Democracy [Debate?]

So we of the western world value democracy in a government. It is a pilar of our civilization and we tend to think of it as the most important thing to have in a government. Now let's have a look at what democracy really is. It's root is from the word "dêmos" meaning the people and "kratos" meaning power. Thus democracy is the power of the people. For the purpose of this thread we will define is as a form of government that allows citizens to all have an equal say in the running of the country.

Now this definition of course doesn't work for effectively any country today. Instead we have indirect democracy. This is when we have the power to elect the people who will run the country. Personally for Canada I would say we have indirect indirect democracy, meaning that we have the power to elect a Parliament who then elects a Prime Minister.

Now the question here is why do we value this ability to vote for who is in power? How is a country better off being run by the people we choose than by people who are say trained from birth to rule a country? What makes democracy better?