The Incumbent-Challenger Advantage and the Winner-Runner-up Advantage

We provide a taxonomy for different variants of the incumbency advantage concept and discuss how they relate. The winner-runner-up advantage can be estimated straightforwardly with Regression Discontinuity Design (RDD), but does not represent the most common variant in theoretical work, i.e., the incumbent-challenger advantage. The latter can be approximated with RDD comparing winners and runners-up under certain conditions. In a two-party system a party level estimate works. If the two-party condition fails, further assumptions are necessary, particularly on the imputed success of runners-up who are compliers (rerun only if won). Finally, we propose a further variant, the winner overall advantage, that allows for both winners and runners-up to rerun for the same post in other constituencies. We show that this last variant is key in understanding differences in incumbency advantage between the UK and the US.