  Despite many examples to the contrary, most models of elections assume that
rules determining the winner will be followed. We present a model where
elections are solely a public signal of the incumbent popularity, and citizens
can protests against leaders that do not step down from power. In this minimal
setup, rule-based alternation of power as well as "semi-democratic" alternation
of power independent of electoral rules can both arise in equilibrium.
Compliance with electoral rules requires there to be multiple equilibria in the
protest game, where the electoral rule serves as a focal point spurring protest
against losers that do not step down voluntarily. Such multiplicity is possible
when elections are informative and citizens not too polarized. Extensions to
the model are consistent with the facts that protests often center around
accusations of electoral fraud and that in the democratic case turnover is
peaceful while semi-democratic turnover often requires citizens to actually
take to the streets.
