Describes the application of Luce's probabilistic theory of choice behavior to the resolution of referential ambiguity by listeners, together with an experimental paradigm for studying such ambiguity. A series of 48 sets of 3 photographs (faces) each and their 144 (3 * 48) subsets of 2 photographs was presented to 126 male undergraduates. An adjective descriptive of the emotional expression of 1 or more faces in each set, was also presented with each set and its 3 subsets. An S's task was to select the photograph in each case that best fitted the descriptive adjective. A referentially ambiguous set or subset was defined as one for which there was an absence of unanimity of choice. Luce's choice axiom accurately predicted the relations obtained between the 2- and 3-choice data. Results suggest that the choice process in referential ambiguity may be some combination of probabilistic and deterministic processes. Also investigated was the quantitative relationship postulated by the Bradley-Terry model between choice probability and an independently obtained measure of the associative strength of a face to the descriptive adjective. The Bradley-Terry model appeared to fit the data but an exact goodness of fit test could not be made. (16 ref.) (PsycINFO Database Record (c) 2016 APA, all rights reserved)