Deferred Acceptance (DA), a widely implemented algorithm, is meant to improve allocations: under classical preferences, it induces preference-concordant rankings. However, recent evidence shows that—in both real, large-stakes applications and experiments—participants frequently play seemingly dominated, significantly costly, strategies that avoid small chances of good outcomes. We show theoretically why, with expectations-based loss aversion, this behavior may be partly intentional. Reanalyzing existing experimental data on random serial dictatorship (a restriction of DA), we show that such reference-dependent preferences, with a degree and distribution of loss aversion that explain common levels of risk aversion elsewhere, fit the data better than do no-loss-aversion preferences.