  Electoral spoilers are such agents that there exists a coalition of agents
whose total gain when a putative spoiler is eliminated exceeds that spoiler's
share in the election outcome. So far spoiler effects have been analyzed
primarily in the context of single-winner electoral systems. We consider this
problem in the context of multi-district party elections. We introduce a formal
measure of a party's excess electoral impact, treating "spoilership" as a
manner of degree. This approach allows us to compare multi-winner social choice
rules according to their degree of spoiler susceptibility. We present
experimental results, as well as analytical results for toy models, for seven
classical rules ($k$-Borda, Chamberlin--Courant, Harmonic-Borda,
Jefferson--D'Hondt, PAV, SNTV, and STV). Since the probabilistic models
commonly used in computational social choice have been developed for non-party
elections, we extend them to be able to generate multi-district party
elections.
