You can think of prference learning as two things:

“Scale People” - pairs

“We are observing the same population, but with different types of noise.”

simple scalability, substitutability, independence. In order of increasingly specific: Transitivity and Simple Scalability => Fechner and Quadrupel Condition => Bradley-Terry Preference Model

“Population People” - menus

“We are observing a heterogeneous population, and we are trying to characterize how they are heterogeneous.”

random utility, elimination by aspects, recommender systems => A softmax predictor follows Luce’s Axiom / independence to irrelavent alternatives