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.
“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.