贝叶斯决策理论研究
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摘要
决策理论的研究最早可以追溯到18世纪，第一个完善的贝叶斯决策理论体系是由萨维奇在其名著《统计学基础》（1954年）一书中构建的。萨维奇的决策理论也被称为传统贝叶斯决策理论或经典贝叶斯决策理论。贝叶斯决策论者认为，理性主体在采取行动的时候应该最大化他们的主观期望效用。为了证明这一观点，他们给出了表示定理，并证明任何决策者，只要他们的信念和愿望满足一定的公理限制条件，就一定会成为一个期望效用最大化者。
然而，由于纽科姆难题等“悖论”的出现，使得贝叶斯主义者关于理性主体的行为方式的看法出现了严重的分歧，贝叶斯决策理论阵营也因此一分为二：证据决策理论和因果决策理论。关于理性主体在面对纽科姆难题时究竟该如何选择的问题，证据决策论者认为，应该选择最吉利的行动。在他们看来，决策者的行动应当根据它们所提供的那些预示着期望结果将出现的证据来评价。但是，因果决策论者却认为，应该选择具有最大功效值的行动。在他们看来，决策者的行动应当根据它们因果地促使期望结果出现的能力来评价，并且，一个理性主体总是会执行一个具有最大功效值的行为来得到期望的结果。
证据决策理论和因果决策理论的分歧主要在于它们对什么是期望效用的看法不同。证据决策论者认为，行动A的期望效用应该等同于行动A的新闻价值或证据价值。因果决策论者认为，行动A的期望效用等同于行动A的功效价值。在大多数情况下，证据决策方法和因果决策方法之间并没有冲突，也就是说，它们关于理性选择的建议都是相同的，因为那些给期望结果提供了最好证据的行动往往也是因果地导致那个结果出现的行动，这就使得功效最大化（因果决策理论的）和效用最大化（证据决策理论的）等价。但是，在纽科姆难题那样的一些特殊问题中，预示性和因果性却并不一致，并且吉利性不再是功效的一个可靠标志，对吉利证据的追求有可能使得主体选择一个非功效行动。在这些情况下，证据决策理论和因果决策理论就给出了完全不同的建议。
乔伊斯引入“想象”法来计算行动的因果期望效用，并构建了一种“特殊的”因果决策理论——条件决策理论。乔伊斯表明，证据决策理论和因果决策理论其实都只是条件决策理论的特例，它们之间的主要区别在于对“假定”这个概念的解释不同。证据性观点把它解释为陈述性的，而因果性观点则把它看做是虚拟性的。该条件决策理论给出了以执行行动A为前提的某些前景X的期望效用。通过转向条件决策理论，我们得到了一个统一的理论框架，在这个框架上，证据决策理论和因果决策理论可以用形式上相似的术语来表示。这就表明，这两者的区别并没有我们通常所认为的那么大，至少在那些我们所关注的最基础的问题上是这样。
但是，这个框架并没有解决人们在面对纽科姆难题时所面临的选择困境。于是，我在“屏蔽”原理和证据可证实性原则的基础上，提出一种混合决策方案，该方案把人的决策过程分为两个阶段：做决定和执行决定。混合决策方案可以很好地解决纽科姆难题给人们带来的选择困惑，并在一定程度上推进了贝叶斯决策理论的研究。
最后，我从哲学和认知的角度对贝叶斯决策理论进行了一个审视和思考，并对将来的一些研究方向进行了展望。
The Study of Decision Theory that can be traced back to18thcentury; the firstintegrated system of Bayesian decision theory was built in Savage’s famous book,“The Foundations of Statistics”(1954). Savage’s decision theory is also calledtraditional Bayesian decision theory or classical Bayesian decision theory. Bayesiandecision theorists argue that, rational agents should maximize their subjectiveexpected utility when adopting actions. In order to demonstrate this view, theyprovide a representation theorem, simultaneously showing that any decision maker, aslong as whose belief and desire satisfy the definite axiom restrictions, would be aBayesian decision theorist that believes expected utility maximization.
