Connecting choice functions and sets of desirable gambles

We study Seidenfeld, Schervish, and Kadane’s notion of choice functions, and want to make them accessible to people who are familiar with sets of desirable gambles. We relate both theories explicitly using their derived strict partial orderings. We give an expression for the most conservative extension of a set of desirable gambles to a choice function. Because it is important for inference purposes, we also make a link with belief structures