Related papers: Is Arrow's Dictator a Drinker?
AI advice is becoming increasingly popular, e.g., in investment and medical treatment decisions. As this advice is typically imperfect, decision-makers have to exert discretion as to whether actually follow that advice: they have to…
As machine learning and algorithmic decision making systems are increasingly being leveraged in high-stakes human-in-the-loop settings, there is a pressing need to understand the rationale of their predictions. Researchers have responded to…
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
We study abstract versions of G\"odel's second incompleteness theorem and formulate generalizations of L\"ob's derivability conditions that work for logics weaker than the classical one. We isolate the role of contraction rule in G\"odel's…
Arbitrary Arrow Update Logic with Common Knowledge (AAULC) is a dynamic epistemic logic with (i) an arrow update operator, which represents a particular type of information change and (ii) an arbitrary arrow update operator, which…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
We derive tractable necessary and sufficient conditions for the absence of buy-and-hold arbitrage opportunities in a perfectly liquid, one period market. We formulate the positivity of Arrow-Debreu prices as a generalized moment problem to…
There is an extensive literature in social choice theory studying the consequences of weakening the assumptions of Arrow's Impossibility Theorem. Much of this literature suggests that there is no escape from Arrow-style impossibility…
M-estimators for Generalized Linear Models are considered under minimal assumptions. Under these preliminaries, strong convergence of the estimators are discussed and an expansion of the estimating operators are given in the non-i.i.d. case…
Relative observability has been introduced and studied in the framework of partially observed discrete-event systems as a condition stronger than observability, but weaker than normality. However, unlike observability, relative…
This essay offers a meta-level analysis in the sociology and history of physics in the context of the so-called "Arrow of Time Problem" or "Two Times Problem," which asserts that the empirically observed directionality of time is in…
We explore the problem of binary classification in machine learning, with a twist - the classifier is allowed to abstain on any datum, professing ignorance about the true class label without committing to any prediction. This is directly…
The Wigner's friend thought experiment was intended to illustrate the difficulty one has in describing an agent as a quantum system when that agent performs a measurement. While it does pose a challenge to the orthodox interpretation of…
The classical Arrow's Theorem answers "how can $n$ voters obtain a collective preference on a set of outcomes, if they have to obey certain constraints?" We give an analogue in the judgment aggregation framework of List and Pettit,…
Observers restricted to the observation of pointer states of apparatus cannot conclusively demonstrate that the pointer of an apparatus A registers the state of a system of interest S without perturbing S. Observers cannot, therefore,…
Recent years have witnessed an increasing number of interpretation methods being developed for improving transparency of NLP models. Meanwhile, researchers also try to answer the question that whether the obtained interpretation is faithful…
Linear logical frameworks with subexponentials have been used for the specification of among other systems, proof systems, concurrent programming languages and linear authorization logics. In these frameworks, subexponentials can be…
The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…
Mathematical proof aims to deliver confident conclusions, but a very similar process of deduction can be used to make uncertain estimates that are open to revision. A key ingredient in such reasoning is the use of a "default" estimate of…
In many scenarios, the interpretability of machine learning models is a highly required but difficult task. To explain the individual predictions of such models, local model-agnostic approaches have been proposed. However, the process…