  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.
