Sets of desirable gambles were proposed by Walley (2000) as a general theory of imprecise probability. The main reasons for this are: it is a very general model, including as particular cases most of the existing theories for imprecise probability; it has a deep and simple axiomatic justification; and mathematical definitions are natural and intuitive. However, there is still a lot of work to be done until the theory of desirable gambles is operative for its use in general reasoning tasks. This paper gives an overview of some of the fundamental concepts expressed in terms of desirable gambles in the finite case, gives a characterization of regular extension, and studies the nature of maximally coherent sets of gambles.
Keywords. Desirable gambles, regular conditioning, zero probabilities, sets of probability measures
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Authors addresses:
Ines Couso
Department of Statistics and O.R.
E.U.I.T. Industrial de Gijon
Modulo 1-Planta 4
Campus Universitario de Viesques
33071 Gijon
Serafín Moral
Dpto. Ciencias de la Computación e IA
ETSI Informática
Universidad de Granada
18071 Granada
SPAIN
E-mail addresses:
| Ines Couso | couso@uniovi.es |
| Serafín Moral | smc@decsai.ugr.es |