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  • 1
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    The extent of non-conglomerability of finitely additive probabilities (1984)
    Springer
    Details
    Publication Date: 1984-01-01
    Print ISSN: 0178-8051
    Electronic ISSN: 1432-2064
    Topics: Mathematics
    Published by Springer
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    PAPER CURRENT
  • 2
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    AncillaritycontraRandomizationas a basis for inference (2018)
    Wiley
    Details
    Publication Date: 2018-12-09
    Print ISSN: 0277-6715
    Electronic ISSN: 1097-0258
    Topics: Mathematics , Medicine
    Published by Wiley
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    PAPER CURRENT
  • 3
    Electronic Resource
    Electronic Resource
    Rejoinder (1988)
    Cambridge : Cambridge University Press
    Economics and philosophy 4 (1988), S. 309-315 
    Details
    ISSN: 0266-2671
    Source: Cambridge Journals Digital Archives
    Topics: Philosophy , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1017/S0266267100001127
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Decision Theory Without “Independence” or Without “Ordering” (1988)
    Cambridge : Cambridge University Press
    Economics and philosophy 4 (1988), S. 267-290 
    Details
    ISSN: 0266-2671
    Source: Cambridge Journals Digital Archives
    Topics: Philosophy , Economics
    Notes: It is a familiar argument that advocates accommodating the so-called paradoxes of decision theory by abandoning the “independence” postulate. After all, if we grant that choice reveals preference, the anomalous choice patterns of the Allais and Ellsberg problems (reviewed in Section 3) violate postulate P2 (“sure thing”) of Savage's (1954) system. The strategy of making room for new preference patterns by relaxing independence is adopted in each of the following works: Samuelson (1950), Kahneman and Tversky's “Prospect Theory” (1979), Allais and Hagen (1979), Fishburn (1981), Chew and MacCrimmon (1979), McClennen (1983), and in closely argued essays by Machina (1982, 1983 [see the latter for an extensive bibliography]).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1017/S0266267100001085
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  • 5
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    Why I am not an Objective Bayesian; Some Reflections Prompted by Rosenkrantz (1979)
    Dordrecht : Periodicals Archive Online (PAO)
    Theory and Decision. 11:4 (1979:Dec.) 413 
    Details
    ISSN: 0040-5833
    Topics: Sociology , Economics
    URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pao:&rft_dat=xri:pao:article:n228-1979-011-04-000006
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  • 6
    Electronic Resource
    Electronic Resource
    The extent of non-conglomerability of finitely additive probabilities (1984)
    Springer
    Probability theory and related fields 66 (1984), S. 205-226 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An arbitrary finitely additive probability can be decomposed uniquely into a convex combination of a countably additive probability and a purely finitely additive (PFA) one. The coefficient of the PFA probability is an upper bound on the extent to which conglomerability may fail in a finitely additive probability with that decomposition. If the probability is defined on a σ-field, the bound is sharp. Hence, non-conglomerability (or equivalently non-disintegrability) characterizes finitely as opposed to countably additive probability. Nonetheless, there exists a PFA probability which is simultaneously conglomerable over an arbitrary finite set of partitions. Neither conglomerability nor non-conglomerability in a given partition is closed under convex combinations. But the convex combination of PFA ultrafilter probabilities, each of which cannot be made conglomerable in a common margin, is singular with respect to any finitely additive probability that is conglomerable in that margin.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00531529
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  • 7
    Electronic Resource
    Electronic Resource
    The Independence Postulate, Hypothetical and Called-off Acts: a further reply to Rabinowicz (2000)
    Springer
    Theory and decision 48 (2000), S. 319-322 
    Details
    ISSN: 1573-7187
    Source: Springer Online Journal Archives 1860-2000
    Topics: Sociology , Economics
