Centripetal Structure under Alienation-Based Abstention
Abstract
Alienation-based abstention makes participation endogenous because the platforms chosen by parties determine who votes. We study how voter tolerance affects the existence, location, and persistence of pure-strategy equilibria in two versions of a two-party spatial model. In the first, office-seeking parties maximize voter plurality; in the second, they care about the policy implemented. We characterize all office-seeking equilibria through a condition called window dominance, which gives a distributional characterisation of profitable deviations both near to and far from a party's platform. For general continuous voter distributions, pure strategy equilibrium in the office seeking game may fail to exist, may be non-unique, and may appear and disappear as tolerance increases. To resolve this, we identify a centripetal structure in the set of positions that can not lose to each rival. When this structure holds, a single anchor defeats every other platform and determines the unique office-seeking equilibrium. The classical Downs and Llavador results are special cases. We show that this structure persists at all larger tolerance radii once it holds at a radius of at least half the policy space and at least twice the median's distance from the center. The centripetal structure emerges before full participation for all voter distributions. Finally, the same structure yields a complete classification of equilibrium when parties care about the policy implemented rather than electoral victory alone.
Related
- Classification with Abstention Under Class-Conditional Error Constraints
- Bayesian Fixed-Confidence Best-Arm Identification with Abstention
- Abstention Spends Its Budget on Local Label Variance More Than on Novelty: Auditing Conformal Calibration and Selective Prediction under Molecular Scaffold Shift
- Certified by Abstention: Distribution-Free Guarantees for Chain-of-Thought Verifiers at Small Calibration Budgets
- Strict weak Hörmander conditions for hypoellipticity and structure equations
BibTeX
@misc{ray2026centripetal,
title = {{Centripetal Structure under Alienation-Based Abstention}},
author = {Aman Ray and Srikanth Pai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.03788},
eprint = {2608.03788},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.03788},
}
RIS
TY - UNPB
TI - Centripetal Structure under Alienation-Based Abstention
AU - Aman Ray
AU - Srikanth Pai
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2608.03788
UR - https://arxiv.org/abs/2608.03788
AB - Alienation-based abstention makes participation endogenous because the platforms chosen by parties determine who votes. We study how voter tolerance affects the existence, location, and persistence of pure-strategy equilibria in two versions of a two-party spatial model. In the first, office-seeking parties maximize voter plurality; in the second, they care about the policy implemented. We characterize all office-seeking equilibria through a condition called window dominance, which gives a distributional characterisation of profitable deviations both near to and far from a party's platform. For general continuous voter distributions, pure strategy equilibrium in the office seeking game may fail to exist, may be non-unique, and may appear and disappear as tolerance increases. To resolve this, we identify a centripetal structure in the set of positions that can not lose to each rival. When this structure holds, a single anchor defeats every other platform and determines the unique office-seeking equilibrium. The classical Downs and Llavador results are special cases. We show that this structure persists at all larger tolerance radii once it holds at a radius of at least half the policy space and at least twice the median's distance from the center. The centripetal structure emerges before full participation for all voter distributions. Finally, the same structure yields a complete classification of equilibrium when parties care about the policy implemented rather than electoral victory alone.
ER -