Aggregating Elo Ratings: An Axiomatization (opens in new tab)

Many environments assign several Elo ratings to the same agent: a chess player has classical, rapid, and blitz ratings; an online platform may rate by time control, mode, or format; an evaluator may rate performance across tasks or roles. This paper axiomatizes when such a vector of ratings can be reduced to a single scalar rating that is itself on the Elo scale. We impose three substantive conditions: same-scale normalization (a uniform profile...