Ah, so not like, A is strongly preferred to B and B is strongly preferred to A, but more of a violation of transitivity. Then I still think that the Broome paper is a place I’d look at, since you get that exact kind of structure in preference aggregation.
The Bradley paper assumes everything is transitive throughout, so I don’t think you get the kind of structure you want there. I’m not immediately aware of any work of that kind of inconsistency in JB that isn’t in the social choice context, but there might be some. I’ll take a look.
There are ways to think about degrees and measures of incoherence, and how that connects up to decision making. I’m thinking mainly of this paper by Schervish, Seidenfeld, and Kadane, Measures of Incoherence: How Not to Gamble if You Must. There might a JB-style version of that kind of work, and if there isn’t, I think it would be good to have one.
But to your core goal or weakening the preference axioms to more realistic standards, you can definitely do that in JB by weakening the preference axioms, but still keeping the background objects of preference be propositions in a single algebra. I think this would still preserve many of what I consider the naturalistic advantages of the JB system. For modifying the preference axioms, I would guess descriptively you might want something like prospect theory, or something else along those broad lines. Also depends on what kinds of agents we want to describe.
I want to be able to describe agents that do not have (vNM, geometric, other) rational preferences because of incompleteness or inconsistency but self-modify to become so.
Eg. In vNM utility theory there is a fairly natural weakening one can do which is ask for a vNM-style representation theorem after dropping transitivity.
[ Incidentally, there is some interesting math here having to do with conservative vs nonconservative vector fields and potentials theory all the way to hodge theory. ]
does JB support this ?
Im confused since in vNM we start with a preference order over probability distributions. But in JB irs over propositions?
Mmmmm
Inconsistent and incomplete preferences are necessary for descriptive agent foundations.
In vNM preference theory an inconsistent preference can be described as cyclic preferences that can be moneypumped.
How to see this in JB ?
Ah, so not like, A is strongly preferred to B and B is strongly preferred to A, but more of a violation of transitivity. Then I still think that the Broome paper is a place I’d look at, since you get that exact kind of structure in preference aggregation.
The Bradley paper assumes everything is transitive throughout, so I don’t think you get the kind of structure you want there. I’m not immediately aware of any work of that kind of inconsistency in JB that isn’t in the social choice context, but there might be some. I’ll take a look.
There are ways to think about degrees and measures of incoherence, and how that connects up to decision making. I’m thinking mainly of this paper by Schervish, Seidenfeld, and Kadane, Measures of Incoherence: How Not to Gamble if You Must. There might a JB-style version of that kind of work, and if there isn’t, I think it would be good to have one.
But to your core goal or weakening the preference axioms to more realistic standards, you can definitely do that in JB by weakening the preference axioms, but still keeping the background objects of preference be propositions in a single algebra. I think this would still preserve many of what I consider the naturalistic advantages of the JB system. For modifying the preference axioms, I would guess descriptively you might want something like prospect theory, or something else along those broad lines. Also depends on what kinds of agents we want to describe.
I want to be able to describe agents that do not have (vNM, geometric, other) rational preferences because of incompleteness or inconsistency but self-modify to become so.
Eg. In vNM utility theory there is a fairly natural weakening one can do which is ask for a vNM-style representation theorem after dropping transitivity.
[ Incidentally, there is some interesting math here having to do with conservative vs nonconservative vector fields and potentials theory all the way to hodge theory. ]
does JB support this ?
Im confused since in vNM we start with a preference order over probability distributions. But in JB irs over propositions?