Related papers: Condorcet's Paradox as Non-Orientability
We present a mechanism for the emergence of strange attractors (observable chaos) in a two-parameter periodically-perturbed family of differential equations on the plane. The two parameters are independent and act on different ways in the…
Election polls play a critical role in political discussions by probing public opinion and enabling political parties to assess their performance before elections. However, traditional polling methods sometimes fail to predict election…
Within the frame of a Group Approach to Quantization anomalies arise in a quite natural way. We present in this talk an analysis of the basic obstructions that can be found when we try to translate symmetries of the Newton equations to the…
We study a class of maps having the Collatz function (famously related to the Collatz Conjecture) as an example, under the topological and ergodic perspectives, including an approach with thermodynamic formalism. By introducing a key…
A cornerstone of social choice theory is Condorcet's paradox which says that in an election where $n$ voters rank $m$ candidates it is possible that, no matter which candidate is declared the winner, a majority of voters would have…
We show that one-dimensional Euclidean preference profiles can not be characterized in terms of finitely many forbidden substructures. This result is in strong contrast to the case of single-peaked and single-crossing preference profiles,…
When making a decision as a group, there are two primary paradigms: aggregating preferences (e.g. voting, mechanism design) and aggregating information (e.g. discussion, consulting, forecasting). Almost all formally-studied group…
Individual choices often depend on the order in which the decisions are made. In this paper, we expose a general theory of measurable systems (an example of which is an individual's preferences) allowing for incompatible (non-commuting)…
Opacity is a generic security property, that has been defined on (non probabilistic) transition systems and later on Markov chains with labels. For a secret predicate, given as a subset of runs, and a function describing the view of an…
A large amount of literature in social choice theory deals with quantifying the probability of certain election outcomes. One way of computing the probability of a specific voting situation under the Impartial Anonymous Culture assumption…
Various structured argumentation frameworks utilize preferences as part of their standard inference procedure to enable reasoning with preferences. In this paper, we consider an inverse of the standard reasoning problem, seeking to identify…
The scope of this paper is two-fold. First, to present to the researchers in combinatorics an interesting implementation of permutations avoiding generalized patterns in the framework of discrete-time dynamical systems. Indeed, the orbits…
The theory of general relativity predicts the existence of closed time-like curves (CTCs), which theoretically would allow an observer to travel back in time and interact with their past self. This raises the question of whether this could…
Social choice has become a foundational component of modern machine learning systems. From auctions and resource allocation to the alignment of large generative models, machine learning pipelines increasingly aggregate heterogeneous…
Graph-based recommender systems have achieved remarkable effectiveness by modeling high-order interactions between users and items. However, such approaches are significantly undermined by popularity bias, which distorts the interaction…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
Coalition formation over graphs is a well studied class of games whose players are vertices and feasible coalitions must be connected subgraphs. In this setting, the existence and computation of equilibria, under various notions of…
We consider voting on multiple independent binary issues. In addition, a weighting vector for each voter defines how important they consider each issue. The most natural way to aggregate the votes into a single unified proposal is…
In this paper, we explore the three-dimensional chaotic set near a homoclinic cycle to a hyperbolic bifocus at which the vector field has negative divergence. If the invariant manifolds of the bifocus satisfy a non-degeneracy condition, a…
We propose a general theory for surface patterning in many different biological systems, including mite and insect cuticles, pollen grains, fungal spores, and insect eggs. The patterns of interest are often intricate and diverse, yet an…