This article redefines arbitrariness not as a normative flaw or a symptom of domination, but as a foundational functional mechanism structuring human systems and interactions. Diverging from critical traditions that conflate arbitrariness with injustice, it posits arbitrariness as a semiotic trait: a property enabling systems - linguistic, legal, or social - to operate effectively while withholding their internal rationale. Building on Ferdinand de Saussure's concept of l'arbitraire du signe, the analysis extends this principle beyond language to demonstrate its cross-domain applicability, particularly in law and social dynamics. The paper introduces the "Motivation -> Constatability -> Contestability" chain, arguing that motivation functions as a crucial interface rendering an act's logic vulnerable to intersubjective contestation. When this chain is broken through mechanisms like "immotivization" or "Conflict Lateralization" (exemplified by "the blur of the wolf drowned in the fish"), acts produce binding effects without exposing their rationale, thus precluding justiciability. This structural opacity, while appearing illogical, is a deliberate design protecting authority from accountability. Drawing on Shannon's entropy model, the paper formalizes arbitrariness as A = H(L|M) (conditional entropy). It thereby proposes a modern theory of arbitrariness as a neutral operator central to control as well as care, an overlooked dimension of interpersonal relations. While primarily developed through human social systems, this framework also illuminates a new pathway for analyzing explainability in advanced artificial intelligence systems.

First-order logic (FOL) can represent the logical entailment semantics of natural language (NL) sentences, but determining natural language entailment using FOL remains a challenge. To address this, we propose the Entailment-Preserving FOL representations (EPF) task and introduce reference-free evaluation metrics for EPF, the Entailment-Preserving Rate (EPR) family. In EPF, one should generate FOL representations from multi-premise natural language entailment data (e.g. EntailmentBank) so that the automatic prover's result preserves the entailment labels. Experiments show that existing methods for NL-to-FOL translation struggle in EPF. To this extent, we propose a training method specialized for the task, iterative learning-to-rank, which directly optimizes the model's EPR score through a novel scoring function and a learning-to-rank objective. Our method achieves a 1.8-2.7% improvement in EPR and a 17.4-20.6% increase in EPR@16 compared to diverse baselines in three datasets. Further analyses reveal that iterative learning-to-rank effectively suppresses the arbitrariness of FOL representation by reducing the diversity of predicate signatures, and maintains strong performance across diverse inference types and out-of-domain data.

Algorithmic modelling relies on limited information in data to extrapolate outcomes for unseen scenarios, often embedding an element of arbitrariness in its decisions. A perspective on this arbitrariness that has recently gained interest is multiplicity-the study of arbitrariness across a set of "good models", i.e., those likely to be deployed in practice. In this work, we systemize the literature on multiplicity by: (a) formalizing the terminology around model design choices and their contribution to arbitrariness, (b) expanding the definition of multiplicity to incorporate underrepresented forms beyond just predictions and explanations, (c) clarifying the distinction between multiplicity and other traditional lenses of arbitrariness, i.e., uncertainty and variance, and (d) distilling the benefits and potential risks of multiplicity into overarching trends, situating it within the broader landscape of responsible AI. We conclude by identifying open research questions and highlighting emerging trends in this young but rapidly growing area of research.

Machine Learning (ML) algorithms are vital for supporting clinical decision-making in biomedical informatics. However, their predictive performance can vary across demographic groups, often due to the underrepresentation of historically marginalized populations in training datasets. The investigation reveals widespread sex- and age-related inequities in chronic disease datasets and their derived ML models. Thus, a novel analytical framework is introduced, combining systematic arbitrariness with traditional metrics like accuracy and data complexity. The analysis of data from over 25,000 individuals with chronic diseases revealed mild sex-related disparities, favoring predictive accuracy for males, and significant age-related differences, with better accuracy for younger patients. Notably, older patients showed inconsistent predictive accuracy across seven datasets, linked to higher data complexity and lower model performance. This highlights that representativeness in training data alone does not guarantee equitable outcomes, and model arbitrariness must be addressed before deploying models in clinical settings.

