Why did nazi prisoners wear a second badge

To identify them as Jews (Red triangle over a Yellow triangle) APEX)

Criminals were marked with green inverted triangles, political with red, "asocials" with black or in the case of Roma in some camps brown triangles. Homosexuals were identified with pink triangles and Jehovah's Witnesses with purple. Non- German prisoners were identified by the first letter of the German name for their home country, which was sewn into their badge. The two triangles forming the Jewish star would both be yellow unless the Jewish prisoner was included in one of the other prisoner categories. A Jewish political prisoner for example would be identified with a yellow triangle under a red triangle. 

Ithink the answer you're looking for is democracy.