相关论文: Nonstandard numbers for qualitative decision makin…

Someone knowledgeable in nonstandard analysis may get the feeling that in the nonlinear theory of generalized functions, too often one works directly on the nets and spends effort to obtain results that should be clear from general…

Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action…

In random expected utility (Gul and Pesendorfer, 2006), the distribution of preferences is uniquely recoverable from random choice. This paper shows through two examples that such uniqueness fails in general if risk preferences are random…

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…

We consider a notion of "numerosity" for sets of tuples of natural numbers, that satisfies the five common notions of Euclid's Elements, so it can agree with cardinality only for finite sets. By suitably axiomatizing such a notion, we show…

Identifying when observed statistics cannot be explained by any reasonable classical model is a central problem in quantum foundations. A principled and universally applicable approach to defining and identifying nonclassicality is given by…

Many results on the convex order in the literature were stated for random variables with finite mean. For instance, a fundamental result in dependence modeling is that the sum of a pair of random random variables is upper bounded in convex…

We consider a general class of non-linear Bellman equations. These open up a design space of algorithms that have interesting properties, which has two potential advantages. First, we can perhaps better model natural phenomena. For…

Hartle and Srednicki have suggested that standard quantum theory does not favor our typicality. Here an alternative version is proposed in which typicality is likely, Eventual Quantum Mechanics. This version allows one to calculate…

The infinite random size-biased order with arbitrary positive size parameters is introduced in terms of independent exponential random variables. We collect basic properties and constructions of the order, some of which belong to the…

In the folklore of linear logic, a common intuition is that the structure of finiteness spaces, introduced by Ehrhard, semantically reflects the strong normalization property of cut-elimination. We make this intuition formal in the context…

Recently, Halpern and Leung suggested representing uncertainty by a weighted set of probability measures, and suggested a way of making decisions based on this representation of uncertainty: maximizing weighted regret. Their paper does not…

It is typically understood that the training of modern neural networks is a process of fitting the probability distribution of desired output. However, recent paradoxical observations in a number of language generation tasks let one wonder…

Tackling the problem of ordinal preference revelation and reasoning, we propose a novel methodology for generating an ordinal utility function from a set of qualitative preference statements. To the best of our knowledge, our proposal…

An important goal of empirical demand analysis is choice and welfare prediction on counterfactual budget sets arising from potential policy-interventions. Such predictions are more credible when made without arbitrary…

Ambiguity and ambiguity aversion have been widely studied in decision theory and economics both at a theoretical and an experimental level. After Ellsberg's seminal studies challenging subjective expected utility theory (SEUT), several…

We develop a theory of quantum rational decision making in the tradition of Anscombe and Aumann's axiomatisation of preferences on horse lotteries. It is essentially the Bayesian decision theory generalised to the space of Hermitian…

We present the model theoretic concepts that allow mathematics to be developed with the notion of the potential infinite instead of the actual infinite. The potential infinite is understood as a dynamic notion, being an indefinitely…

A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…

We show that modularity, a quantity introduced in the study of networked systems, can be generalized and used in the clustering problem as an indicator for the quality of the solution. The introduction of this measure arises very naturally…