Recently, the regression discontinuity
(RD) design has become increasingly popular among social scientists.
One prominent application is the study of close elections. We
explicate several methodological misunderstandings widespread across
disciplines by revisiting the controversy concerning the validity of
RD design when applied to close elections. While many researchers
invoke the local randomization or ``as-if-random'' assumption near
the threshold, it tends to be more stringent than the required
continuity assumption. We show that this seemingly subtle point
determines the appropriateness of various statistical methods and
changes our understanding of how ``sorting'' invalidates the design.
When multiple testing problems are also addressed, we find that
evidence for sorting in US House elections is substantially weaker
and highly dependent on estimation methods. Finally, we caution
that despite the temptation to improve the external validity, the
extrapolation of RD estimates away from the threshold sacrifices the
design's advantage in internal validity.