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Montes, Ignacio; Miranda, Enrique; Destercke, Sébastien
Information sciences, 05/2019, Letnik: 481Journal Article
•We prove some properties of the Pari Mutuel Model as a coherent lower (and upper) probability.•We show that a Pari Mutuel Model is a particular case of a probability interval.•We give the maximal number of extreme points of the credal set associated with a Pari Mutuel Model and we give the form of those extreme points.•We give sufficient and necessary conditions for the Pari Mutuel Model to induce a belief function.•We show how to merge information given in terms of Pari Mutuel Models. The pari-mutuel model is a betting scheme that has its origins in horse racing, and that has been applied in a number of contexts, mostly economics. In this paper, we consider the set of probability measures compatible with a pari-mutuel model, characterize its extreme points, and investigate the properties of the associated lower and upper probabilities. We show that the pari-mutuel model can be embedded within the theory of probability intervals, and prove necessary and sufficient conditions for it to be a belief function or a minitive measure. In addition, we also investigate the combination of different pari-mutuel models and their definition on product spaces.
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