Related papers: Condorcet's Paradox as Non-Orientability

Hydrodynamic discontinuities in an external potential and incompressible flow are investigated. Using the reaction front as an example in a 2D stream, an overdetermined system of equations is obtained that describes its motion in terms of…

Shape(-and-scale) spaces - configuration spaces for generalized Kendall-type Shape(-and-Scale) Theories - are usually not manifolds but stratified manifolds. While in Kendall's own case - similarity shapes - the shape spaces are…

This paper addresses the problem of constructing a cycle-level intersection theory for toric varieties. We show that by making one global choice, we can determine a cycle representative for the intersection of an equivariant Cartier divisor…

Polarization is a well-documented phenomenon across a wide range of social issues. However, prevailing theories often compartmentalize the examination of herding behavior and opinion convergence within different contexts. In this study, we…

In Newcomb's paradox you choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose though, an antagonist uses a prediction algorithm to deduce your choice,…

A common assumption in modern microeconomic theory is that choice should be rationalizable via a binary preference relation, which \citeauthor{Sen71a} showed to be equivalent to two consistency conditions, namely $\alpha$ (contraction) and…

Given a connected manifold with corners of any codimension there is a very basic and computable homology theory called conormal homology defined in terms of faces and orientations of their conormal bundles, and whose cycles correspond…

This study proposes a new efficiency requirement, a minimal almost weak Pareto principle, which says that x is socially better than y whenever the only one individual never prefers y to x, and all the others prefers x to y. Then, I show…

One of the innovative approaches in contemporary philosophical ontology consists in the assumption of a plurality of ontologies based on different metaphysical presuppositions. Such presuppositions involve, among others, the identification…

We use a simple yet Earth-like atmospheric model to propose a new framework for understanding the mathematics of blocking events. Analysing error growth rates along a very long model trajectory, we show that blockings are associated with…

A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological phases can however similarly be…

Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optimization. We introduce the notion of a Lagrangian dual…

Metric distortion in social choice is a framework for evaluating how well voting rules minimize social cost when both voters and candidates exist in a shared metric space, with a voter's cost defined by their distance to a candidate. Voters…

The problem of lifting a preference order on a set of objects to a preference order on a family of subsets of this set is a fundamental problem with a wide variety of applications in AI. The process is often guided by axioms postulating…

In arXiv:1107.4675 Ralph uses our post-selection model of closed timelike curves (P-CTC) to construct an "unproven-theorem" paradox, and claims that this voids our argument that P-CTCs are able to resolve such types of paradoxes. Here we…

There is an extensive literature in social choice theory studying the consequences of weakening the assumptions of Arrow's Impossibility Theorem. Much of this literature suggests that there is no escape from Arrow-style impossibility…

A path-following control algorithm enables a system's trajectories under its guidance to converge to and evolve along a given geometric desired path. There exist various such algorithms, but many of them can only guarantee local convergence…

A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle…

Peculiar measurements can be obtained on systems that undergo both pre- and post-selection. We prove a conjecture from [1] on logical Pre- and Post-Selection (PPS) paradoxes for a restricted case. We prove that all of these paradoxes admit…

We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise…