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**1 - 2**of**2**### Sets of Probability Distributions and Independence

, 2008

"... This paper discusses concepts of independence and their relationship with convexity assumptions in the theory of sets of probability distributions. The paper offers an organized review of the literature and some new ideas (on regular conditional independence and exchangeability/“strong independence” ..."

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This paper discusses concepts of independence and their relationship with convexity assumptions in the theory of sets of probability distributions. The paper offers an organized review of the literature and some new ideas (on regular conditional independence and exchangeability/“strong independence”). Finally, the connection between recent developments on the axiomatization of non-binary preferences, and its impact on “strict” independence, are analyzed.

### PROSPECTS FOR A THEORY OF NON-ARCHIMEDEAN EXPECTED UTILITY: IMPOSSIBILITIES AND POSSIBILITIES

"... In this talk I examine the prospects for a theory of probability aspiring to support a decisiontheoretic interpretation by which principles of probability derive their normative status in virtue of their relationship with principles of rational decision making. More specifically, I investigate the p ..."

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In this talk I examine the prospects for a theory of probability aspiring to support a decisiontheoretic interpretation by which principles of probability derive their normative status in virtue of their relationship with principles of rational decision making. More specifically, I investigate the possibility of a theory of expected utility abiding by distinguished dominance principles which have played a pivotal role in the development of subjective probability and critical discussion thereof. I focus on dominance principles that a theory of real-valued expected utility cannot support, motivating proponents of these principles to develop theories admitting a non-Archimedean range to meet the demands which these principles exact. Thus, specifically, in this talk I examine the prospects for a theory of non-Archimedean expected value and more generally, expected utility. I am certainly not the first to entertain the non-Archimedean possibility. Non-Archimedean representations of uncertainty have captivated the interest of those who wish for rational credal probabilities and expectations either to respect laws supplementing the familiar set of putatively binding laws or to accommodate credal states complementing the familiar set of putatively rational credal states. In other words, at least two distinct considerations have either motivated authors to appeal to a non-Archimedean representation or stirred their excitement about the possibilities such a representation