Related papers: Rationalizing Path-Independent Choice Rules

This paper is devoted to a study of mathematical structures arising from choice functions satisfying the path independence property (Plott functions). We broaden the notion of a choice function by allowing of empty choice. This enables us…

An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…

Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…

Designing networks capable of attaining better performance with an increased inference budget is important to facilitate generalization to harder problem instances. Recent efforts have shown promising results in this direction by making use…

We study random joint choice rules, allowing for interdependence of choice across agents. These capture random choice by multiple agents, or a single agent across goods or time periods. Our interest is in separable choice rules, where each…

In economic theory, an agent chooses from available alternatives -- modeled as a set. In decisions in the field or in the lab, however, agents do not have access to the set of alternatives at once. Instead, alternatives are represented by…

Many regulatory and analytic problems require that a prohibited variable influence a decision only through a designated allowable channel -- a conditional-independence requirement that arises in path-specific fairness, the handling of…

The state of economic theory and accumulated facts from the different branches of the economic science require to analyze the concept of the description of economy systems. The economic reality generates the problems the solution of that is…

This paper introduces the independent choice logic, and in particular the "single agent with nature" instance of the independent choice logic, namely ICLdt. This is a logical framework for decision making uncertainty that extends both logic…

We introduce a new formulation of the axiom of dependent choice that can be viewed as an abstract termination principle, which generalises the recursive path orderings used to establish termination of rewrite systems. We consider several…

Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…

We propose and axiomatize preferences on a product state space in light of uncertainty regarding the dependency of different payoff-relevant factors. Dependence structures allow to decompose probabilities and allow to pin down behavior…

In decision support systems the motivation and justification of the system's diagnosis or classification is crucial for the acceptance of the system by the human user. In Bayesian networks a diagnosis or classification is typically…

For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types…

In the paper, we consider a type of stochastic differential equations driven by G-L\'evy processes. We prove that a kind of their additive functionals has path independence and extend some known results.

We investigate joint probabilistic choice rules describing the behavior of two decision makers, each facing potentially distinct menus. These rules are separable when they can be decomposed into individual choices correlated solely through…

Many modern numerical methods in computational science and engineering rely on derivatives of mathematical models for the phenomena under investigation. The computation of these derivatives often represents the bottleneck in terms of…

We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional…

One of the better studied properties for operators in judgment aggregation is independence, which essentially dictates that the collective judgment on one issue should not depend on the individual judgments given on some other issue(s) in…

Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…