Consensus theories: an oriented survey

This article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).Consensus theories ; Arrowian results ; aggregation rules ; metric consensus rules ; median ; tournament solutions ; restricted domains ; lower valuations ; median semilattice ; complexity

Massive Vector Mesons and Gauge Theory

We show that the requirements of renormalizability and physical consistency imposed on perturbative interactions of massive vector mesons fix the theory essentially uniquely. In particular physical consistency demands the presence of at least one additional physical degree of freedom which was not part of the originally required physical particle content. In its simplest realization (probably the only one) these are scalar fields as envisaged by Higgs but in the present formulation without the ``symmetry-breaking Higgs condensate''. The final result agrees precisely with the usual quantization of a classical gauge theory by means of the Higgs mechanism. Our method proves an old conjecture of Cornwall, Levin and Tiktopoulos stating that the renormalization and consistency requirements of spin=1 particles lead to the gauge theory structure (i.e. a kind of inverse of 't Hooft's famous renormalizability proof in quantized gauge theories) which was based on the on-shell unitarity of the $S$-matrix. We also speculate on a possible future ghostfree formulation which avoids ''field coordinates'' altogether and is expected to reconcile the on-shell S-matrix point of view with the off-shell field theory structure.Comment: 53 pages, version to appear in J. Phys.

Consensus theories: an oriented survey

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2010.htmlDocuments de travail du Centre d'Economie de la Sorbonne 2010.57 - ISSN : 1955-611XThis article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).Cet article présente une vue d'ensemble de sept directions de recherche en théorie du consensus : résultats arrowiens, règles d'agrégation définies au moyen de fédérations, règles définies au moyen de distances, solutions de tournoi, domaines restreints, théories abstraites du consensus, questions de complexité et d'algorithmique. Ce panorama est orienté dans la mesure où il présente principalement – mais non exclusivement – les travaux les plus significatifs obtenus – quelquefois avec d'autres chercheurs – par une équipe de chercheurs français qui sont – ou ont été – membres pléniers ou associés du Centre d'Analyse et de Mathématique Sociale (CAMS)

Distributed Detection and Estimation in Wireless Sensor Networks

In this article we consider the problems of distributed detection and estimation in wireless sensor networks. In the first part, we provide a general framework aimed to show how an efficient design of a sensor network requires a joint organization of in-network processing and communication. Then, we recall the basic features of consensus algorithm, which is a basic tool to reach globally optimal decisions through a distributed approach. The main part of the paper starts addressing the distributed estimation problem. We show first an entirely decentralized approach, where observations and estimations are performed without the intervention of a fusion center. Then, we consider the case where the estimation is performed at a fusion center, showing how to allocate quantization bits and transmit powers in the links between the nodes and the fusion center, in order to accommodate the requirement on the maximum estimation variance, under a constraint on the global transmit power. We extend the approach to the detection problem. Also in this case, we consider the distributed approach, where every node can achieve a globally optimal decision, and the case where the decision is taken at a central node. In the latter case, we show how to allocate coding bits and transmit power in order to maximize the detection probability, under constraints on the false alarm rate and the global transmit power. Then, we generalize consensus algorithms illustrating a distributed procedure that converges to the projection of the observation vector onto a signal subspace. We then address the issue of energy consumption in sensor networks, thus showing how to optimize the network topology in order to minimize the energy necessary to achieve a global consensus. Finally, we address the problem of matching the topology of the network to the graph describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R. Chellapa and S. Theodoridis, Eds., Elsevier, 201

Indeterminateness and `The' Universe of Sets: Multiversism, Potentialism, and Pluralism

In this article, I survey some philosophical attitudes to talk concerning `the' universe of sets. I separate out four different strands of the debate, namely: (i) Universism, (ii) Multiversism, (iii) Potentialism, and (iv) Pluralism. I discuss standard arguments and counterarguments concerning the positions and some of the natural mathematical programmes that are suggested by the various views

The Pareto principle of optimal inequality

inequality aversion, Pareto principle, uncertainty, time consistency

Large-scale Bias and Efficient Generation of Initial Conditions for Non-Local Primordial Non-Gaussianity

We study the scale-dependence of halo bias in generic (non-local) primordial non-Gaussian (PNG) initial conditions of the type motivated by inflation, parametrized by an arbitrary quadratic kernel. We first show how to generate non-local PNG initial conditions with minimal overhead compared to local PNG models for a general class of primordial bispectra that can be written as linear combinations of separable templates. We run cosmological simulations for the local, and non-local equilateral and orthogonal models and present results on the scale-dependence of halo bias. We also derive a general formula for the Fourier-space bias using the peak-background split (PBS) in the context of the excursion set approach to halos and discuss the difference and similarities with the known corresponding result from local bias models. Our PBS bias formula generalizes previous results in the literature to include non-Markovian effects and non-universality of the mass function and are in better agreement with measurements in numerical simulations than previous results for a variety of halo masses, redshifts and halo definitions. We also derive for the first time quadratic bias results for arbitrary non-local PNG, and show that non-linear bias loops give small corrections at large-scales. The resulting well-behaved perturbation theory paves the way to constrain non-local PNG from measurements of the power spectrum and bispectrum in galaxy redshift surveys.Comment: 43 pages, 10 figures. v2: references added. 2LPT parallel code for generating non-local PNG initial conditions available at http://cosmo.nyu.edu/roman/2LP

Local non-Bayesian social learning with stubborn agents

We study a social learning model in which agents iteratively update their beliefs about the true state of the world using private signals and the beliefs of other agents in a non-Bayesian manner. Some agents are stubborn, meaning they attempt to convince others of an erroneous true state (modeling fake news). We show that while agents learn the true state on short timescales, they "forget" it and believe the erroneous state to be true on longer timescales. Using these results, we devise strategies for seeding stubborn agents so as to disrupt learning, which outperform intuitive heuristics and give novel insights regarding vulnerabilities in social learning

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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