Who is a Jew? Jews in the House, and the Senate

So when counting Jewish Representation in Legislatures and in Executive roles, just Who is a Jew anyway?

Jew by birth?
Jew according to Halachah?
Jew despite practicing another religion?

For more on this topic please see:

Rabbi's Corner: Jews in the House, and the Senate

http://www.shirhadash.org/rabbi/08/08/15/house.html

KT
RRW