Braverman studied statistics and economics at Tel Aviv University and received his PhD in economics from Stanford University in the United States. After serving for fourteen years as a senior official in the World Bank in Washington, specializing in economic development with an emphasis on social justice, Braverman returned to Israel to become president of the Ben-Gurion University of the Negev for the next sixteen years. He was well regarded in this position and received an award from the city of Be'er Sheva for his work.
In November 2005, Braverman announced his intention to become involved in politics. Despite rumors that he would join Kadima, in a move viewed as surprising, he ended up joining Labor Party. He was elected to the Knesset in the 2006 elections. Within the party, he was initially associated with Amir Peretz and later with Ami Ayalon.
Prior to the 2009 elections he won fourth place on the party's primaries, retaining his seat in the subsequent election. Braverman opposed the decision of the Labor Party to enter the Netanyahu government in March 2009, but shortly afterwards it was announced that he would be entering the government as Minister without Portfolio, focusing on Minority Affairs, later transformed into the Minister of Minority Affairs. He resigned from the cabinet after Ehud Barak left the Labor Party to establish Independence in January 2011.