We establish an equivalence between two seemingly different theories: one is the traditional axiomatisation of incomplete preferences on horse lotteries based on the mixture independence axiom; the other is the theory of desirable gambles developed in the context of imprecise probability. The equivalence allows us to revisit incomplete preferences from the viewpoint of desirability and through the derived notion of coherent lower previsions. On this basis, we obtain new results and insights: in particular, we show that the theory of incomplete preferences can be developed assuming only the existence of a worst act---no best act is needed---, and that a weakened Archimedean axiom suffices too; this axiom allows us also to address some controversy about the regularity assumption (that probabilities should be positive---they need not), which enables us also to deal with uncountable possibility spaces; we show that it is always possible to extend in a minimal way a preference relation to one with a worst act, and yet the resulting relation is never Archimedean, except in a trivial case; we show that the traditional notion of state independence coincides with the notion called strong independence in imprecise probability---this leads us to give much a weaker definition of state independence than the traditional one; we rework and uniform the notions of complete preferences, beliefs, values; we argue that Archimedeanity does not capture all the problems that can be modelled with sets of expected utilities and we provide a new notion that does precisely that. Perhaps most importantly, we argue throughout that desirability is a powerful and natural setting to model, and work with, incomplete preferences, even in case of non-Archimedean problems. This leads us to suggest that desirability, rather than preference, should be the primitive notion at the basis of decision-theoretic axiomatisations.
One of the most influential works for this paper has been the one carried out by Galaabaatar and Karni (GK) in @cite_10 .
@cite_10
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This article introduces a suite of approaches and measures to study the impact of co-authorship teams based on the number of publications and their citations on a local and global scale. In particular, we present a novel weighted graph representation that encodes coupled author-paper networks as a weighted co-authorship graph. This weighted graph representation is applied to a dataset that captures the emergence of a new field of science and comprises 614 articles published by 1036 unique authors between 1974 and 2004. To characterize the properties and evolution of this field, we first use four different measures of centrality to identify the impact of authors. A global statistical analysis is performed to characterize the distribution of paper production and paper citations and its correlation with the co-authorship team size. The size of co-authorship clusters over time is examined. Finally, a novel local, author-centered measure based on entropy is applied to determine the global evolution of the field and the identification of the contribution of a single author's impact across all of its co-authorship relations. A visualization of the growth of the weighted co-author network, and the results obtained from the statistical analysis indicate a drift toward a more cooperative, global collaboration process as the main drive in the production of scientific knowledge. © 2005 Wiley Periodicals, Inc. Complexity 10: 57–67, 2005 As part of the celebration of twenty-five years of ACM SIGIR conferences we performed a content analysis of all papers published in the proceedings of SIGIR conferences, including those from 2002. From this we determined, using information retrieval approaches of course, which topics had come and gone over the last two and a half decades, and which topics are currently "hot". We also performed a co-authorship analysis among authors of the 853 SIGIR conference papers to determine which author is the most "central" in terms of a co-authorship graph and is our equivalent of Paul Erdos in Mathematics. In the first section we report on the content analysis, leading to our prediction as to the most topical paper likely to appear at SIGIR2003. In the second section we present details of our co-authorship analysis, revealing who is the "Christopher Lee" of SIGIR, and in the final section we give pointers to where readers who are SIGIR conference paper authors may find details of where they fit into the coauthorship graph. We study the maximum of a Gaussian field on @math ( @math ) whose correlations decay logarithmically with the distance. Kahane Kah85 introduced this model to construct mathematically the Gaussian multiplicative chaos in the subcritical case. Duplantier, Rhodes, Sheffield and Vargas DRSV12a DRSV12b extended Kahane's construction to the critical case and established the KPZ formula at criticality. Moreover, they made in DRSV12a several conjectures on the supercritical case and on the maximum of this Gaussian field. In this paper we resolve Conjecture 12 in DRSV12a : we establish the convergence in law of the maximum and show that the limit law is the Gumbel distribution convoluted by the limit of the derivative martingale. We would like to thank Zhen Huang, Mariana D’Angelo, Dhaval Miyani, Wei Huang, Beom Heyn Kim, Sukwon Oh, and Afshar Ganjali for their suggestions and feedback. We also thank the anonymous reviewers for their constructive comments. The research in this paper was supported by an NSERC CGS-M scholarship, a Bell Graduate scholarship, an NSERC Discovery grant, an ORF-RE grant, and a Tier 2 Canada Research Chair.