  To identify the main mechanisms underlying complex opinion formation
processes in social systems, researchers have long been exploring simple
mechanistic mathematical models. Most existing opinion dynamics models are
built on a common micro-foundation, i.e., the weighted-averaging opinion
update. However, we argue that this universally-adopted mechanism features a
non-negligible unrealistic feature, which brings unnecessary difficulties in
seeking a proper balance between model complexity and predictive power. In this
paper, we propose the weighted-median mechanism as a new micro-foundation of
opinion dynamics, which, with minimal assumptions, fundamentally resolves the
inherent unrealistic feature of the weighted-averaging mechanism. Derived from
the cognitive dissonance theory in psychology, the weighted-median mechanism is
supported by online experiment data and broadens the applicability of opinion
dynamics models to multiple-choice issues with ordered discrete options.
Moreover, the weighted-median mechanism, despite being the simplest in form,
captures various non-trivial real-world features of opinion evolution, while
some widely-studied averaging-based models fail to.
