Extension to nonlinear utilities and the Plackett–Luce model

Determine whether analogous finite-sample theoretical treatments apply to nonlinear-in-parameter univariate utility functions and to the Plackett–Luce model, extending the established error analysis beyond linear-in-parameter multivariate utility functions under the Bradley–Terry–Luce framework.

Background

The paper develops identifiability conditions, minimax lower bounds, MLE existence results, and non-asymptotic error bounds for linear-in-parameter multivariate utility functions under the Bradley–Terry–Luce model. The authors identify broader utility specifications and ranking models as natural settings in which it is not known whether the same analytical framework remains valid.

The unresolved scope specifically concerns both nonlinear-in-parameter univariate utility functions and the Plackett–Luce model. The question is stated as an open applicability issue rather than as a result addressed elsewhere in the paper.