I think that one can argue that a computationally bounded agent cannot reason about probabilities with infinite precision, and that therefore preferences have to depend on probabilities in a way which is in some sense sufficiently regular, which can justify the topological condition. It would be nice to make this idea precise. Btw, it seems that the topological condition implies the continuity axiom.
I think that one can argue that a computationally bounded agent cannot reason about probabilities with infinite precision, and that therefore preferences have to depend on probabilities in a way which is in some sense sufficiently regular, which can justify the topological condition. It would be nice to make this idea precise. Btw, it seems that the topological condition implies the continuity axiom.