In some parts of the world it certainly looks that way. An article in the Huffington Post entitled "From Istanbul to Rio and Philly; This Democracy Thing is Broken" certainly gives the impression the author thinks so. I suspect he has a point, certainly the idea that a "majority vote" rules seems to have got lost. Now those who disagree with any elected government regard it as a "right" to conduct campaigns of "civil disobedience" as they try to force a change of policy, ideology or even the government to whatever it is they approve of. The current unrest in Turkey is a case in point, the government of Mr Erdogan was elected by a majority vote in a popular election which was even held up as a "model" for the rest of the region, but it appears there is a substantial group who want to throw him out and replace him with someone else.
That has always been one of the problems with "democracy" you are stuck with whoever the majority voted for, and since many vote in what I shall call a "tribal" manner - in other words they simply can't bring themselves to vote for the candidate of any party other than the one they always vote for - it can mean, in a system such as Britain's or the US, that in some constituencies, the 'tribal' Party will always win, even if the candidate is technically a "Dead Parrot". Most other systems share this problem, the candidates are usually part of a "political elite" who have all the levers of control to the media, the money to promote themselves and sometimes even the tacit support of a large and very influential body entrenched and protecting their own interests in the inevitable bureaucracies that are the real governors of any nation. It is said that it actually takes ten years or more for the economic changes initiated today to filter through the bureaucrats and become a reality for everyone else. A similar 'reality lag' affects almost everything else as well.
We have the illusion of being able to change governments, but I no longer believe this is real. All to often only the faces in the front row change, the same faceless puppeteers remain in the background pulling a new set of strings. Recently I reread an item I have now managed to misplace, which postulated that the 'life' of any democracy is about 200 years, then it degenerates rapidly into a form of oligarchy and dictatorship with burgeoning bureaucracy no longer serving "the people' but turning inwards and protecting its own rights and privileges, while the "Political Class" pull up the drawbridge and place barriers to any threat to their own continued hold on power. Another article raised this again, pointing to the current arguments in the US about the power of the Federal Government and the entrenched power of various Federal Departments. There are certainly echoes of what happened in Rome and in various other "democracies" of antiquity.
Vice Admiral, Horatio, Viscount Nelson made an interesting statement regarding "republics" -
"I have seen much of the world, and I have learnt from experience to hate and detest republics...there is nothing but tyranny & oppression, I have never known a good act done by a Republican, it is contrary to his character under the mask of Liberty...He [Napoleon] is a tyrant, a many headed monster that devours your happiness and property...nothing is free from this monster's grasp. A republic has no affection for its subjects...a King may be ill advised and act wrong, a Republic never acts right, for a knot of villains support each other, and together they do what no single person dare attempt"
While I acknowledge that he is speaking from the perspective of his own era, I have to say that my own experience of living in Republics that he has a point. When I look at some of the "Presidents" purporting to "rule" various nations, I see would be "Emperors" and many of them are not subject to the limitations sensibly imposed by the French post Napoleon, or in the US which limits the President to a maximum of two terms. For many, and even for the "best" examples of democratic societies and governments, I suspect it is an illusion. As long as we have a "ruling political class" and an accompanying and permanent "bureaucracy" we cannot have a true democracy, one in which a candidate is personally known and who, when 'sitting' in whatever legislative body, actually votes according to what his or her constituents want and NOT the "Party Line" because that is what the ideology demands.
I'm not sure I would say "Democracy is broken" but it is certainly not very healthy at the present moment wherever I look at it. What I'm not so sure of, is how it can be cured. Revolutions, as Egypt, Libya, Tunisia, Iraq, Iran, Syria and many others prove, is that the replacement for the overthrown regime is often worse than the one it replaces. Corruption is rampant everywhere, even in the west. There it has a different, quasi-legal face, but it is still present in the manner government contracts are awarded, legislation is 'modified' to suit lobby groups and so on.
Perhaps the Admiral had it right, perhaps the answer is a return to rule by a "King in Council" - but that also has its problems and history is littered with examples. Plato ha.d it right I think, at least his 'model' of the phases of a 'republic' has been validated by history. It remains only to see where ours goes from here ..