Related papers: Selection principles related to $\alpha_i$-propert…
When can a majority of voters find common ground, that is, a position they all agree upon? How does the shape of the political spectrum influence the outcome? When mathematical objects have a social interpretation, the associated theorems…
We examine a weighted-network multi-agent model with preferential selection such that agents choose partners with the probability $p(w)$, where $w$ is the number of their past selections. When $p(w)$ increases sublinearly with the number of…
A real number \alpha is called recursively enumerable if there exists a computable, increasing sequence of rational numbers which converges to \alpha. The randomness of a recursively enumerable real \alpha can be characterized in various…
We study the committee selection problem in the canonical impartial culture model with a large number of voters and an even larger candidate set. Here, each voter independently reports a uniformly random preference order over the…
We deal with the strength of classical second-order versions of the Axiom of Choice (AC) in second-order predicate logic (PLII) with Henkin interpretation (HPL). We use the known relationships between the so-called Zermelo-Asser axioms and…
We extend classical Propositional Logic (PL) by adding a new primitive binary connective $\varphi|\psi$, intended to represent the "superposition" of sentences $\varphi$ and $\psi$, an operation motivated by the corresponding notion of…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
The conjecture about the Orlicz P\'olya-Szeg\"o principle posed in [43] is proved. The cases of equality are characterized in the affine Orlicz P\'olya-Szeg\"o principle with respect to Steiner symmetrization and Schwarz spherical…
We discuss general formation of complementary behaviors, functions and forms in biological species competing for resources. We call orthogonalization the related processes on macro and micro-level of a self-organized formation of…
We study selection principles related to bornological covers using the notion of ideals. We consider ideals $\mathcal I$ and $\mathcal J$ on $\omega$ and standard ideal orderings $KB, K$. Relations between cardinality of a base of a…
We study selection principles related to bornological covers in a topological space $X$ following the work of Aurichi et al., 2019, where selection principles have been investigated in the function space $C_\mathfrak{B}(X)$ endowed with the…
This paper investigates two feature-scoring criteria that make use of estimated class probabilities: one method proposed by \citet{shen} and a complementary approach proposed below. We develop a theoretical framework to analyze each…
Modeling the preferences of agents over a set of alternatives is a principal concern in many areas. The dominant approach has been to find a single reward/utility function with the property that alternatives yielding higher rewards are…
We define a general class of models representing natural selection between two alleles. The population size and spatial structure are arbitrary, but fixed. Genetics can be haploid, diploid, or otherwise; reproduction can be asexual or…
Numerous works propose post-hoc, model-agnostic explanations for learning to rank, focusing on ordering entities by their relevance to a query through feature attribution methods. However, these attributions often weakly correlate or…
Several resource allocation problems involve multiple types of resources, with a different agency being responsible for "locally" allocating the resources of each type, while a central planner wishes to provide a guarantee on the properties…
In the impartial selection problem, a subset of agents up to a fixed size $k$ among a group of $n$ is to be chosen based on votes cast by the agents themselves. A selection mechanism is impartial if no agent can influence its own chance of…
Standard methods for aligning large language models with human preferences learn from pairwise comparisons among sampled candidate responses and regularize toward a reference policy. Despite their effectiveness, the effects of sampling and…
We investigate the possibility of an incentive-compatible (IC, a.k.a. strategy-proof) mechanism for the classification of agents in a network according to their reviews of each other. In the $ \alpha $-classification problem we are…
One of the fundamental principles driving diversity or homogeneity in domains such as cultural differentiation, political affiliation, and product adoption is the tension between two forces: influence (the tendency of people to become…