Dubois in his statement of "stealing the black man's ballot" was probably getting at the idea that those who are being elected by blacks are not representing them to the fullest of their power or potentially at all. During Dubois' time there was still oppressive racial segregation and inequality in the treatment of blacks in America even though there was political enfranchisement or the right to vote for blacks. Dubois could also have been referring to impediments to supporting black voting rights through gerrymandering, or preventing black access to voting, or other anti-black measures in the electoral process.
