The Economical-Ecological Benefits of Matching Non-matching Socks

Socks are produced and replaced at a massive scale, yet their paired use makes them unusually vulnerable to waste, as the loss of a single sock can strand usable wear-capacity and trigger premature replacement. In this study, we quantify the economic and ecological value of pairing non-matching \say{orphan} socks, and the social cost that discourages this behaviour. We formalize sock ownership as a sequential decision problem under uncertainty in which socks wear out and disappear stochastically during laundering, while public exposure induces a person-specific mismatch penalty. We conducted an in-person study to estimate mismatch sensitivity and diversity preference, linking behavioural heterogeneity to optimal mixing strategies. Using these results and a computer simulation-based evaluation of interpretable pairing policies, we show that strict matching can appear resource-frugal largely because it generates many sockless days, whereas controlled tolerance for mismatch sustains service and reduces stranded capacity across loss regimes. This study establishes the feasibility of matching non-matching socks while outlining its limitations and challenges.