Critics of “top-two” sometimes argue that “top-two” is even more favorable to incumbent office-holders than normal elections are. A look at Louisiana’s U.S. House elections, 1978 through 2006, tends to confirm this criticism. Louisiana held 120 regularly-scheduled U.S. House elections in that period, the period in which Louisiana used “top-two” for Congressional elections. Special elections are excluded from this study, since virtually by definition, there is no incumbent in a special election.
Out of those 120 U.S. House elections, an incumbent was defeated only three times. And in two of those three instances, it was impossible for an incumbent not to lose, because one incumbent was running against another incumbent, due to redistricting.
But, when Louisiana abandoned “top-two” in Congressional elections starting in 2008, and used ordinary elections in which each party chose its own nominee in closed or semi-closed primaries, two incumbents were defeated in the general election, out of seven races. The two incumbents who were defeated in the general election of 2008 were William Jefferson, a Democrat from New Orleans, and Don Cazayoux, a Democrat from Baton Rouge. Both of the 2008 elections in which the incumbent lost were multi-party races, in which the winner was elected with a plurality, but not a majority.
During the years Louisiana used “top-two” for Congressional elections, the only incumbent who lost and who wasn’t running against another incumbent was Claude Leach in 1980. The two incumbents who lost to other incumbents were Jerry Huckaby and Clyde Holloway, both of whom were defeated in 1992, after Louisiana lost one seat in the House due to the 1990 census.