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Different variants of the incumbency advantage concept have been applied in different settings, making cross-country comparisons difficult. We discuss these different variants and one that should be used in cross-country analysis. The incumbent-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). Also, upper and lower bounds must be specified. We show that the upper-bound of the estimate of the incumbent-challenger advantage is equivalent to the upper-bound of the incumbent-runner-up advantage. Thus, the `upper-bound incumbency advantage' can be estimated in most settings and has a clear meaning across concepts. We show results comparing this object across a series of countries.