Related papers: A Savage-Like Axiomatization for Nonstandard Expec…
We present Nonstandard Analysis by three axioms: the {\em Extension, Transfer and Saturation Principles} in the framework of the superstructure of a given infinite set. We also present several applications of this axiomatic approach to…
We propose an axiomatic approach which economically underpins the representation of dynamic preferences in terms of a stochastic utility function, sensitive to the information available to the decision maker. Our construction is iterative…
We provide sufficient conditions under which a utility function may be recovered from a finite choice experiment. Identification, as is commonly understood in decision theory, is not enough. We provide a general recoverability result that…
This paper presents an axiomatic framework for qualitative decision under uncertainty in a finite setting. The corresponding utility is expressed by a sup-min expression, called Sugeno (or fuzzy) integral. Technically speaking, Sugeno…
In this paper, we first consider a Bayesian framework and model the "utility function" in terms of fuzzy random variables. On the basis of this model, we define the "prior (fuzzy) expected utility" associated with each action, and the…
How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences.…
L.J. Savage once hoped to show that "the superficially incompatible systems of ideas associated on the one hand with [subjective Bayesianism] and on the other hand with [classical statistics]...lend each other mutual support and…
Mutually exclusive decisions have been studied for decades. Many well-known decision theories have been defined to help people either to make rational decisions or to interpret people's behaviors, such as expected utility theory, regret…
We develop a tractable model of realization utility that studies the role of reference-dependent S-shaped preferences in a dynamic investment setting with reinvestment. Our model generates both voluntarily realized gains and losses. It…
Combining short-term experimental data with observational data enables credible long-term policy evaluation. The literature offers two key but non-nested assumptions, namely the latent unconfoundedness (LU; Athey et al., 2020) and…
This paper studies axioms for nonmonotonic consequences from a semantics-based point of view, focusing on a class of mathematical structures for reasoning about partial information without a predefined syntax/logic. This structure is called…
Subjective expected utility theory assumes that decision-makers possess unlimited computational resources to reason about their choices; however, virtually all decisions in everyday life are made under resource constraints - i.e.…
Decision theory does not traditionally include uncertainty over utility functions. We argue that the a person's utility value for a given outcome can be treated as we treat other domain attributes: as a random variable with a density…
To study the assumption that the utility maximization hypothesis implicitly adds to consumer theory, we consider a mathematical representation of pre-marginal revolution consumer theory based on subjective exchange ratios. We introduce two…
We examine behavioral axioms in decision theory that are satisfied approximately rather than exactly. We demonstrate that in key domains -- decisions under risk, uncertainty, and intertemporal choice -- behavior that \emph{almost} satisfies…
People care about decision outcomes and how decisions get made, both when making decisions and reflecting on decisions. But formalizing the full range of normative concerns that drive decisions is an open challenge. We introduce Axiomatic…
How can we extract theoretical insights from machine learning algorithms? We take a familiar lesson: researchers often turn their intuitions into theoretical insights by constructing "anomalies" -- specific examples highlighting…
A variety of statistical graphical models have been defined to represent the conditional independences underlying a random vector of interest. Similarly, many different graphs embedding various types of preferential independences, as for…
We bound features of counterfactual choices in the nonparametric random utility model of demand, i.e. if observable choices are repeated cross-sections and one allows for unrestricted, unobserved heterogeneity. In this setting, tight bounds…
Synthetic data algorithms are widely employed in industries to generate artificial data for downstream learning tasks. While existing research primarily focuses on empirically evaluating utility of synthetic data, its theoretical…