Model multiplicity, the phenomenon where multiple models achieve similar performance despite different underlying learned functions, introduces arbitrariness in model selection. While this arbitrariness may seem inconsequential in expectation, its impact on individuals can be severe. This paper explores various individual concerns stemming from multiplicity, including the effects of arbitrariness beyond final predictions, disparate arbitrariness for individuals belonging to protected groups, and the challenges associated with the arbitrariness of a single algorithmic system creating a monopoly across various contexts. It provides both an empirical examination of these concerns and a comprehensive analysis from the legal standpoint, addressing how these issues are perceived in the anti-discrimination law in Canada. We conclude the discussion with technical challenges in the current landscape of model multiplicity to meet legal requirements and the legal gap between current law and the implications of arbitrariness in model selection, highlighting relevant future research directions for both disciplines.

Machine learning (ML) is widely used to moderate online content. Despite its scalability relative to human moderation, the use of ML introduces unique challenges to content moderation. One such challenge is predictive multiplicity: multiple competing models for content classification may perform equally well on average, yet assign conflicting predictions to the same content. This multiplicity can result from seemingly innocuous choices during model development, such as random seed selection for parameter initialization. We experimentally demonstrate how content moderation tools can arbitrarily classify samples as toxic, leading to arbitrary restrictions on speech. We discuss these findings in terms of human rights set out by the International Covenant on Civil and Political Rights (ICCPR), namely freedom of expression, non-discrimination, and procedural justice. We analyze (i) the extent of predictive multiplicity among state-of-the-art LLMs used for detecting toxic content; (ii) the disparate impact of this arbitrariness across social groups; and (iii) how model multiplicity compares to unambiguous human classifications. Our findings indicate that the up-scaled algorithmic moderation risks legitimizing an algorithmic leviathan, where an algorithm disproportionately manages human rights. To mitigate such risks, our study underscores the need to identify and increase the transparency of arbitrariness in content moderation applications. Since algorithmic content moderation is being fueled by pressing social concerns, such as disinformation and hate speech, our discussion on harms raises concerns relevant to policy debates. Our findings also contribute to content moderation and intermediary liability laws being discussed and passed in many countries, such as the Digital Services Act in the European Union, the Online Safety Act in the United Kingdom, and the Fake News Bill in Brazil.

Machine learning models in modern mass-market applications are often updated over time. One of the foremost challenges faced is that, despite increasing overall performance, these updates may flip specific model predictions in unpredictable ways. In practice, researchers quantify the number of unstable predictions between models pre and post update -- i.e., predictive churn. In this paper, we study this effect through the lens of predictive multiplicity -- i.e., the prevalence of conflicting predictions over the set of near-optimal models (the Rashomon set). We show how traditional measures of predictive multiplicity can be used to examine expected churn over this set of prospective models -- i.e., the set of models that may be used to replace a baseline model in deployment. We present theoretical results on the expected churn between models within the Rashomon set from different perspectives. And we characterize expected churn over model updates via the Rashomon set, pairing our analysis with empirical results on real-world datasets -- showing how our approach can be used to better anticipate, reduce, and avoid churn in consumer-facing applications. Further, we show that our approach is useful even for models enhanced with uncertainty awareness.

Variance in predictions across different trained models is a significant, under-explored source of error in fair binary classification. In practice, the variance on some data examples is so large that decisions can be effectively arbitrary. To investigate this problem, we take an experimental approach and make four overarching contributions: We: 1) Define a metric called self-consistency, derived from variance, which we use as a proxy for measuring and reducing arbitrariness; 2) Develop an ensembling algorithm that abstains from classification when a prediction would be arbitrary; 3) Conduct the largest to-date empirical study of the role of variance (vis-a-vis self-consistency and arbitrariness) in fair binary classification; and, 4) Release a toolkit that makes the US Home Mortgage Disclosure Act (HMDA) datasets easily usable for future research. Altogether, our experiments reveal shocking insights about the reliability of conclusions on benchmark datasets. Most fair binary classification benchmarks are close-to-fair when taking into account the amount of arbitrariness present in predictions -- before we even try to apply any fairness interventions. This finding calls into question the practical utility of common algorithmic fairness methods, and in turn suggests that we should reconsider how we choose to measure fairness in binary classification.