## Objective Bayesianism, Bayesian Conditionalisation (2008)

Citations: | 7 - 6 self |

### BibTeX

@MISC{Voluntarism08objectivebayesianism,,

author = {Voluntarism and Jon Williamson},

title = {Objective Bayesianism, Bayesian Conditionalisation},

year = {2008}

}

### OpenURL

### Abstract

Objective Bayesianism has been criticised on the grounds that objective Bayesian updating, which on a finite outcome space appeals to the maximum entropy principle, differs from Bayesian conditionalisation. The main task of this paper is to show that this objection backfires: the difference between the two forms of updating reflects negatively on Bayesian conditionalisation rather than on objective Bayesian updating. The paper also reviews some existing criticisms and justifications of conditionalisation, arguing in particular that the diachronic Dutch book justification fails because diachronic Dutch book arguments are subject to a reductio: in certain circumstances one can Dutch book an agent however she changes her degrees of belief. One may also criticise objective Bayesianism on the grounds that its norms are not compulsory but voluntary, the result of a stance. It is argued that this second objection also misses the mark, since objective

### Citations

522 | Probability Theory: the Logic of Science
- Jaynes
(Show Context)
Citation Context ...e Finetti’s case, Calibration. It wasn’t until the work of Jaynes and Rosenkrantz that these principles were reunited, in the form of contemporary objective Bayesianism (see, e.g., Rosenkrantz, 1977; =-=Jaynes, 2003-=-). This is ‘Bayesianism’ in the sense that probabilities are are construed as degrees of belief, as in Bayes (1764), not in the sense that probabilities are updated by Bayesian conditionalisation: as ... |

379 | An essay towards solving a problem in the doctrine of chances - Bayes - 1763 |

360 | A Treatise on Probability - Keynes - 1921 |

229 | Truth and probability - Ramsey - 1964 |

80 |
Bayes or Bust
- Earman
- 1992
(Show Context)
Citation Context ...-exchangeable. 8 Even advocates of conditionalisation admit that this is unsatisfactory and that conditionalisation may need to be overridden when a prior is re-evaluated (see, e.g., Lange, 1999, §2; =-=Earman, 1992-=-). But these advocates of conditionalisation offer little in the way of a general rule for updating. Of course a vague prescription like ‘conditionalise unless an update that does not conform to condi... |

62 |
D: Philosophical Theories of Probability
- Gillies
- 2000
(Show Context)
Citation Context ... set-up, but when the string e of evidence indicates that the data is being produced by a Markovian process, rather than a sequence of independent trials, exchangeable degrees of belief are disaster (=-=Gillies, 2000-=-, pp. 77–83; Williamson, 2007a); however, the agent is not permitted by conditionalisation to change her degrees of belief to be non-exchangeable. 8 Even advocates of conditionalisation admit that thi... |

56 | Laws and Symmetry - Fraassen - 1989 |

48 |
Bayesian Nets and Causality: Philosophical and Computational Foundations
- Williamson
- 2005
(Show Context)
Citation Context ...et of individuals that satisfy R. 4sas χ is consistent, the agent’s probability function pβ should lie within the set Pβ = [Pχ], the convex closure of the set of probability functions that satisfy χ (=-=Williamson, 2005-=-, §5.3). Otherwise some consistency maintenance procedure needs to be invoked. 4 Third (Equivocation), pβ should be as close as possible to an equivocator p = , a function that is maximally non-commit... |

43 | Belief and the will - Fraassen - 1984 |

22 |
Inference, Method, And Decision: Towards A Bayesian Philosophy Of Science
- Rosenkrantz
- 1977
(Show Context)
Citation Context ...ivocation and, in de Finetti’s case, Calibration. It wasn’t until the work of Jaynes and Rosenkrantz that these principles were reunited, in the form of contemporary objective Bayesianism (see, e.g., =-=Rosenkrantz, 1977-=-; Jaynes, 2003). This is ‘Bayesianism’ in the sense that probabilities are are construed as degrees of belief, as in Bayes (1764), not in the sense that probabilities are updated by Bayesian condition... |

22 | Conditionalization and observation - Teller - 1973 |

21 | Motivating objective Bayesianism: From empirical constraints to objective probabilities - Williamson - 2007 |

