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Modeling uncertainty using accept & reject statements

Erik Quaeghebeur (UGent) , Gert De Cooman (UGent) and Filip Hermans (UGent)
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Abstract
Uncertainty and preference is often modeled using linear previsions and linear orders. Some more expressive models use sets of probabilities, lower previsions, or partial orders (see, e.g., the work of Seidenfeld et al. and Walley). In the discussion of these more expressive models, or even to justify them, alternative representations in terms of sets of so-called acceptable, favorable, or desirable gambles appear (cf. the work of Williams, Seidenfeld et al., and Walley). Such ‘sets of gambles’-based models are attractive because of their geometric nature. We generalize these ‘sets of gambles’-based models by considering a pair of sets, one with accepted gambles and one with rejected gambles. We develop a framework based on a small number of axioms—No Confusion, Deductive Closure, No Limbo, and Indifference to Status Quo—and provide an interesting characterization of the resulting models. Furthermore, we define a pair of equivalent gamble relations that generalize the partial orders mentioned earlier; the corresponding characterization result is also given.
Keywords
statements, preference, accept, reject, acceptability, indifference, favorability, desirability, prevision

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Chicago
Quaeghebeur, Erik, Gert De Cooman, and Filip Hermans. 2012. “Modeling Uncertainty Using Accept & Reject Statements.” In Frontiers of Rationality and Decision, Abstracts.
APA
Quaeghebeur, E., De Cooman, G., & Hermans, F. (2012). Modeling uncertainty using accept & reject statements. Frontiers of Rationality and Decision, Abstracts. Presented at the Frontiers of Rationality and Decision.
Vancouver
1.
Quaeghebeur E, De Cooman G, Hermans F. Modeling uncertainty using accept & reject statements. Frontiers of Rationality and Decision, Abstracts. 2012.
MLA
Quaeghebeur, Erik, Gert De Cooman, and Filip Hermans. “Modeling Uncertainty Using Accept & Reject Statements.” Frontiers of Rationality and Decision, Abstracts. 2012. Print.
@inproceedings{2977779,
  abstract     = {Uncertainty and preference is often modeled using linear previsions and linear orders. Some more expressive models use sets of probabilities, lower previsions, or partial orders (see, e.g., the work of Seidenfeld et al. and Walley). In the discussion of these more expressive models, or even to justify them, alternative representations in terms of sets of so-called acceptable, favorable, or desirable gambles appear (cf. the work of Williams, Seidenfeld et al., and Walley). Such {\textquoteleft}sets of gambles{\textquoteright}-based models are attractive because of their geometric nature. We generalize these {\textquoteleft}sets of gambles{\textquoteright}-based models by considering a pair of sets, one with accepted gambles and one with rejected gambles. We develop a framework based on a small number of axioms---No Confusion, Deductive Closure, No Limbo, and Indifference to Status Quo---and provide an interesting characterization of the resulting models. Furthermore, we define a pair of equivalent gamble relations that generalize the partial orders mentioned earlier; the corresponding characterization result is also given.},
  author       = {Quaeghebeur, Erik and De Cooman, Gert and Hermans, Filip},
  booktitle    = {Frontiers of Rationality and Decision, Abstracts},
  keyword      = {statements,preference,accept,reject,acceptability,indifference,favorability,desirability,prevision},
  language     = {eng},
  location     = {Groningen, The Netherlands},
  pages        = {2},
  title        = {Modeling uncertainty using accept \& reject statements},
  year         = {2012},
}