Probabilistic models of choice (between sure prospects) have become a standard modeling practice since the 1980s, notably through the widespread use of the Logit Multinomial Model pioneered by McFadden (1974). However, the idea to model consumer’s behavior as a probabilistic behavior, hence accounting for some kind of behavioral instability in the pure theory of rational choice, dates back to the 1930s and led to significant investigations in the 1950s. It is the purpose of this article to confront three attempts by economists at developing models of individual choice that go beyond standard ordinalist utility theory through introducing principles of probabilistic behavior. We discuss first Georgescu-Roegen’s neglected contributions to this subject, though he pioneered the definition of probabilistic preference in 1936 and came back on the subject intensively in the 1950s. We then present Marschak’s (and his co-authors) attempts at axiomatizing a probabilistic model of choice in the same period. The third contribution studied is that of Quandt, who provides a more operational style of modeling. This set of contributions is discussed against a general background of transformations of the theory of rational behavior and of the methods proper to it.