Related papers: Computational geometry and the U.S. Supreme Court

We present a unifying framework encompassing many social choice settings. Viewing each social choice setting as voting in a suitable metric space, we consider a general model of social choice over metric spaces, in which---similarly to the…

The significance and influence of US Supreme Court majority opinions derive in large part from opinions' roles as precedents for future opinions. A growing body of literature seeks to understand what drives the use of opinions as precedents…

In this paper, we argue that simulation platforms enable a novel type of embodied spatial reasoning, one facilitated by a formal model of object and event semantics that renders the continuous quantitative search space of an open-world,…

Many algorithms used are based on geometrical computation. There are several criteria in selecting appropriate algorithm from already known. Recently, the fastest algorithms have been preferred. Nowadays, algorithms with a high stability…

Starting from the (apparently) elementary problem of deciding how many different topological spaces can be obtained by gluing together in pairs the faces of an octahedron, we will describe the central role played by hyperbolic geometry…

A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…

The space of possible behaviors complex biological systems may exhibit is unimaginably vast, and these systems often appear to be stochastic, whether due to variable noisy environmental inputs or intrinsically generated chaos. The brain is…

Large language models are increasingly used to predict human preferences in both scientific and business endeavors, yet current approaches rely exclusively on analyzing model outputs without considering the underlying mechanisms. Using…

We consider a spatial voting model where both candidates and voters are positioned in the $d$-dimensional Euclidean space, and each voter ranks candidates based on their proximity to the voter's ideal point. We focus on the scenario where…

Citizen-focused democratic processes where participants deliberate on alternatives and then vote to make the final decision are increasingly popular today. While the computational social choice literature has extensively investigated voting…

GPT-style language models are sensitive to single-token changes at generation points where the predicted probability distribution is spread across multiple tokens. Viewing this sensitivity as a geometric property, we derive an…

In many settings people must give numerical scores to entities from a small discrete set. For instance, rating physical attractiveness from 1--5 on dating sites, or papers from 1--10 for conference reviewing. We study the problem of…

Recent studies show that deep vision-only and language-only models--trained on disjoint modalities--nonetheless project their inputs into a partially aligned representational space. Yet we still lack a clear picture of where in each network…

In multi-objective decision planning and learning, much attention is paid to producing optimal solution sets that contain an optimal policy for every possible user preference profile. We argue that the step that follows, i.e, determining…

This work examines the Conditional Approval Framework for elections involving multiple interdependent issues, specifically focusing on the Conditional Minisum Approval Voting Rule. We first conduct a detailed analysis of the computational…

In computational social choice, the distortion of a voting rule quantifies the degree to which the rule overcomes limited preference information to select a socially desirable outcome. This concept has been investigated extensively, but…

Argumentation accommodates various rhetorical devices, such as questions, reported speech, and imperatives. These rhetorical tools usually assert argumentatively relevant propositions rather implicitly, so understanding their true meaning…

Spatial linguistic surveys often reveal well defined geographical zones where certain linguistic forms are dominant over their alternatives. It has been suggested that these patterns may be understood by analogy with coarsening in models of…

This survey concerns probabilistic models motivated by cooperative sequential adsorption (CSA) models. CSA models are widely used in physics and chemistry for modelling adsorption processes in which adsorption rates depend on the spatial…

Recently, implicit neural representations have gained popularity for learning-based 3D reconstruction. While demonstrating promising results, most implicit approaches are limited to comparably simple geometry of single objects and do not…