Related papers: Selection principles related to $\alpha_i$-propert…
We introduce and develop a class of \textit{Cantor-winning} sets that share the same amenable properties as the classical winning sets associated to Schmidt's $(\alpha,\beta)$-game: these include maximal Hausdorff dimension, invariance…
A principal must allocate a set of heterogeneous tasks (or objects) among multiple agents. The principal has preferences over the allocation. Each agent has preferences over which tasks they are assigned, which are their private…
This article offers a gentle introduction to the axiom of choice. We introduce the axiom, discuss some common objections to it, and present three kinds of reasons to accept it. Although the exposition is aimed at non-experts in set theory,…
After sketching the basic theory of injective ideals of homogeneous polynomials, we characterize injective polynomial ideals by means of a domination property and applications of this characterization to some classical operator ideals and…
We consider the specification of effects of numerical actor attributes in statistical models for directed social networks. A fundamental mechanism is homophily or assortativity, where actors have a higher likelihood to be tied with others…
We study a discrete fair division problem where $n$ agents have additive valuation functions over a set of $m$ goods. We focus on the well-known $\alpha$-EFX fairness criterion, according to which the envy of an agent for another agent is…
We study multiwinner elections with approval-based preferences. An instance of a multiwinner election consists of a set of alternatives, a population of voters---each voter approves a subset of alternatives, and the desired committee size…
The axiom of countable choice for reals is one of the most basic fragments of the axiom of choice needed in many parts of mathematics. Descriptive choice principles are a further stratification of this fragment by the descriptive complexity…
This work contributes to a foundational question in economic theory: how do individual-level cognitive biases interact with collective choice mechanisms? We study a setting where voters hold intrinsic preference rankings over a set of…
In this paper, it is shown that $\alpha$-permanent in algebra is closely related to loop soup in probability. We give explicit expansions of $\alpha$-permanents of the block matrices obtained from matrices associated to $*$-forests, which…
Qualitative Choice Logic (QCL) and Conjunctive Choice Logic (CCL) are formalisms for preference handling, with especially QCL being well established in the field of AI. So far, analyses of these logics need to be done on a case-by-case…
A simple mechanism for allocating indivisible resources is sequential allocation in which agents take turns to pick items. We focus on possible and necessary allocation problems, checking whether allocations of a given form occur in some or…
Consider a population of heterogenous agents whose choice behaviors are partially \textit{comparable} according to a given \textit{primitive ordering}.The set of choice functions admissible in the population specifies a \textit{choice…
Selectional restrictions are semantic constraints on forming certain complex types in natural language. The paper gives an overview of modeling selectional restrictions in a relational type system with morphological and syntactic types. We…
This paper investigates image inpainting with preference alignment. Instead of introducing a novel method, we go back to basics and revisit fundamental problems in achieving such alignment. We leverage the prominent direct preference…
For a tensor triangulated category and any regular cardinal $\alpha$ we study the frame of $\alpha$-localizing tensor ideals and its associated space of points. For a well-generated category and its frame of localizing tensor ideals we…
This work explores properties of Strong Data-Processing constants for R\'enyi Divergences. Parallels are made with the well-studied $\varphi$-Divergences, and it is shown that the order $\alpha$ of R\'enyi Divergences dictates whether…
Nowadays there is an increasing interest of physicists in finding regularities related to social phenomena. This interest is clearly motivated by applications that a statistical mechanical description of the human behavior may have in our…
We study real numbers defined by multidimensional automatic arrays weighted by multiplicatively independent bases. Let $a_1, \dots, a_r\geq 2$ be integers such that $\log a_1, \dots, \log a_r$ are $\mathbb Q$-linearly independent. Given…
In school choice, students make decisions based on their expectations of particular schools' suitability, and the decision to gather information about schools is influenced by the acceptance odds determined by the mechanism in place. We…