Related papers: Incompleteness, Independence, and Negative Dominan…
This paper studies a general class of social choice problems in which agents' payoff functions (or types) are privately observable random variables, and monetary transfers are not available. We consider cardinal social choice functions…
Negative probability has found diverse applications in theoretical physics. Thus, construction of sound and rigorous mathematical foundations for negative probability is important for physics. There are different axiomatizations of…
We provide an in-depth study of the recently introduced notion of completely incompatible observables and its links to the support uncertainty and to the Kirkwood-Dirac nonclassicality of pure quantum states. The latter notion has recently…
Dependence logic, introduced in [8], cannot be axiomatized. However, first-order consequences of dependence logic sentences can be axiomatized, and this is what we shall do in this paper. We give an explicit axiomatization and prove the…
The classical concept of bounded completeness and its relation to sufficiency and ancillarity play a fundamental role in unbiased estimation, unbiased testing, and the validity of inference in the presence of nuisance parameters. In this…
In Newcomb's paradox you choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose, a prediction algorithm deduces your choice, and fills the two boxes based…
We review a minimum set of notions from our previous paper on structural properties of SAT at arXiv:0802.1790 that will allow us to define and discuss the "complete internal independence" of a decision problem. This property is strictly…
Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…
We consider collective decision making when the society consists of groups endowed with voting weights. Each group chooses an internal rule that specifies the allocation of its weight to the alternatives as a function of its members'…
May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to…
How can we monitor, in real time, whether one uncertain prospect has any upside over another? To answer this question, we develop a novel family of sequential, anytime-valid tests for stochastic dominance (SD; also known as stochastic…
Logarithmic score and information divergence appear in information theory, statistics, statistical mechanics, and portfolio theory. We demonstrate that all these topics involve some kind of optimization that leads directly to regret…
We propose a framework for strategic voting when a voter may lack knowledge about the preferences of other voters, or about other voters' knowledge about her own preference. In this setting we define notions of manipulation, equilibrium,…
We represent preferences that exhibit absolute or relative attitudes towards ambiguity without assuming convexity of preferences. Our analysis is motivated by the recent experimental evidence by Baillon and Placido (2019) indicating that…
Unaided human decision making appears to systematically violate consistency constraints imposed by normative theories; these biases in turn appear to justify the application of formal decision-analytic models. It is argued that both claims…
We provide a formal framework accounting for a widespread idea in the theory of economic design: analytically established incompatibilities between given axioms should be qualified by the likelihood of their violation. We define the degree…
In submodular optimization we often deal with the expected value of a submodular function $f$ on a distribution $\mathcal{D}$ over sets of elements. In this work we study such submodular expectations for negatively dependent distributions.…
Armstrong's axioms of functional dependency form a well-known logical system that captures properties of functional dependencies between sets of database attributes. This article assumes that there are costs associated with attributes and…
For certain weak versions of the Axiom of Choice (most notably, the Boolean Prime Ideal theorem), we obtain equivalent formulations in terms of partial orders, and filter-like objects within them intersecting certain dense sets or…
Lebesgue's dominated convergence theorem is a crucial pillar of modern analysis, but there are certain areas of the subject where this theorem is deficient. Deeper criteria for convergence of integrals are described in this article.