“…Thurstone’s Law of Comparative Judgment essentially states that such pairwise comparisons correspond to an internal, unknown utility scale (Thurstone, 1927). Recovering this hidden information from such qualitative preference is studied in various areas such as ranking theory (Marden, 1995), social choice theory (Rossi, Venable, & Walsh, 2011), voting theory (Coughlin, 2008), sports (Langville & Meyer, 2012), negotiation theory (Druckman, 1993), decision theory (Bouyssou et al, 2002), democratic peace theory (Cuhadar & Druckman, 2014), and marketing research (Rao, Green, & Wind, 2007). Thus, many results in preference learning are based on established statistical models for ranking data, such as the Plackett–Luce (Luce, 1959; Plackett, 1975) or Bradley–Terry (Bradley & Terry, 1952) models, which allow an analyst to model probability distributions over rankings.…”