The result of Brexit has been analyzed in several ways. Some people suggest the influence of silver democracy. Thus many elder citizens voted to Brexit to be adopted. Brexit vote was dominant in rural areas, whereas Londoners chose to remain. People in high society seems to regret this result. This referendum has revealed several chasms existing in British people.
From other countries, the determination of Brexit means that political correctness was overwhelmed by populism. Acceptance of immigration, free trade, and international collaboration seem quite good as a policy. But, British people prioritized their daily lives, in which the fear they would lose the job because of immigrants was dominant. In this context, Brexit is reflecting the popularity of Donald Trump in the US.
On the other hand, I think this case represents the risk to rely on direct democracy.
As far as my understanding, ruling conservative party did not support Brexit, although some politicians were arguing. UKIP has been on the side of Brexit, of course. But nobody believes that this referendum means that British people supported UKIP. Thus, representatives of citizens were unlikely to choose Brexit.
However, Cameron decided to conduct a referendum.
It was a bitter decision for him. To suppress the complaint of voters, he had to make an opportunity for direct democracy. His thought is understandable.
But, it is not always true that the sum of all citizens' thought is the wisest thought for a nation.
All humans are equal. However, our talents and abilities are various. Some people bake a good bread. Some are good at mathematics. And, most people are not so familiar with politics.
Politics is a theory to make a future, as I wrote. To make the best policy, we have to compromise the present life to some extent. This dilemma to what degree we can sacrifice the present for the future is a problem not to be easily solved.
If we adopt direct politics, we will be eager to gain profit immediately, rather than invest for the future. It is nature of human.
In the ancient Greece, direct democracy was adopted. I am not sure it was functional. At least, they had many slaves to work for them, so they had much time to think about policies.
Direct democracy seems desirable to overcome present problems in modern policy making such as deceiving politicians. The development of IT will realize it at least theoretically. Nonetheless, I believe we should be cautious to adopt it.