We develop a hierarchy of families of stochastic choice rules in terms of increasing complexity based on the concepts of a conditional probability space (Renyi, 1955) and a dimensionally-ordered system of measures (Renyi, 1956). The levels of our hierarchy are single-valued or point conditional probability spaces (PCPS’s); conditional probability spaces; probabilistic mixtures of PCPS’s; mutually absolutely continuous mixtures of PCPS’s; absolutely continuous mixtures of PCPS’s; and signed probability mixtures of PCPS’s.We show at a general measure-theoretic level that the first five levels are strictly nested. In the finite case, the sixth level nests all the other levels (the general case here appears to be open). Our hierarchy organizes various well-known axioms for stochastic choice and identifies some new relationships among them. It also offers a precise definition of contextuality in stochastic choice and, from this, a new classification of some leading behavioral effects in choice.

We model choices of a person (a doer) whose preferences and considerations sets can be strategically manipulated by another agent (a planner) via costly unobserved incentives. This interpretation can be interpersonal—where the planner and the doer are distinct individuals—or intrapersonal where the planner motivates her future self. In general, doers can be motivated by advertising, monetary transfers, commitments, and other techniques. We model choice functions that are consistent with a broad class of such incentive schemes. Our main axiom relaxes the classic WARP, but in a way different than the rationalization and inattention effects in Manzini and Mariotti (2007) and Masatlioglu, Nakajima, and Ozbay (2012) respectively. Besides axiomatic foundations, we provide revelation principles in all of these frameworks. Without loss in generality, every incentive scheme can be identified as a utility function that is imposed on the doer. Equivalently, the planner can select the doer’s consideration sets without perturbing his utility. The interpretations with unobserved monetary transfers allow a simple welfare analysis. Our model has natural extensions to incomplete datasets and preferences over menus.

In this paper, I refine the random utility model (RUM) of Block and Marschak (1959) to represent stochastic choice data with quasi-linear types. In my framework, choices are observed across pairs of goods and money. The random quasi-linear utility function is identified uniquely in my model. This identification implies a unique social welfare aggregator that is consistent with the Pareto efficiency criteria. In general, the uniqueness of the quasi-linear tie-breaking rule is not guaranteed, but it can be obtained in a special case where the tie-breaking is uniform. I also characterize a special case where the set of possible types is binary. (A continuation under the same name was published as a joint paper, but there is still some novel material in this version that might be used later in a separate paper.)

To delegate future choices, planners can influence doers in various ways. In the intrapersonal case, a planner can motivate her future self by commitments, promises, deadlines etc. In the interpersonal case, doers can be selected and/or persuaded to change their beliefs.

This article models litigation in signaling games with an imperfectly informed victim and a perfectly informed defendant. I compare a two-agent game and a three-agent extension where the victim can hire a lawyer who is perfectly informed but who pursues a selfish objective in his advice.