Related papers: Great Expectations. Part II: Generalized Expected …
The form and justification of inductive inference rules depend strongly on the representation of uncertainty. This paper examines one generic representation, namely, incomplete information. The notion can be formalized by presuming that the…
Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…
We propose a control-theoretic interpretation of recommender systems and use this perspective to analyze how fairness interventions shape long-term system behavior. Fairness concerns arise for both users and creators, ranging from opinion…
In decision theory an act is a function from a set of conditions to the set of real numbers. The set of conditions is a partition in some algebra of events. The expected value of an act can be calculated when a probability measure is given.…
A simple mathematical model is proposed to study the effect of the average trend of a population on the opinion of each individual, when a group decision has to be made by voting. It is shown that if such effect is strong enough a…
We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that…
We design two mechanisms that ensure that the majority preferred option wins in all equilibria. The first one is a simultaneous game where agents choose other agents to cooperate with on top of the vote for an alternative, thus overcoming…
This note proves a law of large numbers for predicting several steps ahead, which, in the case of uniformly bounded random variables, generalizes the standard law of large numbers for martingales; the standard law of large numbers…
This survey reviews recent developments in revealed preference theory. It discusses the testable implications of theories of choice that are germane to specific economic environments. The focus is on expected utility in risky environments;…
We consider finite games in strategic form with Choquet expected utility. Using the notion of (unambiguously) believed, we define Choquet rationalizability and characterize it by Choquet rationality and common beliefs in Choquet rationality…
Although many investigators affirm a desire to build reasoning systems that behave consistently with the axiomatic basis defined by probability theory and utility theory, limited resources for engineering and computation can make a complete…
Classic decision-theory is based on the maximum expected utility (MEU) principle, but crucially ignores the resource costs incurred when determining optimal decisions. Here we propose an axiomatic framework for bounded decision-making that…
This paper provides a model to analyze and identify a decision maker's (DM's) hypothetical reasoning. Using this model, I show that a DM's propensity to engage in hypothetical thinking is captured exactly by her ability to recognize…
Shepard's universal law of generalization is a remarkable hypothesis about how intelligent organisms should perceive similarity. In its broadest form, the universal law states that the level of perceived similarity between a pair of stimuli…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
We advance a general theory of coherent preference that surrenders restrictions embodied in orthodox doctrine. This theory enjoys the property that any preference system admits extension to a complete system of preferences, provided it…
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…
Biological approximations, which are universal for diverse species, are well known. With no other experimental data, their invariance to transformations from one species to another yields exact conservation (with respect to biological…
Well protected human and laboratory animal populations with abundant resources are evolutionary unprecedented, and their survival far beyond reproductive age may be a byproduct rather than tool of evolution. Physical approach, which takes…
In mechanical design, there is often unavoidable uncertainty in estimates of design performance. Evaluation of design alternatives requires consideration of the impact of this uncertainty. Expert heuristics embody assumptions regarding the…