Skip to main content
SpringerLink
Log in

Representability of Ordinal Relations on a Set of Conditional Events

  • Published:
Theory and Decision Aims and scope Submit manuscript

Abstract

Any dynamic decision model should be based on conditional objects and must refer to (not necessarily structured) domains containing only the elements and the information of interest. We characterize binary relations, defined on an arbitrary set of conditional events, which are representable by a coherent generalized decomposable conditional measure and we study, in particular, the case of binary relations representable by a coherent conditional probability.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • R.J. Aumann (1962) ArticleTitleUtility theory without the completeness axiom Econometrica 30 445–462

    Google Scholar 

  • B. Bouchon-Meunier G. Coletti C. Marsala (2002) ArticleTitleIndependence and possibilistic conditioning Annals of Mathematics and Artificial Intelligence 35 107–124 Occurrence Handle10.1023/A:1014579015954

    Article  Google Scholar 

  • A. Capotorti G. Coletti B. Vantaggi (1998) ArticleTitleNon-additive ordinal relations representable by lower or upper probabilities Kybernetika 34 IssueID1 79–90

    Google Scholar 

  • A. Chateauneuf J.Y. Jaffray (1984) ArticleTitleArchimedean qualitative probability Journal of Mathematical Psychology 28 191–204 Occurrence Handle10.1016/0022-2496(84)90026-9

    Article  Google Scholar 

  • A. Chateauneuf (1985) ArticleTitleOn the existence of a probability measure compatible with a total preorder on a boolean algebra Journal of Mathematical Economics 14 43–52 Occurrence Handle10.1016/0304-4068(85)90025-4

    Article  Google Scholar 

  • A. Chateauneuf R. Kast A. Lapied (2001) ArticleTitleConditioning capacities and choquet integrals: the role of comonotony Theory and Decision 51 367–386 Occurrence Handle10.1023/A:1015567329595

    Article  Google Scholar 

  • G. Coletti (1990) ArticleTitleCoherent qualitative probability Journal of Mathematical Psychology 34 297–310 Occurrence Handle10.1016/0022-2496(90)90034-7

    Article  Google Scholar 

  • G. Coletti G. Regoli (1992) ArticleTitleHow can an expert system help in choosing the optimal decision? Theory and Decision 33 IssueID3 253–264 Occurrence Handle10.1007/BF00133644

    Article  Google Scholar 

  • G. Coletti A. Gilio R. Scozzafava (1993) ArticleTitleComparative probability for conditional events: a new look through coherence Theory and Decision 35 IssueID3 237–258 Occurrence Handle10.1007/BF01075200

    Article  Google Scholar 

  • G. Coletti (1994) ArticleTitleCoherent numerical and ordinal Probabilistic assessments IEEE Trasactions on Systems, Man, and Cybernetics 24 IssueID12 1747–1754 Occurrence Handle10.1109/21.328932

    Article  Google Scholar 

  • G. Coletti (1996) ArticleTitleCoherence principles for handling qualitative and quantitative partial probabilistic assessments Mathware and Soft Computing 3 159–172

    Google Scholar 

  • G. Coletti R. Scozzafava (2001) ArticleTitleFrom conditional events to conditional measures: a new axio matic approach Annals of Mathematics and Artificial Intelligence 32 373–392 Occurrence Handle10.1023/A:1016786121626

    Article  Google Scholar 

  • Coletti, G. and Scozzafava, R. (2001b). Locally additive comparative probabilities, Proceedings of the 2nd International Symposium on Imprecise Probabilities and their Applications, Ithaca, pp. 83–92.

  • G. Coletti R. Scozzafava (2002) Probabilistic Logic in a Coherent Setting Trends in logic no 15, Kluwer Dordrecht/Boston/London

    Google Scholar 

  • Coletti, G. and Scozzafava R. (2003). Toward a general theory of conditional beliefs. Proceedings of the 6th Workshop on Uncertainty Processing, Hejnice, pp. 65–76.

  • B. Finetti Particlede (1931) ArticleTitleSul significato soggettivo della, probabilità Fundamenta Matematicae 17 293–329

    Google Scholar 

  • de Finetti, B. (1949). Sull’Impostazione Assiomatica del Calcolo delle Probabilità, Annali Univ. Trieste 19, 3–55. (Engl. transl: Ch. 5 in , Piobability, Induction, Statistics, Wiley, London, 1972).

  • de Finetti, B. (1970). Teoria della Probabilità. Torino: Einaudi (Engl. transl. (1974) Theory of probability, London: Wiley & Sons).

