Violating the Continuity Axiom is bad because it allows you to be money pumped.
Violations of continuity aren’t really vulnerable to proper/standard money pumps. The author calls it “arbitrarily close to pure exploitation” but that’s not pure exploitation. It’s only really compelling if you assume a weaker version of continuity in the first place, but you can just deny that.
I think transitivity (+independence of irrelevant alternatives) and countable independence (or the countable sure-thing principle) are enough to avoid money pumps, and I expect give a kind of expected utility maximization form (combining McCarthy et al., 2019andRussell & Isaacs, 2021).
Against the requirement of completeness (or the specific money pump argument for it by Gustafsson in your link), see Thornley here.
To be clear, countable independence implies your utilities are “bounded” in a sense, but possibly lexicographic. See Russell & Isaacs, 2021.
Violations of continuity aren’t really vulnerable to proper/standard money pumps. The author calls it “arbitrarily close to pure exploitation” but that’s not pure exploitation. It’s only really compelling if you assume a weaker version of continuity in the first place, but you can just deny that.
I think transitivity (+independence of irrelevant alternatives) and countable independence (or the countable sure-thing principle) are enough to avoid money pumps, and I expect give a kind of expected utility maximization form (combining McCarthy et al., 2019 and Russell & Isaacs, 2021).
Against the requirement of completeness (or the specific money pump argument for it by Gustafsson in your link), see Thornley here.
To be clear, countable independence implies your utilities are “bounded” in a sense, but possibly lexicographic. See Russell & Isaacs, 2021.