You can avoid losing pointlessly without having complete preference orderings. Having complete preference orderings is unnecessary work. Like Dilbert, I love the sweet smell of unnecessary work!
You can avoid being Dutch Booked without Independence. A sufficient principle to avoid being Dutch Booked is “don’t get Dutch Booked.” That can be achieved without Independence. For example, people who choose as Allais noted most do in the Allais Paradox thereby violate (the complete axiom set including, it seems especially including) Independence. But they do not thereby get Dutch Booked.
Yes, I like your “unlosing agents” approach a lot. It is more modest than some interpretations of utility, and largely for that reason, a big step in the right direction, in my view.
I disagree that Allais choosers will get Dutch Booked if they remain consistent, unless perhaps you mean “consistent” to build in some very strong set of other axioms of decision theory. They simply make more distinctions among gambles and sequences of gambles than traditional theory allows for. An Allais chooser can reasonably object, for example, that a sequence of choices and randomized events is different from a single choice followed by a single randomized event, even if decision theory treats them as “equivalent”.
If you’re an active investor, the markets or the universe can punish you for deviating from independence unless you’re paying very close attention.
But this is again my general point—the mode decision you have to make (including decisions not to do something) the closer an unlosing agent resembles an expected utility maximiser.
I probably agree with you, but what’s your exact point?
You can avoid losing pointlessly without having complete preference orderings. Having complete preference orderings is unnecessary work. Like Dilbert, I love the sweet smell of unnecessary work!
You can avoid being Dutch Booked without Independence. A sufficient principle to avoid being Dutch Booked is “don’t get Dutch Booked.” That can be achieved without Independence. For example, people who choose as Allais noted most do in the Allais Paradox thereby violate (the complete axiom set including, it seems especially including) Independence. But they do not thereby get Dutch Booked.
“avoid getting dutch booked” is essentially what unlosing agents do.
And people who make non-independent choices in the Allais paradox will get dutch booked if they remain consistent to their non-independent choices.
Your point about completeness not being needed ahead of time is very valid.
Yes, I like your “unlosing agents” approach a lot. It is more modest than some interpretations of utility, and largely for that reason, a big step in the right direction, in my view.
I disagree that Allais choosers will get Dutch Booked if they remain consistent, unless perhaps you mean “consistent” to build in some very strong set of other axioms of decision theory. They simply make more distinctions among gambles and sequences of gambles than traditional theory allows for. An Allais chooser can reasonably object, for example, that a sequence of choices and randomized events is different from a single choice followed by a single randomized event, even if decision theory treats them as “equivalent”.
If you’re an active investor, the markets or the universe can punish you for deviating from independence unless you’re paying very close attention.
But this is again my general point—the mode decision you have to make (including decisions not to do something) the closer an unlosing agent resembles an expected utility maximiser.