Read the whole paragraph.
"We want to open up existing provision to competition from new providers with different ways of doing things. ... in other areas it will mean people competing against one another through the democratic process to gain citizens’ votes."Doesn't the highlighted sentence describe the process of electing councillors and MPs? In which case, why is it in a paragraph about the provision of public services? Was this a cut 'n' paste error? Or does it mean that we will vote for who provides the public services in an area?