Having been first elected in a 1969 special election, Burke has since been reelected thirteen times, in 1971, 1975, 1979, 1983, 1987, 1991, 1995, 1999, 2003, 2007, 2011, 2015, and 2019. After Burke's first campaign for alderman, he has been unopposed in most of his re-election campaigns. In 2007, Burke faced his first opponent since 1971, a school teacher who had never run for office. A Burke supporter unsuccessfully challenged the validity of the opponent's ballot application, but the case was tied up in court for most of the campaign, and Burke went on to win with nearly 90 percent of the vote.