Related papers: The Limits of Tolerance
Two key identifying assumptions used to justify difference-in-differences are parallel trends and no anticipation, yet both may fail in practice. I propose a class of assumptions on anticipation and derive closed-form, sharp bounds on the…
Rating aggregation plays a crucial role in various fields, such as product recommendations, hotel rankings, and teaching evaluations. However, traditional averaging methods can be affected by participation bias, where some raters do not…
The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterizations of approximate stationarity and transversality of collections of sets are exposed, analyzed and refined,…
The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…
An identity s=t is linear if each variable occurs at most once in each of the terms s and t. Let T be a tolerance relation of an algebra A in a variety defined by a set of linear identities. We prove that there exist an algebra B in the…
Limit can be defined by two axioms: 1. Strict inequality between limits implies, ultimately, strict inequality between functions. 2. For constant functions limit is trivial. How can basic results on convergence be derived from these axioms?…
We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a…
We take an axiomatic approach to study redistribution problems when agents report income and needs. We formalize axioms reflecting ethical and operational principles such as additivity, impartiality and individual rationality. Different…
We study a two-alternative voting game where voters' preferences depend on an unobservable world state and each voter receives a private signal correlated to the true world state. We consider the collective decision when voters can…
We analyze the adversarial examples problem in terms of a model's fault tolerance with respect to its input. Whereas previous work focuses on arbitrarily strict threat models, i.e., $\epsilon$-perturbations, we consider arbitrary valid…
We prove a central limit theorem for the length of the longest subsequence of a random permutation which follows one of a class of repeating patterns. This class includes every fixed pattern of ups and downs having at least one of each,…
Capability indices are dimensionless quantities measuring the aptitude of a process to manufacture items whose characteristics must be within a specified tolerance ranges. The usual indices $C_p$, $C_{pk}$, $C_{pm}$, and $C_{pmk}$ are used…
We explore a model of non-Bayesian information aggregation in networks. Agents non-cooperatively choose among Friedkin-Johnsen type aggregation rules to maximize payoffs. The DeGroot rule is chosen in equilibrium if and only if there is…
Laws of large numbers guarantee that given a large enough sample from some population, the measure of any fixed sub-population is well-estimated by its frequency in the sample. We study laws of large numbers in sampling processes that can…
Residential segregation is analyzed via the Schelling model, in which two types of agents attempt to optimize their situation according to certain preferences and tolerance levels. Several variants of this work are focused on urban or…
We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…
The paper proposes another extension of the extremal principle. A new extremality model involving collections of arbitrary families of sets is studied. It generalizes the conventional model based on linear translations of given sets as well…
Many learning paradigms self-select training data in light of previously learned parameters. Examples include active learning, semi-supervised learning, bandits, or boosting. Rodemann et al. (2024) unify them under the framework of…
We develop original models to study interacting agents in financial markets and in social networks. Within these models randomness is vital as a form of shock or news that decays with time. Agents learn from their observations and learning…
In this paper we analyze judgement aggregation problems in which a group of agents independently votes on a set of complex propositions that has some interdependency constraint between them(e.g., transitivity when describing preferences).…