  • L.E. Dubins (1975) ArticleTitleFinitely additive conditional probabilities, conglomerability and disintegration Annals of Probability 3 89–99

    Google Scholar 

  • J. Dubra J. Maccheroni E.A. Ok (2004) ArticleTitleExpected utility theory without the completeness axiom Journal of Economic Theory 115 118–133 Occurrence Handle10.1016/S0022-0531(03)00166-2

    Article  Google Scholar 

  • P.H. Krauss (1968) ArticleTitleRepresentation of conditional probability measures on Boolean algebras Acta Math. Acad. Scient. Hungar 19 229–241 Occurrence Handle10.1007/BF01894506

    Article  Google Scholar 

  • W. Fenchel (1951) Convex Cones Sets and Functions Lectures at Princeton University Princeton NJ

    Google Scholar 

  • T.L. Fine (1973) Theories of Probability Academic Press New York

    Google Scholar 

  • J.Y. Halpern (1999) ArticleTitleA counterexample to theorems of Cox and Fine Journal of Artificial Intelligence Research 10 6785

    Google Scholar 

  • S. Holzer (1985) ArticleTitleOn coherence and conditional prevision Bollettino UMI, Serie VI–C IV IssueID1 441–460

    Google Scholar 

  • D. Lehmann (1996) Generalized qualitative probability: Savage revisited Horvitz Jensen (Eds) Proceeding of the Twelfth Conference on Uncertainty in Artificial Intelligence Portland Oregon Morgan, Kaufmann 381–388

    Google Scholar 

  • R.S. Lehman (1955) ArticleTitleOn confirmation and rational betting The Journal of Symbolic Logic 20 251–262

    Google Scholar 

  • Y. Kannai (1963) ArticleTitleExistence of a utility in infinite dimensional partially ordered spaces Israel Journal of Mathematics 1 229–234

    Google Scholar 

  • B.O. Koopman (1940) ArticleTitleThe axioms and algebra of intuitive probability Annals of Mathematics 41 269–292 Occurrence Handle10.2307/1969003

    Article  Google Scholar 

  • C.H. Kraft J.W. Pratt A. Seidenberg (1959) ArticleTitleIntuitive probability on finite sets Annals of Mathematical Statistics 30 408–419

    Google Scholar 

  • K.R. Popper (1959) The Logic of Scientific Discovery Routledge London

    Google Scholar 

  • T.S. Seidenfeld M.J. Schervish J.B. Kadane (1995) ArticleTitleA representation of partially ordered preferences The Annals of Statistics 23 2168–2217 Occurrence Handle10.1214/aos/1034713653

    Article  Google Scholar 

  • E. Regazzini (1985) ArticleTitleFinitely additive conditional probabilities Rendiconti Sem. Mat. Fis. Milano 55 69–89 Occurrence Handle10.1007/BF02924866

    Article  Google Scholar 

  • L.J. Savage (1954) The Foundations of Statistics Wiley New York

    Google Scholar 

  • D. Scott (1964) ArticleTitleMeasurement structures and linear inequalities Journal of Mathematical Psychology 1 233–247 Occurrence Handle10.1016/0022-2496(64)90002-1

    Article  Google Scholar 

  • K. Vind (2000) ArticleTitlevon Neumann-Morgenstern preferences Journal of Mathematical Economics 33 109–122 Occurrence Handle10.1016/S0304-4068(99)00004-X

    Article  Google Scholar 

  • P. Wakker (1981) ArticleTitleAgreeing probability measures for comparative probability structures Annals of Statistics 9 658–662

    Google Scholar 

  • Williams, P.M. (1975). Notes on conditional previsions, School of Mathematical and Physical Sciences, Working Paper, The University of Sussex.

  • S.K.M. Wong Y.Y. Yao P. Bollmann H.C. Burger (1991) ArticleTitleAxiomatization of qualitative belief structure IEEE Transactions on Systems Man Cybernetics 21 726–734 Occurrence Handle10.1109/21.108290

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dip. Metodi e Modelli Matematici, Università “La Sapienza” Roma, via Scarpa 16, 00161, Roma, Italy

    Giulianella Coletti & Barbara Vantaggi

Authors
  1. Giulianella Coletti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Barbara Vantaggi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Barbara Vantaggi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Coletti, G., Vantaggi, B. Representability of Ordinal Relations on a Set of Conditional Events. Theor Decis 60, 137–174 (2006). https://doi.org/10.1007/s11238-005-4570-4

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11238-005-4570-4

Keywords

Search

Navigation