相关论文: Differentiating Infinite Voting Populations using …

We study the structure of the Rudin-Frolik order on countably complete ultrafilters under the assumption that this order is directed. This assumption, called the Ultrapower Axiom, holds in all known canonical inner models. It turns out that…

Arrow's Impossibility Theorem establishes bounds on what we can require from voting systems. Given satisfaction of a small collection of "fairness" axioms, it shows votes can only exist as dictatorships in which one voter determines all…

This article explicitly constructs and classifies all arrovian voting systems on three or more alternatives. If we demand orderings to be complete, we have, of course, Arrow's classical dictator theorem, and a closer look reveals the…

An earlier paper, entitled "P-hierarchy on $\beta\omega$", investigated the relations between ordinal ultrafilters and the so-called P-hierarchy. This study is continued in the present paper and focuses on the aspects of characterization of…

We consider social welfare functions that satisfy Arrow's classic axioms of independence of irrelevant alternatives and Pareto optimality when the outcome space is the convex hull of some finite set of alternatives. Individual and…

We study two generalizations of the Rudin-Keisler ordering to ultrafilters on complete Boolean algebras. To highlight the difference between them, we develop new techniques to construct incomparable ultrafilters in this setting.…

We survey some recent results about the order structure of various kinds of ultrafilters. More precisely, we study Rudin-Keisler and Tukey reducibility in classes of selective, stable ordered-union, and P-point ultrafilters. Although these…

This paper initiates the reverse mathematics of social choice theory, studying Arrow's impossibility theorem and related results including Fishburn's possibility theorem and the Kirman--Sondermann theorem within the framework of reverse…

We study the nature (i.e., constructive as opposed to non-constructive) of social welfare orders on infinite utility streams, and their representability by means of real-valued functions. We assume finite anonymity and introduce a new…

We consider the social welfare function a la Arrow, where some voters are not qualified to evaluate some alternatives. Thus, the inputs of the social welfare function are the preferences of voters on the alternatives that they are qualified…

We study various combinatorial properties, and the implications between them, for filters generated by infinite-dimensional subspaces of a countable vector space. These properties are analogous to selectivity for ultrafilters on the natural…

Arrow's celebrated Impossibility Theorem asserts that an election rule, or Social Welfare Function (SWF), between three or more candidates meeting a set of strict criteria cannot exist. Maskin suggests that Arrow's conditions for SWFs are…

Arrow's Theorem concerns a fundamental problem in social choice theory: given the individual preferences of members of a group, how can they be aggregated to form rational group preferences? Arrow showed that in an election between three or…

Arrow's `impossibility' theorem asserts that there are no satisfactory methods of aggregating individual preferences into collective preferences in many complex situations. This result has ramifications in economics, politics, i.e., the…

Ultrafilters are very useful and versatile objects with applications throughout mathematics: in topology, analysis, combinarotics, model theory, and even theory of social choice. Proofs based on ultrafilters tend to be shorter and more…

The visualization and detection of anomalies (outliers) are of crucial importance to many fields, particularly cybersecurity. Several approaches have been proposed in these fields, yet to the best of our knowledge, none of them has…

We present a novel, perspicuous framework for building iterated ultrapowers. Furthermore, our framework naturally lends itself to the construction of a certain type of order indiscernibles, here dubbed tight indiscernibles, which are shown…

We view voting rules as classifiers that assign a winner (a class) to a profile of voters' preferences (an instance). We propose to apply techniques from formal explainability, most notably abductive and contrastive explanations, to…

Social welfare orders seek to combine the disparate preferences of an infinite sequence of generations into a single, societal preference order in some reasonably-equitable way. In [2] Dubey and Laguzzi study a type of social welfare order…

We treat collaborative filtering as a univariate time series estimation problem: given a user's previous votes, predict the next vote. We describe two families of methods for transforming data to encode time order in ways amenable to…