Editing Bayesian probability (section)

===Dutch book approach===
{{main|Dutch book}}
[[Bruno de Finetti]] proposed the Dutch book argument based on betting. A clever [[bookmaker]] makes a [[Dutch book]] by setting the [[odds]] and bets to ensure that the bookmaker profits—at the expense of the gamblers—regardless of the outcome of the event (a horse race, for example) on which the gamblers bet. It is associated with [[probability|probabilities]] implied by the odds not being [[Coherence (philosophical gambling strategy)|coherent]].

However, [[Ian Hacking]] noted that traditional Dutch book arguments did not specify Bayesian updating: they left open the possibility that non-Bayesian updating rules could avoid Dutch books. For example, [[Ian Hacking|Hacking]] writes<ref>Hacking (1967), Section 3, page 316</ref><ref>Hacking (1988, page 124)</ref> "And neither the Dutch book argument, nor any other in the personalist arsenal of proofs of the probability axioms, entails the dynamic assumption. Not one entails Bayesianism. So the personalist requires the dynamic assumption to be Bayesian. It is true that in consistency a personalist could abandon the Bayesian model of learning from experience. Salt could lose its savour."

In fact, there are non-Bayesian updating rules that also avoid Dutch books (as discussed in the literature on "[[probability kinematics]]"<ref>{{cite journal |last=Skyrms |first=Brian |date=1987-01-01 |title=Dynamic Coherence and Probability Kinematics |journal=Philosophy of Science |volume=54 |issue=1 |pages=1–20 |doi=10.1086/289350 |jstor=187470 |citeseerx=10.1.1.395.5723 |s2cid=120881078 |df=dmy-all}}</ref> following the publication of [[Richard Jeffrey|Richard C. Jeffrey]]'s rule, which is itself regarded as Bayesian<ref>{{cite encyclopedia |url=http://plato.stanford.edu/entries/bayes-theorem/ |title=Bayes' Theorem |publisher =stanford.edu |df=dmy-all|last = Joyce|first = James|encyclopedia= The Stanford Encyclopedia of Philosophy |date =30 September 2003 }}</ref>). The additional hypotheses sufficient to (uniquely) specify Bayesian updating are substantial<ref>{{Cite book |title=Probability in Physics |url=https://archive.org/details/probabilityphysi00benm |url-access=limited |last1=Fuchs |first1=Christopher A. |last2=Schack |first2=Rüdiger |chapter=Bayesian Conditioning, the Reflection Principle, and Quantum Decoherence |date=2012-01-01 |publisher=Springer Berlin Heidelberg |isbn=9783642213281 |editor-last1=Ben-Menahem |editor-first1=Yemima |series=The Frontiers Collection |pages=[https://archive.org/details/probabilityphysi00benm/page/n245 233]–247 |language=en |arxiv=1103.5950 |doi=10.1007/978-3-642-21329-8_15 |s2cid=119215115 |editor-last2=Hemmo |editor-first2=Meir |df=dmy-all}}</ref> and not universally seen as satisfactory.<ref>{{cite book |author-link=Bas van Fraassen |last=van Frassen |first=Bas |year=1989 |title=Laws and Symmetry |publisher=Oxford University Press |isbn=0-19-824860-1}}</ref>