However, the Newcomb problem makes the Bayesian decision theorists havedifferent views about how the rational agent should behave, and forces them into twoseparate schools, that is, the schools of “evidential decision theorists” and “causaldecision theorists” differentiated by how rational agents should choose when facedwith Newcomb problems. Evidential decision theorists believe that the mostauspicious option should always be selected. In their opinion, actions should beevaluated by the evidence they provide for thinking that desirable outcomes willresult. On the other hand, causal decision theorists argue that the most efficaciousaction should be selected. In their view, the actions should be assessed on the basis oftheir ability to causally promote desirable outcomes, and rational agents will alwaysperform an act that is maximally efficacious in bringing about desirable outcomes.
The main divergence between evidential decision theory and causal decisiontheory is about the different opinions of what expected utility is. Evidential decisiontheorists think, expected utility and news or evidential value of act A should be equalbetween each other. Causal decision theorists think, act A’s expected utility should bethe same with its efficacy value. There is usually no conflict between evidentialdecision method and causal decision method, in other words, both of them have theidentical advice about rational choice, because the action providing those expectedoutcomes with the best evidence is also the one of causally causing the appearance ofthe outcomes, which makes that efficacy maximization (of causal decision theory) and utility maximization (of evidential decision theory) are equal in value. However,causing and indicating come apart in some special cases, for example, like in thedecision situation showed by Newcomb paradox, meanwhile auspiciousness is nolonger a reliable sign of efficacy, since pursuit of auspicious evidence that could makerational agents choose an inefficacy act. Under these situations, evidential decisiontheory and causal decision theory provide the completely different suggestions.
Joyce brings the “image” method to calculate causal expected utility of actions,at the same time, construct a special causal decision theory: conditional decisiontheory. Joyce indicates, actually evidential decision theory and causal decision theoryboth are just special examples of a more general conditional decision theory, theunique difference between the two theories is about the different interpretations to theconcept of “supposition” or “hypothesis”. Evidential perspective explains that thesupposition is indicative, but causal perspective sees it as something to be subjunctive.This conditional decision theory provides expected utility of taking to implement actA as the prospect X. We obtain a united theoretical frame, through turning toconditional decision theory, evidential decision theory and causal decision theorycould be represented by terminologies that are similar in form, upon this frame. Thisalso indicates that the difference between evidential decision theory and causaldecision theory is not as significant as we have usually thought.
However, this frame still fails to solve choice dilemma that people areconfronted with Newcomb paradox. Hence, I raise a mixed decision approach basedon the principle of screen off and the maxim of evidential ratifiability, this theorydivides the process of people’s decision making into two stages: the making andimplementation of decision. This approach may well resolve the choice dilemma topeople brought by Newcomb paradox, and also somewhat advance the study ofBayesian decision theory.
At the end, I review and reconsider the Bayesian decision theory from theperspective of philosophy and cognition, and give some directions for future research.
