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Spoiler Susceptibility in Multi-District Party Elections

<span lang="en">Spoiler Susceptibility in Multi-District Party Elections</span>

Autorzy: Daria Boratyn, Wojciech Słomczyński, Dariusz Stolicki, Stanisław Szufa

Projekt: Efekty spoilerów w wyborach partyjnych, Wzory wyborcze: efekty polityczne wybranych systemów wyborczych w perspektywie ilościowej

arXiv: 2205.05115 [cs.GT]


An electoral spoiler is usually defined as a losing candidate whose removal would affect the outcome by changing the winner. So far spoiler effects have been analyzed primarily for single-winner electoral systems. We consider this subject in the context of party elections, where the election outcome of interest is the allocation of resources (e.g. parliamentary seats) among competing parties. In such elections, there is no longer a sharp distinction between winners and losers. Hence, we propose a more general definition, under which a party is a spoiler if their elimination causes any other party’s share in the outcome to decrease.

We characterize spoiler-proof electoral allocation rules for zero-sum voting methods. In particular, we prove that for seats-votes functions only identity is spoiler-proof. We also show that spoilers are ubiquitous under some of the most common electoral rules. However, their impact can vary depending on the rule. Hence, we introduce a measure of spoilership, which enables us not merely to test for the presence of the spoilers but also to measure the magnitude of their impact. This allows us to experimentally compare a number of multiwinner social choice rules according to their spoiler susceptibility. We present experimental results for seven classical rules ($k$-Borda, Chamberlin--Courant, Harmonic-Borda, Jefferson--D'Hondt, $k$-PAV, SNTV, and STV). Since the probabilistic models used in COMSOC have been developed for non-party elections, we extend them to generate multi-district party elections.