A Note on Assortativeness Measures
Kenzo Imamura, Suguru Otani, Tohya Sugano, Koji Yokote
Abstract
Chiappori et al. (2025) study several indices of assortativeness in matching, including the aggregate likelihood ratio and the odds ratio. We provide a counterexample showing that their axiomatization of the aggregate likelihood ratio is not valid as stated. We identify the exact class of indices characterized by the axioms in Chiappori et al. (2025). We then show that the axiomatization of the aggregate likelihood ratio can be recovered by adding new axioms. In addition, we point out errors in the axiomatizations of other measures in Chiappori et al. (2025). Finally, we offer a generalization of the odds ratio from two-type markets to multi-type markets.