然而，由于纽科姆难题等“悖论”的出现，使得贝叶斯主义者关于理性主体的行为方式的看法出现了严重的分歧，贝叶斯决策理论阵营也因此一分为二：证据决策理论和因果决策理论。关于理性主体在面对纽科姆难题时究竟该如何选择的问题，证据决策论者认为，应该选择最吉利的行动。在他们看来，决策者的行动应当根据它们所提供的那些预示着期望结果将出现的证据来评价。但是，因果决策论者却认为，应该选择具有最大功效值的行动。在他们看来，决策者的行动应当根据它们因果地促使期望结果出现的能力来评价，并且，一个理性主体总是会执行一个具有最大功效值的行为来得到期望的结果。
证据决策理论和因果决策理论的分歧主要在于它们对什么是期望效用的看法不同。证据决策论者认为，行动A的期望效用应该等同于行动A的新闻价值或证据价值。因果决策论者认为，行动A的期望效用等同于行动A的功效价值。在大多数情况下，证据决策方法和因果决策方法之间并没有冲突，也就是说，它们关于理性选择的建议都是相同的，因为那些给期望结果提供了最好证据的行动往往也是因果地导致那个结果出现的行动，这就使得功效最大化（因果决策理论的）和效用最大化（证据决策理论的）等价。但是，在纽科姆难题那样的一些特殊问题中，预示性和因果性却并不一致，并且吉利性不再是功效的一个可靠标志，对吉利证据的追求有可能使得主体选择一个非功效行动。在这些情况下，证据决策理论和因果决策理论就给出了完全不同的建议。
乔伊斯引入“想象”法来计算行动的因果期望效用，并构建了一种“特殊的”因果决策理论——条件决策理论。乔伊斯表明，证据决策理论和因果决策理论其实都只是条件决策理论的特例，它们之间的主要区别在于对“假定”这个概念的解释不同。证据性观点把它解释为陈述性的，而因果性观点则把它看做是虚拟性的。该条件决策理论给出了以执行行动A为前提的某些前景X的期望效用。通过转向条件决策理论，我们得到了一个统一的理论框架，在这个框架上，证据决策理论和因果决策理论可以用形式上相似的术语来表示。这就表明，这两者的区别并没有我们通常所认为的那么大，至少在那些我们所关注的最基础的问题上是这样。
但是，这个框架并没有解决人们在面对纽科姆难题时所面临的选择困境。于是，我在“屏蔽”原理和证据可证实性原则的基础上，提出一种混合决策方案，该方案把人的决策过程分为两个阶段：做决定和执行决定。混合决策方案可以很好地解决纽科姆难题给人们带来的选择困惑，并在一定程度上推进了贝叶斯决策理论的研究。
最后，我从哲学和认知的角度对贝叶斯决策理论进行了一个审视和思考，并对将来的一些研究方向进行了展望。
The Study of Decision Theory that can be traced back to18thcentury; the firstintegrated system of Bayesian decision theory was built in Savage’s famous book,“The Foundations of Statistics”(1954). Savage’s decision theory is also calledtraditional Bayesian decision theory or classical Bayesian decision theory. Bayesiandecision theorists argue that, rational agents should maximize their subjectiveexpected utility when adopting actions. In order to demonstrate this view, theyprovide a representation theorem, simultaneously showing that any decision maker, aslong as whose belief and desire satisfy the definite axiom restrictions, would be aBayesian decision theorist that believes expected utility maximization.
However, the Newcomb problem makes the Bayesian decision theorists havedifferent views about how the rational agent should behave, and forces them into twoseparate schools, that is, the schools of “evidential decision theorists” and “causaldecision theorists” differentiated by how rational agents should choose when facedwith Newcomb problems. Evidential decision theorists believe that the mostauspicious option should always be selected. In their opinion, actions should beevaluated by the evidence they provide for thinking that desirable outcomes willresult. On the other hand, causal decision theorists argue that the most efficaciousaction should be selected. In their view, the actions should be assessed on the basis oftheir ability to causally promote desirable outcomes, and rational agents will alwaysperform an act that is maximally efficacious in bringing about desirable outcomes.
The main divergence between evidential decision theory and causal decisiontheory is about the different opinions of what expected utility is. Evidential decisiontheorists think, expected utility and news or evidential value of act A should be equalbetween each other. Causal decision theorists think, act A’s expected utility should bethe same with its efficacy value. There is usually no conflict between evidentialdecision method and causal decision method, in other words, both of them have theidentical advice about rational choice, because the action providing those expectedoutcomes with the best evidence is also the one of causally causing the appearance ofthe outcomes, which makes that efficacy maximization (of causal decision theory) and utility maximization (of evidential decision theory) are equal in value. However,causing and indicating come apart in some special cases, for example, like in thedecision situation showed by Newcomb paradox, meanwhile auspiciousness is nolonger a reliable sign of efficacy, since pursuit of auspicious evidence that could makerational agents choose an inefficacy act. Under these situations, evidential decisiontheory and causal decision theory provide the completely different suggestions.
