), liberals and…other… shrill groups who enforce their world views on the majority under the guise of social justice and so on.
I understand the concept of "tyranny of the majority" but I can't help but think of comparing it to: "In a family of 5, one of the daughters wants to burn the house down. She is clearly the minority. The other 4 members of the family disagree and stop her." Are they being tyrannical?
There could be safe-guards put in place against violations of human rights.
Now, to address the "uneducated people voting" issues.
I believe direct democracy can only work if there is a vetting process in place to earn your voting license. We have to study for exams in school, college, hell even to get a drivers license. Yet the most important civil right we have - the vote - doesn't require any qualifications. You are deciding the fate of a nation, I'd say that is enough responsibility to warrant a test and the fulfillment of some criteria (for instance, people on welfare don't get to vote).
The test could consist of some basic politics, basic economic knowledge and so on.
If people say "but muh basic human right" - my answer is "you have the right to drive, but that doesn't mean you can just hop in a car and go for it. You have the right to EARN your drivers license". It is your choice whether you want to or not.
The second implementation that direct democracy would require is another type of voting system. I personally am for online voting, where you vote using your webcam, and holding up some form of ID. Everybody has a smartphone with a camera so it would be easy. No voting lines, no lazy/apathetic voters, less voter intimidation, faster results.
The votes would then be sent to a government agency as well as a few private companies for independent tallying.
That having been said, I understand the arguments for the vote to be anonymous, but it's in that anonymity that the fraud occurs. I for one am not ashamed of what I believe in, and when asked, would answer who I vote for and why.
As an European, I've been thinking of inter-country vote counting. For instance a highly corrupt country like Greece, or Spain or Romania (where voting is laughably fraudulent) would send out their votes to disinterested parties like Switzerland to count the votes, ensuring the least amount of voter fraud.
Thoughts?