Abstract
We investigate how to model indifference with choice functions. We take the coherence axioms for choice functions proposed by Seidenfeld, Schervisch and Kadane as a source of inspiration, but modify them to strengthen the connection with desirability. We discuss the properties of choice functions that are coherent under our modified set of axioms and the connection with desirability. Once this is in place, we present an axiomatisation of indifference in terms of desirability. On this we build our characterisation of indifference in terms of choice functions.
| Original language | English |
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| Title of host publication | Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications |
| Editors | Thomas Augustin, Enrique Miranda, Serena Doria, Erik Quaeghebeur |
| Pages | 305-314 |
| Number of pages | 10 |
| Publication status | Published - 2015 |
| Externally published | Yes |
| Event | 9th International Symposium on Imprecise Probability: Theories and Applications, ISIPTA 2015 - Pescara, Italy Duration: 20 Jul 2015 → 24 Jul 2015 |
Conference
| Conference | 9th International Symposium on Imprecise Probability: Theories and Applications, ISIPTA 2015 |
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| Country/Territory | Italy |
| City | Pescara |
| Period | 20/07/15 → 24/07/15 |
Funding
Gert de Cooman’s research was partly funded through project number 3G012512 of the Research Foundation Flanders (FWO). Erik Quaeghebeur’s contribution is part of the Safe Statistics project financed by the Netherlands Organisation for Scientific Research (NWO). Enrique Miranda acknowledges financial support by project TIN2014-59543-P. The authors would like to express their gratitude to anonymous reviewers for their helpful comments and suggestions, and to Jasper De Bock for the undominated background noise and stimulating discussion.
Keywords
- Choice function
- Coherence
- E-admissibility
- Indifference
- Maximality
- Set of desirable gambles