The Fundamental Concepts of Classical Equilibrium Statistical Mechanics

A critical examination of some basic conceptual issues in classical statistical mechanics is attempted, with a view to understanding the origins, structure and statuts of that discipline. Due attention is given to the interplay between physical and mathematical aspects, particularly regarding the role of probability theory. The focus is on the equilibrium case, which is currently better understood, serving also as a prelude for a further discussion of non-equilibrium statistical mechanics.Comment: 33 pages, overview, conceptual discussio

Modular Theory, Non-Commutative Geometry and Quantum Gravity

This paper contains the first written exposition of some ideas (announced in a previous survey) on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states and categories of observables in a covariant theory. Care has been taken to provide a coverage of the relevant background on modular theory, its applications in non-commutative geometry and physics and to the detailed discussion of the main foundational issues raised by the proposal.Comment: Special Issue "Noncommutative Spaces and Fields

Teaching Economics As a Science: The 1930 Yale Lectures of Ragnar Frisch

This paper is prepared for the forthcoming publication of Frisch's 1930 Yale lecture notes, A Dynamic Approach to Economic Theory: The Yale Lectures of Ragnar Frisch (details at: http://www.routledgeeconomics.com/books/A-Dynamic-Approach-to-Economic-Theory-isbn9780415564090). As the lecture series was given just as the Econometric Society was founded in 1930. We provide as background, a blow-by-blow story of how the Econometric Society got founded with emphasis on Frisch's role. We then outline how the Yale lecture notes came into being, closely connected to Frisch's econometric work at the time. We comment upon the lectures, relating them to Frisch's later works and, more important, to subsequent developments in economics and econometrics.History of econometrics

Measuring power and satisfaction in societies with opinion leaders: An axiomatization

URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/documents-de-travail/Documents de travail du Centre d'Economie de la Sorbonne 2011.18 - ISSN : 1955-611XA well-known model in sociology and marketing is that of opinion leadership. Opinion leaders are actors who are able to affect the behavior of their followers. Hence, opinion leaders have some power over their followers, and they can exercise this power by influencing their followers choice of action. We study a two-action model for a society with opinion leaders. We assume that each member of the society has an inclination to choose one of these actions and that the collective choice is made by simple majority of the actions chosen by each member. For this model, we axiomatize satisfaction and power scores, which allow us to investigate the effects of different opinion leader-follower structures.Un modèle bien connu en sociologie et gestion est celui du leadership d'opinion. Les leaders d'opinion sont des acteurs qui peuvent influer sur les comportements de leurs disciples. En conséquence, les leaders d'opinion ont un certain pouvoir sur leurs disciples et ils peuvent exercer ce pouvoir en influençant le choix d'action de leurs disciples. Nous étudions un modèle de deux actions pour une société avec des leaders d'opinion. Nous supposons que chaque membre de la société a une inclination de choisir une des actions et que le choix collectif est fait par la majorité simple des actions choisies par chaque membre. Pour ce modèle, nous axiomatisons les scores de satisfaction et de pouvoir, ce qui nous permet d'examiner les effets des différentes structures de leader d'opinion - disciples

Measuring Power and Satisfaction in Societies with Opinion Leaders: Dictator and Opinion Leader Properties

A well known and established model in communication policy in sociology and marketing is that of opinion leadership. Opinion leaders are actors in a society who are able to affect the behavior of other members of the society called followers. Hence, opinion leaders might have a considerable impact on the behavior of markets and other social agglomerations being made up of individual actors choosing among a number of alternatives. For marketing or policy purposes it appears to be interesting to investigate the effect of different opinion leader-follower structures in markets or any other collective decision-making situations in a society. We study a two-action model in which the members of a society are to choose one action, for instance, to buy or not to buy a certain joint product, or to vote yes or no on a specific proposal. Each of the actors has an inclination to choose one of the actions. By definition opinion leaders have some power over their followers, and they exercise this power by influencing the behavior of their followers, i.e. their choice of action. After all actors have chosen their actions, a decision-making mechanism determines the collective choice resulting out of the individual choices. Making use of bipartite digraphs we introduce novel satisfaction and power scores which allow us to analyze the actors' satisfaction and power with respect to the collective choice for societies with different opinion leader-follower structures. Moreover, we study common dictator and opinion leader properties of the above scores and illustrate our findings for a society with five members.Bipartite digraph ; influence ; inclination ; collective choice ; opinion leader ; follower ; satisfaction ; power ; dictator properties ; opinion leader properties