    Notes: Abstract The Independence postulate links current preferences between called-off acts with current preferences between constant acts. Under the assumption that the chance-events used in compound von Neumann-Morgenstern lotteries are value-neutral, current preferences between these constant acts are linked to current preferences between hypothetical acts, conditioned by those chance events. Under an assumption of stability of preferences over time, current preferences between these hypothetical acts are linked to future preferences between what are then and there constant acts. Here, I show that a failure of Independence with respect to current preferences leads to an inconsistency in sequential decisions. Two called-off acts are constructed such that each is admissible in the same sequential decision and yet one is strictly preferred to the other. This responds to a question regarding admissibility posed by Rabinowicz ([2000] Preference stability and substitution of indifferents: A rejoinder to Seidenfeld, Theory and Decision 48: 311–318 [this issue]).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005206710831
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  • 8
    Electronic Resource
    Electronic Resource
    Why I am not an objective Bayesian; some reflections prompted by Rosenkrantz (1979)
    Springer
    Theory and decision 11 (1979), S. 413-440 
    Details
    ISSN: 1573-7187
    Source: Springer Online Journal Archives 1860-2000
    Topics: Sociology , Economics
    Notes: Summary The objective Bayesian program has as its fundamental tenet (in addition to the three Bayesian postulates) the requirement that, from a given knowledge base a particular probability function is uniquely appropriate. This amounts to fixing initial probabilities, based on relatively little information, because Bayes' theorem (conditionalization) then determines the posterior probabilities when the belief state is altered by enlarging the knowledge base. Moreover, in order to reconstruct orthodox statistical procedures within a Bayesian framework, only privileged ‘ignorance’ probability functions will work. To serve all these ends objective Bayesianism seeks additional principles for specifying ‘ignorance’ and ‘partial information’ probabilities. H. Jeffreys' method of invariance (or Jaynes' modification thereof) is used to solve the former problem, and E. Jaynes' rule of maximizing entropy (subject to invariance for continuous distributions) has recently been thought to solve the latter. I have argued that neither policy is acceptable to a Bayesian since each is inconsistent with conditionalization. Invariance fails to give a consistent representation to the state of ignorance professed. The difficulties here parallel familiar weaknesses in the old Laplacean principle of insufficient reason. Maximizing entropy is unsatisfactory because the ‘partial information’ it works with fails to capture the effect of uncertainty about related nuisance factors. The result is a probability function that represents a state richer in empirical content than the belief state targeted for representation. Alternatively, by conditionalizing on information about a nuisance parameter one may move from a distribution of lower to higher entropy, despite the obvious increase in information available. Each of these two complaints appear to me to be symptoms of the program's inability to formulate rules for picking privileged probability distributions that serve to represent ignorance or near ignorance. Certainly the methods advocated by Jeffreys, Jaynes and Rosenkrantz are mathematically convenient idealizations wherein specified distributions are elevated to the roles of ‘ignorance’ and ‘partial information’ distributions. But the cost that goes with the idealization is a violation of conditionalization, and if that is the ante that we must put up to back objective Bayesianism then I propose we look for a different candidate to earn our support.31
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00139451
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  • 9
    Electronic Resource
    Electronic Resource
    Substitution of indifferent options at choice nodes and admissibility: a reply to Rabinowicz (2000)
    Springer
    Theory and decision 48 (2000), S. 305-310 
    Details
    ISSN: 1573-7187
    Keywords: Sequential decisions ; Independence postulate ; Ordering postulate ; Admissibility ; Indifference
    Source: Springer Online Journal Archives 1860-2000
    Topics: Sociology , Economics
    Notes: Abstract Tiebreak rules are necessary for revealing indifference in non- sequential decisions. I focus on a preference relation that satisfies Ordering and fails Independence in the following way. Lotteries a and b are indifferent but the compound lottery 〈 0.5f, 0.5b〉 is strictly preferred to the compound lottery 〈0.5f, 0.5a〉. Using tiebreak rules the following is shown here: “In sequential decisions when backward induction is applied, a preference like the one just described must alter the preference relation between a and b at certain choice nodes, i.e., indifference between a and b is not stable.” Using this result, I answer a question posed by Rabinowicz (1997) concerning admissibility in sequential decisions when indifferent options are substituted at choice nodes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005056315776
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