Allocation Multiplicity: Evaluating the Promises of the Rashomon Set

The Rashomon set of equally-good models promises less discriminatory algorithms, reduced outcome homogenization, and fairer decisions through model ensembles or reconciliation. However, we argue from the perspective of allocation multiplicity that these promises may remain unfulfilled. When there are more qualified candidates than resources available, many different allocations of scarce resources can achieve the same utility. This space of equal-utility allocations may not be faithfully reflected by the Rashomon set, as we show in a case study of healthcare allocations. We attribute these unfulfilled promises to several factors: limitations in empirical methods for sampling from the Rashomon set, the standard practice of deterministically selecting individuals with the lowest risk, and structural biases that cause all equally-good models to view some qualified individuals as inherently risky.