I’m trying to understand partition dependence in causal decision theories and I’m struggling to think of a case where an act (as opposed to simply the expected utility) is partition dependent. Some detail (very much in order of what I’m wanting to figure out):
1.) I known that Joyce’s causal decision theory is partition-invariant but Sobel’s and Lewis’s theories aren’t and require some specification of what partition is adequate. What happens if such a specification isn’t provided? More specifically, what’s an example of a decision problem where the acts are partition dependent if you don’t ensure you use only adequate partitions?
2.) Extending this: If you do make sure to only use adequate partitions, are there still problems with partition-dependence (other than the small world/grand world problem that Joyce talks about)? In other words, do current definitions of adequate partions:
i.) Ensure that no act will be partition dependent in decision problems that can be discussed.
ii.) Allow all decision problems to be discussed.
I guess what I’m trying to figure out is what the problem of decision dependence is. Is the problem that it means you require a definition of adequate partitions (but that such a definition is easy to find and solves the problem)? Or even with such a definition, does partition dependence still cause problems? Are these problems just about small world/grand world stuff or are they about other partition related issues as well?
I can’t seem to get my head around it and was hoping some concrete answers to my questions would help. Anyone able to help?
Decision theory and partition dependence
I’m trying to understand partition dependence in causal decision theories and I’m struggling to think of a case where an act (as opposed to simply the expected utility) is partition dependent. Some detail (very much in order of what I’m wanting to figure out):
1.) I known that Joyce’s causal decision theory is partition-invariant but Sobel’s and Lewis’s theories aren’t and require some specification of what partition is adequate. What happens if such a specification isn’t provided? More specifically, what’s an example of a decision problem where the acts are partition dependent if you don’t ensure you use only adequate partitions?
2.) Extending this: If you do make sure to only use adequate partitions, are there still problems with partition-dependence (other than the small world/grand world problem that Joyce talks about)? In other words, do current definitions of adequate partions:
i.) Ensure that no act will be partition dependent in decision problems that can be discussed.
ii.) Allow all decision problems to be discussed.
I guess what I’m trying to figure out is what the problem of decision dependence is. Is the problem that it means you require a definition of adequate partitions (but that such a definition is easy to find and solves the problem)? Or even with such a definition, does partition dependence still cause problems? Are these problems just about small world/grand world stuff or are they about other partition related issues as well?
I can’t seem to get my head around it and was hoping some concrete answers to my questions would help. Anyone able to help?