Brady studies political participation and elections in the United States and other countries, voting machines and voting systems, higher education policy, and welfare policy. He is a member of the Lincoln Project of the American Academy of Arts and Sciences which is exploring the future of American higher education. He works with the Campaign for College Opportunity (Oakland California) which lobbies for college access and opportunity in California. He has looked at the factors which impede and enhance political participation of all kinds, and has investigated the strengths and weaknesses of various voting systems. He was an expert witness in the 2000 Butterfly Ballot case in Palm Beach, Florida, and he testified before the Carter-Baker Commission on Federal Election Reform. His work on welfare shows that poor families with disabled children face substantial barriers to moving off welfare.