Theory Dec. DOI 10.1007/s11238-016-9564-x A note on a recent paper by Dagsvik on IIA and random utilities P. O. Lindberg 1,2 · Tony E. Smith 3 © Springer Science+Business Media New York 2016 Abstract In a recent paper in this journal, Dagsvik derives the class of independent random utility representations that are “equivalent” to the independence-from- irrelevant-alternatives (IIA) assumption by Luce (Individual choice behavior: a theoretical analysis. Wiley, New York, 1959). In this short note, we clarify the relations between this paper by Dagsvik, and a paper in Lindberg’s 2012 thesis. Keywords Random utility · IIA (Independence from irrelevant alternatives) · Choice probabilities 1 Introduction In a recent paper in this journal, Dagsvik (2016) addresses the question of what independent random utility (RU) representations are equivalent 1 to the famous independence-from-irrelevant-alternatives (IIA) assumption of Luce (1959). There 1 The term “equivalent” in the title of Dagsvik’s paper is somewhat misleading since additional condi- tions are required, including infinitely expandable choice sets. Indeed, it is shown by counterexample in Lindberg (2012b) that the stated equivalence does not hold without this latter assumption. Tony E. Smith was the Opponent to P. O. Lindberg’s thesis. B Tony E. Smith tesmith@seas.upenn.edu P. O. Lindberg polin@kth.se 1 Centre for Transport Studies, KTH Royal Institute of Technology, Stockholm, Sweden 2 Swedish National Road and Transport Research Institute, Stockholm, Sweden 3 Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, USA 123