Joyce brings the “image” method to calculate causal expected utility of actions,at the same time, construct a special causal decision theory: conditional decisiontheory. Joyce indicates, actually evidential decision theory and causal decision theoryboth are just special examples of a more general conditional decision theory, theunique difference between the two theories is about the different interpretations to theconcept of “supposition” or “hypothesis”. Evidential perspective explains that thesupposition is indicative, but causal perspective sees it as something to be subjunctive.This conditional decision theory provides expected utility of taking to implement actA as the prospect X. We obtain a united theoretical frame, through turning toconditional decision theory, evidential decision theory and causal decision theorycould be represented by terminologies that are similar in form, upon this frame. Thisalso indicates that the difference between evidential decision theory and causaldecision theory is not as significant as we have usually thought.
However, this frame still fails to solve choice dilemma that people areconfronted with Newcomb paradox. Hence, I raise a mixed decision approach basedon the principle of screen off and the maxim of evidential ratifiability, this theorydivides the process of people’s decision making into two stages: the making andimplementation of decision. This approach may well resolve the choice dilemma topeople brought by Newcomb paradox, and also somewhat advance the study ofBayesian decision theory.
At the end, I review and reconsider the Bayesian decision theory from theperspective of philosophy and cognition, and give some directions for future research.
引文
①von Neumann, J.,&Morgenstern, O.(1944). Theory of Games and Economic Behavior. Princeton: PrincetonUniversity Press.
②Nash, J. F.(1950). Equilibrium points in n-person games. Proceedings of the national academy of sciences,36(1).pp.48-49.
①Skyrms, B.(1990). The Dynamics of Rational Deliberation. Cambridge, MA: Harvard University Press.
②江天骥.归纳逻辑导论[M].长沙:湖南人民出版社,1987:256
①Slovic, P.,&Tversky, A.(1974). Who accepts Savage's axiom? Behavioral science,19(6),368-373.
①Allais, M.(1953). Le comportement de l'homme rationnel devant le risque: Critique des postulats et axiomes del'école Américaine. Econometrica,21(4),503-546.
②Bernoulli, D.(1954). Exposition of a New Theory on the Measurement of Risk. Econometrica,22(1),23-36.(Translation of Bernoulli D.1738Specimen theoriae novae de mensura sortis; Paper Imp. Acad. Sci. St.Petersburg5175-192)
③Bayes, T.(1763). An Essay towards solving a Problem in the Doctrine of Chances. Philosophical Transactions(1683-1775),53,370-418.
①Savage, L. J.(1972). The foundations of statistics (2nd edition). New York: Dover Publications.(First editionwas published in1954)
①Adams, E.(1965). The logic of conditionals. Inquiry,8(1-4),166-197.
①Nozick, R.(1969). Newcomb's Problem and Two Principles of Choice. In N. Rescher (Ed.), Essays in honor ofCarl G. Hempel (pp.114-146). Dordrecht: Reidel.
③Nozick, R.(1969). Newcomb's Problem and Two Principles of Choice. In N. Rescher (Ed.), Essays in honor ofCarl G. Hempel (pp.114-146). Dordrecht: Reidel.
①Gibbard, A., Harper, W. L.(1981). Counterfactuals and Two Kinds of Expected Utility. In William L. Harper,Glenn Pearce (Ed.), Ifs: conditionals, belief, decision, chance, and time (pp.153-190). Dordrecht: D. ReidelPublishing Company.
②Skyrms, B.(1980). Causal necessity: a pragmatic investigation of the necessity of laws. New Haven: YaleUniversity Press.
③Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30.
①Aristotle.(2004). Nicomachean Ethics (R. Crisp, Trans.). Cambridge: Cambridge University Press.p.105
①Armendt, B.(1986). A Foundation for Causal Decision Theory. Topoi,5(1),3-19.
