Democracy means, not “I am as good as you are,” but, “You are as good as I am.”

Reinhold Niebuhr (1892-1971) American theologian and clergyman

The Children of Light and the Children of Darkness, foreward (1944)

This quote was difficult to track down. It's quoted everywhere -- but often attributed to Theodore Parker (as I previously did) or James Russell Lowell. I couldn't find, however, any specific citation from either gentleman.

Rev. John Murray Atwood, in his essay "Universalism and Educational Ideas" in 1770-1920 - From Good Luck to Gloucester, ed. Rev. Frederick A Bisbee (1920), writes:

But he who not only feels that he himself has unknown, divine possibilities, but so has his fellow, that democracy means, not I am as good as you are, but you are as good as I am, who seeks as the expression of his own true nature the larger liberty and life for others, is the kind of man essential to construct a new world.

The book is a history of Universalism, which may tie into Theodore Parker's Unitarian career. At any rate, the wording does seem to precede Niebuhr, but lacking a solid citation, I'll leave it with him.