Related papers: Condorcet's Paradox as Non-Orientability

Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…

We study social choice mechanisms in an implicit utilitarian framework with a metric constraint, where the goal is to minimize \textit{Distortion}, the worst case social cost of an ordinal mechanism relative to underlying cardinal…

We introduce a single-winner perspective on voting on matchings, in which voters have preferences over possible matchings in a graph, and the goal is to select a single collectively desirable matching. Unlike in classical matching problems,…

Preference-based many-objective optimization faces two obstacles: an expanding space of trade-offs and heterogeneous, context-dependent human value structures. Towards this, we propose a Bayesian framework that learns a small set of latent…

We introduce a novel family of mechanisms for constrained allocation problems which we call local priority mechanisms. These mechanisms are parameterized by a function which assigns a set of agents, the local compromisers, to every…

A central push in operations models over the last decade has been the incorporation of models of customer choice. Real world implementations of many of these models face the formidable stumbling block of simply identifying the `right' model…

Bayesian networks are directed acyclic graphs representing independence relationships among a set of random variables. A random variable can be regarded as a set of exhaustive and mutually exclusive propositions. We argue that there are…

Motivated by questions like: which spatial structures may be characterized by means of modal logic, what is the logic of space, how to encode in modal logic different geometric relations, topological logic provides a framework for studying…

The Stokes paradox is the statement that in a viscous two dimensional fluid, the "linear response" problem of fluid flow around an obstacle is ill-posed. We present a simple consequence of this paradox in the hydrodynamic regime of a Fermi…

We prove special cases of a general conjecture: If an invertible field theory admits a projectively topological boundary theory, then it has finite order in the abelian group of invertible field theories. One can substitute `gapped' for…

Preferences play a key role in determining what goals/constraints to satisfy when not all constraints can be satisfied simultaneously. In this work, we study preference-based planning in a stochastic system modeled as a Markov decision…

A venerable problem in combinatorics and geometry asks whether a given incidence relation may be realized by a configuration of points and lines. The classic version of this would ask for algebraic lines over some field or possibly real…

We consider synchronous iterative voting, where voters are given the opportunity to strategically choose their ballots depending on the outcome deduced from the previous collective choices.We propose two settings for synchronous iterative…

The concepts of topology have a profound impact on physics research spanning the fields of condensed matter, photonics and acoustics and predicting topological states that provide unprecedented versatility in routing and control of waves of…

When composing multiple preferences characterizing the most suitable results for a user, several issues may arise. Indeed, preferences can be partially contradictory, suffer from a mismatch with the level of detail of the actual data, and…

We consider arbitrary orderings of the edges entering each vertex of the (downward directed) Pascal graph. Each ordering determines an adic (Bratteli-Vershik) system, with a transformation that is defined on most of the space of infinite…

This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…

Filtered probability spaces (called "filtrations" for short) are shown to satisfy such a topological zero-one law: for every property of filtrations, either the property holds for almost all filtrations, or its negation does. In particular,…

Experiments on decision making under uncertainty are known to display a classical pattern of risk aversion and risk seeking referred to as "fourfold pattern" (or "reflection effect") , but recent experiments varying the speed and order of…

Network topologies can be non-trivial, due to the complex underlying behaviors that form them. While past research has shown that some processes on networks may be characterized by low-order statistics describing nodes and their neighbors,…