🤖 AI Summary
This paper investigates the “spoiler effect” under proportional representation (PR) systems—where small parties significantly alter vote-share distributions among major parties—a phenomenon previously studied only in single-winner settings and with binary spoiler classifications.
Method: We propose a continuous metric, “Party Excess Electoral Impact,” to quantify spoiler influence, extending spoiler analysis to multi-district PR systems for the first time. We develop a comparability-preserving framework for assessing anti-spoiler robustness, uniformly evaluating seven canonical apportionment and ranked-choice rules (e.g., PAV, D’Hondt, STV). Combining analytical modeling with large-scale simulations, we characterize the spectrum of spoiler sensitivity across rules.
Contribution/Results: We identify a fundamental trade-off between proportionality and anti-spoiler robustness. Our framework provides the first computationally tractable, cross-rule metric for electoral system robustness—enabling principled, evidence-based design of resilient PR institutions.
📝 Abstract
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.
