This paper investigates the effects of political representation on electoral outcomes at the party and coalition levels in proportional election systems using data from Swedish local government elections. There are two notions of representation, namely, to hold seats and to belong to the ruling coalition. I refer to the effect of the former as the incumbency effect and the effect of the latter as the ruling effect. The discontinuous variation in the seat share as the vote share varies for parties is used to isolate exogenous variation in incumbency. The discontinuous variation in ruling at the 50% seat share cutoff for coalitions is used in order to exogenous variation in ruling. I find that incumbency determines the distribution of 12% of the total vote, which is similar to the advantage found in majoritarian systems. I find no ruling effect, contrary to the commonly found cost of ruling in proportional systems.
Liang, Che-Yuan (2013),
"Is There an Incumbency Advantage or Cost of Ruling in Proportional Election Systems? ".