Spoiler Susceptibility in Party Elections

TL;DR

This work generalizes the notion of electoral spoilers to party elections and develops a rigorous framework based on monotonic projections and vote redistribution to study how removing a party affects others. It establishes an impossibility result: the only spoiler-proof seats-votes function is the identity, and for zero-sum methods spoiler-proofness coincides with party independence of irrelevant alternatives. The authors introduce a continuous measure of spoiler susceptibility and extend probabilistic models to multidistrict party elections to compare common apportionment rules (FPTP, JDH, WSL, LR) under various voting schemes. Experimental results show that more proportional rules (e.g., WSL, LR with Borda-based apportionment) exhibit substantially lower spoiler susceptibility, and increasing district magnitude mitigates spoiler effects. The findings offer a principled basis for designing multiwinner party-electoral rules with reduced spoiler impact and set the stage for approximate spoiler-proofness and broader applications beyond seat-based elections.

Abstract

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 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. However, even if spoilers are unavoidable under common electoral rules, their expected impact can vary depending on the rule. Hence, we introduce a measure of spoilership, which allows us to experimentally compare a number of multiwinner social choice rules according to their spoiler susceptibility. Since the probabilistic models used in COMSOC have been developed for nonparty elections, we extend them to generate multidistrict party elections.

Figures (7)

• Figure 1: Geometric interpretation of Definitions \ref{['def:spoiler']} and \ref{['def:spoilership']}.
• Figure 2: Spoiler susceptibility of electoral rules -- apportionment on the basis of first preferences. Committee size, $k = 5$, is constant in each district. Note that the vertical scale differs between rows.
• Figure 3: Spoiler susceptibility of electoral rules -- apportionment on the basis of Borda scores. Committee size, $k = 5$, is constant in each district. The vertical scale is logarithmic and differs between rows.
• Figure 4: Spoiler susceptibility of electoral rules -- apportionment on the basis of first preferences. Committee size, $k = 10$, is constant in each district. Note that the vertical scale differs between rows.
• Figure 5: Spoiler susceptibility of electoral rules -- apportionment on the basis of Borda scores. Committee size, $k = 10$, is constant in each district. Note that the vertical scale differs between rows.

Theorems & Definitions (24)

• Definition 1: Election
• Definition 2: Allocation Rule
• Definition 3: Monotonic Projection
• Definition 4: Individual Independence of Irrelevant Alternatives
• Definition 5: Vote Redistribution Function
• Definition 6: Electoral Spoiler
• Corollary 1
• Definition 7: Spoiler-Proofness
• Definition 8: Excess Electoral Impact
• Remark 3.1