20 |
Bayesian conditionalisation and the principle of minimum information
- Williams
- 1980
(Show Context)
Citation Context ... constraint that e imposes in the context of β is p(e) = 1. The following is a reformulation of a result, versions of which are well-known to both proponents and opponents of maximum entropy methods (=-=Williams, 1980-=-; Seidenfeld, 1986, Result 1): Theorem 4.2 If e is a domain event, is simple with respect to β, χ ′ is consistent, and pβ(·|e) satisfies χ, then pβ ′(a) = pβ(a|e). This result clearly states condition... |

19 |
Entropy and uncertainty
- Seidenfeld
- 1987
(Show Context)
Citation Context ...een taken to reflect negatively on the former rule rather than the latter (see, e.g., Friedman and Shimony, 1971; Shimony, 1973; Seidenfeld, 1979; Dias and Shimony, 1981; Shimony, 1985; Skyrms, 1985; =-=Seidenfeld, 1986-=-). Thus the standard line of argument is: maxent is incompatible with Bayesian conditionalisation, but conditionalisation is well-established and intuitive, and so maxent should be rejected. Here I sh... |

16 |
Hume’s problem: Induction and the justification of belief
- Howson
(Show Context)
Citation Context ...ulty, while Bayesian conditionalisation requires that p(e) = 1 when e is learned. Howson has argued compellingly that Bayesian conditionalisation is inconsistent in some situations (Howson, 1997, §3; =-=Howson, 2000-=-, p. 136). Consider the following example, cast in subjectivist terms. Today you are certain of a, so p(a) = 1, but suppose you think that tomorrow you may be significantly less than certain about a, ... |

16 | The Empirical Stance - Fraassen - 2002 |

13 | Probability update: conditioning vs. cross-entropy - Grove, Halpern - 1997 |

11 | The constraint rule of the maximum entropy principle
- Uffink
- 1996
(Show Context)
Citation Context ...he probability space Bayesian conditionalisation can be applied to this problem; this update differs from the objective Bayesian update, though for slightly different reasons to the previous example (=-=Uffink, 1996-=-, §6). 7 §4 Four Kinds of Incompatibility In the literature thus far, any incompatibility between maximum entropy updating (maxent for short) and Bayesian conditionalisation has normally been taken to... |

9 | Working Without a Net - Foley - 1993 |

8 |
Calibration and the Epistemological Role of Bayesian Conditionalization
- Lange
- 1999
(Show Context)
Citation Context ... belief to be non-exchangeable. 8 Even advocates of conditionalisation admit that this is unsatisfactory and that conditionalisation may need to be overridden when a prior is re-evaluated (see, e.g., =-=Lange, 1999-=-, §2; Earman, 1992). But these advocates of conditionalisation offer little in the way of a general rule for updating. Of course a vague prescription like ‘conditionalise unless an update that does no... |

7 |
Jaynes’s maximum entropy prescription and probability theory
- Friedman, Shimony
- 1971
(Show Context)
Citation Context ...incompatibility between maximum entropy updating (maxent for short) and Bayesian conditionalisation has normally been taken to reflect negatively on the former rule rather than the latter (see, e.g., =-=Friedman and Shimony, 1971-=-; Shimony, 1973; Seidenfeld, 1979; Dias and Shimony, 1981; Shimony, 1985; Skyrms, 1985; Seidenfeld, 1986). Thus the standard line of argument is: maxent is incompatible with Bayesian conditionalisatio... |

7 | Inductive influence - Williamson |

6 | Objective Bayesian probabilistic logic - Williamson |

5 | Against conditionalization - Bacchus, Kyburg, et al. - 1990 |

5 |
Why I am not an objective Bayesian. Theory and Decision
- Seidenfeld
- 1979
(Show Context)
Citation Context ...ating (maxent for short) and Bayesian conditionalisation has normally been taken to reflect negatively on the former rule rather than the latter (see, e.g., Friedman and Shimony, 1971; Shimony, 1973; =-=Seidenfeld, 1979-=-; Dias and Shimony, 1981; Shimony, 1985; Skyrms, 1985; Seidenfeld, 1986). Thus the standard line of argument is: maxent is incompatible with Bayesian conditionalisation, but conditionalisation is well... |

