Data as a Lever: A Neighbouring Datasets Perspective on Predictive Multiplicity

Abstract: Multiplicity -- the existence of distinct models with comparable performance -- has received growing attention in recent years. While prior work has largely emphasized modelling choices, the critical role of data in shaping multiplicity has been comparatively overlooked. In this work, we introduce a neighbouring datasets framework to examine the most granular case: the impact of a single-data-point difference on multiplicity. Our analysis yields a seemingly counterintuitive finding: neighbouring datasets with greater inter-class distribution overlap exhibit lower multiplicity. This reversal of conventional expectations arises from a shared Rashomon parameter, and we substantiate it with rigorous proofs. Building on this foundation, we extend our framework to two practical domains: active learning and data imputation. For each, we establish natural extensions of the neighbouring datasets perspective, conduct the first systematic study of multiplicity in existing algorithms, and finally, propose novel multiplicity-aware methods, namely, multiplicity-aware data acquisition strategies for active learning and multiplicity-aware data imputation techniques.