Coherent choice functions, desirability and indifference
Arthur Van Camp (Universiteit Gent)
Gert de Cooman (Universiteit Gent)
Enrique Miranda (Universidad de Oviedo)
Erik Quaeghebeur (TU Delft - Wind Energy)
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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 definition of indifference in terms of choice functions, which we discuss in some detail.
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