Is it possible to have democracy without capitalism?
Yes, although it is highly unlikely. Lenin theorized that in order to fully implement communism, violence and dictatorship were necessary. He felt the wealthy and privileged classes would never surrender their power or wealth voluntarily, and that dictatorship was necessary "for the good of the masses."
But there are varying degrees of capitalism, as both the United States and Denmark are representative democracies, yet Denmark is perhaps the clearest example of western-style socialism, with 70% tax rates and cradle-to-grave programs for the citizens. Surely that's not pure capitalism, yet democracy thrives there.
In Chile in 1970, Salvador Allende was popularly elected by the people of that country, despite heavy CIA investment and interference in the election. In essence, the people of Chile voted against capitalism in a democratic election. The backlash, foreign interference and violent coup against Allende turned into a dictatorship that then "preserved" capitalism. So philosophically and ideologically, if capitalism can and does exist within dictatorship, then communism and socialism can exist within democracy. To be sure, however, it has been exceedingly rare.
Point well taken. But since capitalism, in all of its varying degrees and forms, exists and has existed in such clearly undemocratic countries such as China, Saudi Arabia, Vietnam, Iran and, though it is ironically involuntary, Cuba, can we still argue that democracy and capitalism are so linked and interdependent?
While liberals and conservatives would agree that freedoms are essential in a democracy, can we say that freedom of speech is more important than freedom from hunger? Can we really say that a country that willingly allows hunger and poverty, and employs an economic system that to some degree depends on a percentage of its population living in poverty, is still truly democratic? FDR's Four Freedoms speech acknowledged the importance of Freedom of Speech and Religion explicitly, and also called for Freedom from Want--the human right to an adequate standard of living--and Freedom from Fear. These last two are often missing from countries we classify as democracies.
Conservatives, however, would argue that there cannot be democracy without capitalism. We know that democracy is more than just elections. In order for a country to be truly democratic, it must guarantee its people certain rights. We could not conceive of a democracy without the freedom of speech and we would not call a country a democracy if it did not have guarantees against things like illegal searches and seizure. Similarly, to many conservatives, a country could not be democratic if it did not allow capitalism. Conservatives tend to see capitalism as a freedom on par with freedom of speech or religion. Therefore, a country with elections but no capitalism would not be a democracy to them.