Ridesharing platforms are a type of two-sided marketplace where "supply-demand balance" is critical for market efficiency and yet is complex to define and analyze. We present a unified analytical framework based on the graph-based equilibrium metric (GEM) for quantifying the supply-demand spatiotemporal state and efficiency of a ridesharing marketplace. GEM was developed as a generalized Wasserstein distance between the supply and demand distributions in a ridesharing market and has been used as an evaluation metric for algorithms expected to improve supply-demand alignment. Building upon GEM, we develop SD-GEM, a dual-perspective (supply- and demand-side) representation of rideshare market equilibrium. We show that there are often disparities between the two views and examine how this dual-view leads to the notion of market efficiency, in which we propose novel statistical tests for capturing improvement and explaining the underlying driving factors.

Graph smoothing methods are an extremely popular family of approaches for semi-supervised learning. The choice of graph used to represent relationships in these learning problems is often a more important decision than the particular algorithm or loss function used, yet this choice is less well-studied in the literature. In this work, we demonstrate that for social networks, the basic friendship graph itself may often not be the appropriate graph for predicting node attributes using graph smoothing. More specifically, standard graph smoothing is designed to harness the social phenomenon of homophily whereby individuals are similar to “the company they keep.” We present a decoupled approach to graph smoothing that decouples notions of “identity” and “preference,” resulting in an alternative social phenomenon of monophily whereby individuals are similar to “the company they're kept in,” as observed in recent empirical work. Our model results in a rigorous extension of the Gaussian Markov Random Field (GMRF) models that underlie graph smoothing, interpretable as smoothing on an appropriate auxiliary graph of weighted or unweighted two-hop relationships.