5 | Symmetries of personal probability kinematics - Fraassen - 1987 |

5 | Objective Bayesianism with predicate languages. Synthese
- Williamson
- 2008
(Show Context)
Citation Context ... applied to uncountable domains in statistics, but in these cases the equivocators and the measures of distance are more complicated, and, while highly constrained, pβ may not be uniquely determined (=-=Williamson, 2008-=-a; Williamson, 2008b, §19). The lessons of this paper carry over to these more complex situations, but for simplicity of exposition we stick with finite domains here. For simplicity we shall also focu... |

5 | Participant observation - P - 1997 |

4 |
A critique of Jaynes’ maximum entropy principle
- Dias, Shimony
- 1981
(Show Context)
Citation Context ...short) and Bayesian conditionalisation has normally been taken to reflect negatively on the former rule rather than the latter (see, e.g., Friedman and Shimony, 1971; Shimony, 1973; Seidenfeld, 1979; =-=Dias and Shimony, 1981-=-; Shimony, 1985; Skyrms, 1985; Seidenfeld, 1986). Thus the standard line of argument is: maxent is incompatible with Bayesian conditionalisation, but conditionalisation is well-established and intuiti... |

4 | Coherence - Skyrms - 1987 |

3 |
Ars Conjectandi. The Johns Hopkins
- Bernoulli
- 1713
(Show Context)
Citation Context ...ulli. Bernoulli maintained that probability and degree of certainty were to be identified: ‘Probability, indeed, is degree of certainty, and differs from the latter as a part differs from the whole’ (=-=Bernoulli, 1713-=-, p. 211). He argued that in the absence of knowledge one should equivocate, but that evidence should take precedence over equivocation: For example, three ships set sail from port. After some time it... |

3 |
Comment on the interpretation of inductive probabilities
- Shimony
- 1973
(Show Context)
Citation Context ... his degrees of belief by conditionalising on E. It turns out that if Sylvester’s updated degrees of belief are to match Olive’s, he would have to have given prior probability 1 to the outcome E = 2 (=-=Shimony, 1973-=-). This seems ridiculous, since it amounts to prior certainty that the initial probability will not be revised. Of course Sylvester is a subjectivist and is rationally permitted to believe E = 2 to an... |

3 |
Maximum entropy inference as a special case of conditionalization. Synthese
- Skyrms
- 1985
(Show Context)
Citation Context ...has normally been taken to reflect negatively on the former rule rather than the latter (see, e.g., Friedman and Shimony, 1971; Shimony, 1973; Seidenfeld, 1979; Dias and Shimony, 1981; Shimony, 1985; =-=Skyrms, 1985-=-; Seidenfeld, 1986). Thus the standard line of argument is: maxent is incompatible with Bayesian conditionalisation, but conditionalisation is well-established and intuitive, and so maxent should be r... |

3 | A problem for relative information minimizers in probability kinematics - Fraassen - 1981 |

2 |
The status of the principle of maximum entropy. Synthese
- Shimony
- 1985
(Show Context)
Citation Context ...itionalisation has normally been taken to reflect negatively on the former rule rather than the latter (see, e.g., Friedman and Shimony, 1971; Shimony, 1973; Seidenfeld, 1979; Dias and Shimony, 1981; =-=Shimony, 1985-=-; Skyrms, 1985; Seidenfeld, 1986). Thus the standard line of argument is: maxent is incompatible with Bayesian conditionalisation, but conditionalisation is well-established and intuitive, and so maxe... |

1 |
Bayesian rules of updating. Erkenntnis
- Howson
- 1997
(Show Context)
Citation Context ...Bayesians have advocated conditionalisation (Jaynes, 2003) (as have proponents of logical probability such as Carnap), while some subjectivists have only endorsed conditionalisation in a limited way (=-=Howson, 1997-=-). The points I make in the following sections remain: objective Bayesians need not advocate conditionalisation, and indeed should not where conditionalisation disagrees with the objective Bayesian ap... |

1 | The insufficiency of the Dutch Book argument - Rowbottom - 2007 |

1 | How to change it: modes of engagement, rationality, and stance voluntarism. Synthese, This volume - Rowbottom, Bueno - 2008 |

1 | A problem for relative information minimisers, continued - Fraassen, Hughes, et al. - 1986 |