Abstract: Following the work in Hammond and Troccoli Moretti (2026) on rational behaviour in finite decision trees with consequence chains, we focus here on consequences that may include a “menu” of consequence chains that are feasible in the continuation subtree which starts at the relevant consequence node. Introducing menu consequences allows prerational behaviour rules, as defined in Hammond (2022), to accommodate a plethora of phenomena that otherwise superficially violate “consequentialism”. Prominent examples include apparent violations of the ordinality and independence axioms of expected utility theory. Other instances of “menu effects” arise because of preferences for when uncertainty is resolved, as well as Epstein–Zin (1989) preferences, and the influence of temptation.

Abstract: Evidence from psychology and neuroscience suggests that negative emotions can weaken self-control. We study dynamic choice when disappointment, used as a proxy for negative emotion, makes future self-control harder. To do so, we develop an axiomatic history-dependent model of choice for an agent who is vulnerable to emotionally driven internal conflicts, but who is otherwise a completely standard economic agent. By dynamic consistency, anticipated future self-control costs enter current choices over risk, so a forward-looking agent may sacrifice first-period welfare to avoid later temptation. The model predicts Dynamic Avoidance of Temptations
and generates temptation-dependent risk attitudes. Certainty has extra value because it eliminates both consumption risk and future self-control risk, while, away from certainty, additional risk may sometimes hedge severe self-control problems. The framework provides a parsimonious decision-theoretic mechanism through which adverse histories affect choices in poverty, addiction, and other economically important environments.

Abstract: Given a consequence domain, following an idea due to Vickrey (1964), Hammond (1976) showed that a behaviour rule defined at every decision node in an unrestricted domain of finite decision trees, including continuation decision trees, will have a set of consequences that depends only on the feasible set of consequences if and only if behaviour maximises a complete and transitive weak preference relation. This result was extended in Hammond (1998a, b) to trees that include chance and event nodes, and to preferences that satisfy the independence axiom with risk, and Anscombe and Aumann’s (1963) sure thing principle if there is also uncertainty. If preferences are continuous on Marschak triangles, behaviour must maximise the expectation of each utility function in a unique cardinal equivalence class. This previous work followed Raiffa (1968) by limiting attention to trees with consequences that accrue only at a terminal node. Here, for the case of trees without event nodes, we extend these earlier results to trees that admit finite chains of consequence nodes that accrue along any path, for which intertemporal utility can be expressed as the sum of history-dependent temporal utility functions. A subsequent paper considers a further extension allowing menu consequences.

Abstract: In this paper, we study choice under objective risk where the primitive is enriched to include an exogenous equivalence relation on the space of lotteries. We seek conditions on this enlarged primitive, ensuring the existence of an expected utility representation in which the Bernoulli utility index may depend on the partition generated by the equivalence relation. We term this model the Partition Dependent Expected Utility (PDEU) and show examples of recent choice models in the literature on non-expected utility that fall into this class. We prove representation theorems characterizing PDEU preferences when the partition generates convex cells, and under different continuity assumptions. Our theorems address partitions with both countable and uncountable elements, with cells that can be lower-dimensional, fully dimensional, or a combination of both. We show that for fully dimensional cells, the parameters of the representation are suitably unique, but this is not the case for lower-dimensional cells. We conclude with a discussion of the technical challenges that may arise when studying partitions with non-convex cells.

Abstract: Classically, testing whether decision makers belong to specific preference classes involves two main approaches. The first, known as the functional approach, assumes access to an entire demand function. The second, the revealed preference approach, constructs inequalities to test finite demand data.

This paper bridges these methods by using the functional approach to test finite data through preference learnability results. We develop a computationally efficient algorithm that generates tests for choice data based on functional characterizations of preference families. We provide these restrictions for various applications, including homothetic and weakly separable preferences, where the latter’s revealed preference characterization is provably NP-Hard.

We also address choice under uncertainty, offering tests for betweenness preferences. Lastly, we perform a simulation exercise demonstrating that our tests are effective in finite samples and accurately reject demands not belonging to a specified class.