There have been held multiple debates on this topic and both, the proponents and opponents have given multiple arguments over this. Some scholars say that it is permissible to elect a leader by casting vote while others say that it is not permissible according to islamic regulation to elect someone through this way. Since, it is extremely serious to say something is un-islamic or islamic, so best way is to stick to the scholarly point of view.
Elections in themselves are not an un-islamic practice, it is it's use which makes it permissible or impermissible. Today, we see that in both muslim and non muslim societies, democratic process is based on most un-islamic rules. The constitution of most islamic countries contains some clauses which are not islamic. Similarly, the leadership in almost all islamic countries is also not chosen based on the requirements of islam.
In islamic state, a leader must be the one who knows Quran and Sunnah, and can judge the matters according to them. A leader must be an expert and knowledgeable person. He should be of indisputable character and honest. Where in reality, the leaders which are put to vote to be chosen by people are not even close to these requirements.
Similarly, in an islamic state, any law or practice which is to be effective should be according to islamic law and principles. There is no way that any un islamic rule or practice can be passed and made effective in islamic governance system. Everything an islamic state does or has should be according to islam. But in reality, almost all the modern practices in islamic states are un-islamic.
Therefore, it is not wrong to say that today's election system is not in accordance with islam. No leader or rule of law is made considering tenants of islam rather they are passed and chosen for the sake of modernism and secularism. In fact, now a days, a school of thought as emerged who says that islamic and politics are two different things which is totally in opposition to islam.
In what cases is election system permissible:
Elections are permissible in any matter only if they comply to the following rules or thresholds as per scholarly point of view.
If no islamic rule of law is broken by elections then it is permissible. More over, in an islamic society, if the practice which is to be put ot elections is not contradictory to quran or sunnah in anyway, then it can be put to vote. If the practice to be put to vote is not helping non-islamic interest in anyway, then it is permissible to vote. And, if the said practice which is to be put to vote is not going to violate or weaken the islamic system in future, or to be used against islam in any non islamic way, then it is permissible to put such a matter to vote.
Keeping in mind the above mentioned points, it would be fair enough and honest enough to say that the people and laws we choose and make effective today are no where islamic. So, todays voting system is not permissible because it does not fit with islam. And ALLAH knows the best.