②Joyce, J. M.(1999). The foundations of causal decision theory. Cambridge; New York: Cambridge UniversityPress.
①Levi, I.(2000). The foundations of causal decision theory(Book Review). Journal of Philosophy,97(7),387-402.
①江天骥.归纳逻辑导论[M].长沙:湖南人民出版社,1987.
②李伯聪.关于纽科姆问题[J].哲学研究,2004,(5),70-76.
③方钦.可能世界中的选择:纽康姆难题[J].社会科学战线,2006,(3),38-55.
④熊立文.贝叶斯决策理论与归纳逻辑[J].北京师范大学学报:社会科学版,2005,(2),108-113.
①熊卫.贝叶斯决策理论的理性观及其相对性[J].科学技术与辩证法,2006,(5),35-38.
②熊卫.经典决策理论的基础及发展[J].求是学刊,2007,(6),28-31.
③马文俊,熊卫.旧证据问题:一种动态的消解方案[J].逻辑学研究,2011,(2),81-92.
①任晓明,李章吕.贝叶斯决策理论的发展概况和研究动态[J].科学技术哲学研究,2013,(1).（待发）
②李章吕.论证据决策理论的困境与出路[J].哲学动态,2011,(6),84-89.
③李章吕.支持理论对标准概率理论的超越和发展[J].学术论坛,2010(8),10-15.
①Morgenstern, O.,&von Neumann, J.([1944]1953). Theory of games and economic behavior. Princeton:Princeton University Press.
②熊立文.贝叶斯决策理论与归纳逻辑[J].北京师范大学学报（社会科学版）,2005,(2).
①Savage, L. J.(1972). The foundations of statistics (2nd edition). New York: Dover Publications.pp.13-14.
①Jeffrey, R. C.(1983). The Logic of Decision(2nd Edition). Chicago: University of Chicago Press.p.84
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge UniversityPress.pp.67-68
①Arnauld, A., Nicole, P.,&Buroker, J. V.(1996). Logic, or, The Art of Thinking: Containing, Besides CommonRules, Several New Observations Appropriate for Forming Judgment. New York: Cambridge University Press.pp.273-274
②Arnauld, A., Nicole, P.,&Buroker, J. V.(1996). Logic, or, The Art of Thinking: Containing, Besides CommonRules, Several New Observations Appropriate for Forming Judgment. New York: Cambridge University Press.pp.275-276
③关于这个问题的最著名讨论请参见Todhunter, I.(1865). History of the Mathematical Theory of Probabilityfrom the time of Pascal to that of Laplace. Cambridge; London: Macmillan and Co.. pp.7-21
①Jeffrey, R. C.(1992). Probability and the Art of Judgement. New York: Cambridge University Press.pp.213
②Bentham, J.(1823). An Introduction to the Principles of Morals and Legislation. London: Pickering.p.12
①de Finetti, B.([1937]1964). Foresight: Its logical laws, its subjective sources. In H. E. Kyburg&H. E. Smokler(Eds.), Studies in Subjective Probability (pp.53-118). New York: Wiley.
①James M. Joyce. The Foundations of Causal Decision Theory. New York: Cambridge University Press,1999.p.79
①Ramsey, F. P.(1931). Truth and probability. In R. B. Braithwaite (Ed.), The Foundations of Mathmatics andOther Logical Essays (pp.156-198). London: Routledge and Kegan Paul.pp.178-179
②Ramsey, F. P.(1931). Truth and probability. In R. B. Braithwaite (Ed.), The Foundations of Mathmatics andOther Logical Essays (pp.156-198). London: Routledge and Kegan Paul.p.179
③Ramsey, F. P.(1931). Truth and probability. In R. B. Braithwaite (Ed.), The Foundations of Mathmatics andOther Logical Essays (pp.156-198). London: Routledge and Kegan Paul.pp.179-180
①Ramsey, F. P.(1931). Truth and probability. In R. B. Braithwaite (Ed.), The Foundations of Mathmatics andOther Logical Essays (pp.156-198). London: Routledge and Kegan Paul.p.182
②Ramsey, F. P.(1931). Truth and probability. In R. B. Braithwaite (Ed.), The Foundations of Mathmatics andOther Logical Essays (pp.156-198). London: Routledge and Kegan Paul.p.180
④Leonard J. Savage. The Foundations of Statistics(2nd Edition). New York: Dover Publications, Inc.1972.[1stEdition,1954].p.21
②G rdenfors, P.,&Sahlin, N.-E.(1988). Decision, probability, and utility: selected readings. New York:Cambridge University Press.
