The axiomatic foundations of Bayesian decision theory.
dc.contributor.author | Joyce, James Michael | en_US |
dc.contributor.advisor | Sklar, Lawrence | en_US |
dc.contributor.advisor | Gibbard, Allan | en_US |
dc.date.accessioned | 2014-02-24T16:31:09Z | |
dc.date.available | 2014-02-24T16:31:09Z | |
dc.date.issued | 1992 | en_US |
dc.identifier.other | (UMI)AAI9226930 | en_US |
dc.identifier.uri | http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:9226930 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/105921 | |
dc.description.abstract | Bayesian decision theorists argue that rational agents should always perform acts that maximize subjective expected utility. To justify this claim, they prove representation theorems which are designed to show that any decision maker whose beliefs and desires satisfy reasonable axiomatic constraints will necessarily behave like an expected utility maximizer. The existence of such a representation result is a prerequisite for any adequate account of rational choice because one is only able to determine what a decision theory says about beliefs and desires by looking at the axioms used in the proof of its representation result. I examine a number of versions of decision theory and their representation theorems. Particular attention is paid to so-called causal and evidential decision theories. It is argued that only the latter has an adequate representation which is found in a theorem due to Ethan Bolker which was adapted to the decision theoretic context by R. Jeffrey. I remove the single outstanding problem with Bolker's theorem by reformulating it in a way which yields a unique probability and utility representation. This is possible because, unlike Bolker, I make use of axioms which govern not only preference but comparative probability. I show how this reformulated version of Bolker's result can be further generalized to a representation theorem for a generic theory of conditional expected utility whose basic term is a function which measures the strength of an agent's desires when he supposes that various hypotheses are true. Evidential and causal decision theories are show to be special cases of this generic theory. They differ only in the interpretation they give to the notion of supposition. The evidential account interprets it indicatively, while the causal account views it subjunctively. Finally, I show how my generic representation theorem for conditional decision theory can serve as a foundation for both causal and evidential decision theories. This provides the first fully adequate representation result for causal decision theory, thereby removing its most serious defect. | en_US |
dc.format.extent | 250 p. | en_US |
dc.subject | Mathematics | en_US |
dc.subject | Philosophy | en_US |
dc.subject | Economics, Theory | en_US |
dc.title | The axiomatic foundations of Bayesian decision theory. | en_US |
dc.type | Thesis | en_US |
dc.description.thesisdegreename | PhD | en_US |
dc.description.thesisdegreediscipline | Philosophy | en_US |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/105921/1/9226930.pdf | |
dc.description.filedescription | Description of 9226930.pdf : Restricted to UM users only. | en_US |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
Files in this item
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.