Bayesianism, Infinite Decisions, and Binding Export

@article{citeulike:3840182, abstract = {We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as Trumped' (Arntzenius and McCarthy 1997), Rouble trouble' (Arntzenius and Barrett 1999), The airtight Dutch book' (McGee 1999), and The two envelopes puzzle' (Broome 1999). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably additive. The resolution also shows that when infinitely many decisions are involved, the difference between making the decisions simultaneously and making them sequentially can be the difference between riches and ruin. Finally, the resolution reveals a new way in which the ability to make binding commitments can save perfectly rational agents from sure losses. 10.1093/mind/113.450.251}, author = {Arntzenius, Frank and Elga, Adam and Hawthorne, John}, citeulike-article-id = {3840182}, citeulike-linkout-0 = {http://dx.doi.org/10.1093/mind/113.450.251}, citeulike-linkout-1 = {http://mind.oxfordjournals.org/cgi/content/abstract/113/450/251}, day = {1}, doi = {10.1093/mind/113.450.251}, journal = {Mind}, keywords = {bayesian, overcomingbias, philosophy, probability}, month = {April}, number = {450}, pages = {251--283}, posted-at = {2009-01-01 20:07:58}, priority = {0}, title = {Bayesianism, Infinite Decisions, and Binding}, url = {http://dx.doi.org/10.1093/mind/113.450.251}, volume = {113}, year = {2004} }

TY - JOUR ID - citeulike:3840182 L3 - citeulike-article-id:3840182 N2 - We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as Trumped' (Arntzenius and McCarthy 1997), Rouble trouble' (Arntzenius and Barrett 1999), The airtight Dutch book' (McGee 1999), and The two envelopes puzzle' (Broome 1999). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably additive. The resolution also shows that when infinitely many decisions are involved, the difference between making the decisions simultaneously and making them sequentially can be the difference between riches and ruin. Finally, the resolution reveals a new way in which the ability to make binding commitments can save perfectly rational agents from sure losses. 10.1093/mind/113.450.251 IS - 450 JF - Mind EP - 283 TI - Bayesianism, Infinite Decisions, and Binding VL - 113 SP - 251 KW - bayesian KW - overcomingbias KW - philosophy KW - probability AU - Arntzenius, Frank AU - Elga, Adam AU - Hawthorne, John PY - 2004/04/01/ UR - http://dx.doi.org/10.1093/mind/113.450.251 ER -