As Boozer points out, socialism is an economic system.  Democracy is a political system.  In many countries, including ours, socialism and democracy exist together.  Socialism involves having the government, at one or several levels, provide services for the community members.  Think of our infrastructure as an example.  Think of libraries as examples.  Think of our public safety system as an example. Think of both our criminal and civil court systems as examples.  Think of our educational system as an example. Think of public transportation as an example.  Think of our public parks and open space properties as examples.  The list goes on................

Speaking of socialism and democracy as antithetical evidences a lack of understanding of socialism, democracy or both.