Conglomerable Coherent Lower Previsions

Walley’s theory of coherent lower previsions builds upon the former theory by Williams with the explicit aim to make it deal with conglomerability. We show that such a construction has been only partly successful because Walley’s founding axiom of joint coherence does not entirely capture the implications of conglomerability. As a way to fully achieve Walley’s original aim, we propose then the new theory of conglomerable coherent lower previsions. We show that Walley’s theory coincides with ours when all conditioning events have positive lower probability, or when conditioning partitions are nested.

Authors and Affiliations

1. Department of Statistics and Operations Research, University of Oviedo, 33007, Oviedo, Spain

   Enrique Miranda

2. IDSIA, 6928, Manno, Lugano, Switzerland

   Marco Zaffalon

Corresponding author

Correspondence to Enrique Miranda .

Editors and Affiliations

1. Faculty of Computer Science, Otto-von-Guericke University of Magdebur, Geb. 29, Raum 008, Universitätsplatz 2, Magdeburg, 39106, Germany

   Rudolf Kruse

2. , FB Informatik & Informationswissenschaft, University of Konstanz, Konstanz, 78457, Germany

   Michael R. Berthold

3. of Magdeburg, Faculty of Computer Science, Otto-von-Guericke University, Geb. 29, Universitätsplatz 2 008, Magdeburg, 39106, Germany

   Christian Moewes

4. , Department of Statistics and OR, University of Oviedo, C/ Calvo Sotelo, s/n, Oviedo, 33007, Spain

   María Ángeles Gil

5. Systems Research Institute, Polish Academy of Sciences, Newelska 6, Warsaw, 01-447, Poland

   Przemysław Grzegorzewski

6. Systems Research Institute, Polish Academy of Sciences, Newelska 6, Warsaw, 01-447, Poland

   Olgierd Hryniewicz

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