①更多论述请参见Savage, L. J.(1972). The foundations of statistics (2nd edition). New York: DoverPublications.p.25
①Allais, M.(1953). Le comportement de l'homme rationnel devant le risque: Critique des postulats et axiomes del'école Américaine. Econometrica,21,503-546.
②对于阿莱斯悖论的经验证据，可以参见Kahneman, D.,&Tversky,A.(1979). Prospect theory:An analysis ofdecision under risk. Econometrica,47,263-291.
①Ellsberg, D.(1961). Risk, ambiguity, and the Savage axioms. The Quarterly Journal of Economics,75(4),643-669.
①Kahneman, D.,&Tversky, A.(1979). Prospect theory: An analysis of decision under risk. Econometrica,47,263-291.
①James M. Joyce. The Foundations of Causal Decision Theory. New York: Cambridge University Press,1999.p.115-116
①James M. Joyce. The Foundations of Causal Decision Theory. New York: Cambridge University Press,1999.p.115
③Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30.p.5
①Savage, L. J.(1972). The foundations of statistics (2nd edition). New York: Dover Publications.p.15
②Brecher, R., Brecher, E. M.,&Herzog, A.(1963). The Consumers Union Report on Smoking and the PublicInterest: Consumers Union, Mount Vernon, New York.p.69
①James M. Joyce. The Foundations of Causal Decision Theory. New York: Cambridge University Press,1999.pp.115-116
①Jeffrey, R. C.(1983). The Logic of Decision(2nd Edition). Chicago: University of Chicago Press.p.22
①Jeffrey, R. C.(1983). The Logic of Decision(2nd Edition). Chicago: University of Chicago Press.p.22
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge UniversityPress.pp.54-56
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.148
①Nozick, R.(1969). Newcomb's Problem and Two Principles of Choice. In N. Rescher (Ed.), Essays in honor ofCarl G. Hempel (pp.114-146). Dordrecht: Reidel.
①Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1).p.5
②Aristotle.(2004). Nicomachean Ethics (R. Crisp, Trans.). Cambridge: Cambridge University Press.p.105
②Gibbard, A., Harper, W.(1981). Counterfactuals and Two Kinds of Expected Utility. In W. Harper, R. Stalnaker&G. Pearce (Eds.), Ifs: conditionals, belief, decision, chance, and time (pp.153-190). Dordrecht: D. ReidelPublishing Company.
①Jeffrey, R. C.(1983). The Logic of Decision(2nd Edition). Chicago: University of Chicago Press.P.84.
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.150
②Gibbard, A., Harper, W.(1981). Counterfactuals and Two Kinds of Expected Utility. In W. Harper, R. Stalnaker&G. Pearce (Eds.), Ifs: conditionals, belief, decision, chance, and time (pp.153-190). Dordrecht: D. ReidelPublishing Company.
①Heap, S. H., Hollis, M., Lyons, B.,&Sugden, R. etc.(1992). The Theory of Choice: A Critical Guide. Oxford:
Basil Blackwell. p.342.
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.154
①参见Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30.; Skyrms, B.(1980). Causal necessity: A Pragmatic Investigation of the Necessity of Laws. New Haven: Yale University Press.;Skyrms, B.(1984). Pragmatics and Empiricism. New Haven: Yale University Press.; Armendt, B.(1986). AFoundation for Causal Decision Theory. Topoi,5(1),3-19.
①Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30.p.13
②Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30.pp.11-14
①参见Huppes, P.(1970). A Probabilistic Theory of Causality. Amsterdam: North Holland Publishing Company..;Cartwright, N.(1979). Causal Laws and Effective Strategies. Nous,13(4),419-437.; Eells, E.(1991). Probabilisticcausality. New York: Cambridge University Press.; Hitchcock, C. R.(1993). A Generalized Probabilistic Theoryof Causal Relevance. Synthese,97(3),335-364.
①Skyrms, B.(1980). Causal necessity: A Pragmatic Investigation of the Necessity of Laws. New Haven: YaleUniversity Press. p.133.
②参见Lewis, D.(1980).ASubjectivist’s Guide to Objective Chance. In R. Jeffrey (Ed.), Studies in InductiveLogic and Probability (Vol.2, pp.263-294). Berkeley: University of California Press.; Lewis, D.(1994). Chanceand Credence: Humean Supervenience Debugged. Mind,103,473-490.; Skyrms, B.(1988). Conditional Chance.In J. Fetzer (Ed.), Probability and Causality: Essays in Honor of Wesley C. Salmon (pp.161-178). Dordrecht:Kluwer.; Gaifman, H.(1988). A theory of Higher Order Probabilities. In B. Skyrms (Ed.), Causality, Chance andChoice (pp.191-219). Dordrecht: Kluwer.
②参见Skyrms, B.(1984). Pragmatics and Empiricism. New Haven: Yale University Press.
③Stalnaker, R.(1981). Letter to David Lewis. In William Harper, Robert Stalnaker, and and Glenn Pearce (Ed.),Ifs: Conditionals, Belief, Decision, Chance, and Time (pp.151-152). Dordrecht: D. Reidel Publishing Company.
④Gibbard, A., Harper, W.(1981). Counterfactuals and Two Kinds of Expected Utility. In William Harper, RobertStalnaker, and Glenn Pearce (Ed.), Ifs: conditionals, belief, decision, chance, and time (pp.153-190). Dordrecht: D.Reidel Publishing Company.
①Stalnaker, R.(1968). A theory of conditionals. In N. Rescher (Ed.), Studies in logical theory (pp.98-112).Oxford: Blackwell.
①Lewis, D.(1979). Counterfactual Dependence and Time's Arrow. No s,13,455-476. pp.456-457.
②Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.179
②Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30. p.5.
③Harper, W.,&Skyrms, B.(1988). Causation in Decision, Belief Change, and Statistics (Vol.2). Dordrecht:Kluwer Academic Publishers.p.x.
③Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30.p.13
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.176
②Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30.p.11
③Sobel, J. H.(1994). Taking chances: essays on rational choice. New York: Cambridge University Press. p.161
①Eells, E.(1985). Levi's" The Wrong Box". The Journal of Philosophy,82(2),91-104. p.102
②Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.177
③Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.177
④Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge UniversityPress.pp.172-176
①Lewis, D.(1973). Counterfactuals. Cambridge: Harvard University Press. pp.71-83
②Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30.p.23
①Gibbard, A., Harper, W.(1981). Counterfactuals and Two Kinds of Expected Utility. In W. Harper, R. Stalnaker&G. Pearce (Eds.), Ifs: conditionals, belief, decision, chance, and time (pp.153-190). Dordrecht: D. ReidelPublishing Company.p.189
①详细论述可以参见Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: CambridgeUniversity Press.pp.198-199
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.178
①Anderson, E.(1993). Value in Ethics and Economics. Cambridge: Harvard University Press.
①Adams, E.(1965). The logic of conditionals. Inquiry,8(1-4),166-197.
①对这个问题感兴趣的读者请参见Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York:Cambridge University Press.pp.224-242
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge UniversityPress.pp.82-84
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge UniversityPress.pp.181-251
①Egan, A.(2007). Some Counterexamples to Causal Decision Theory. Philosophical Review,116(1),93-114.
①Egan, A.(2007). Some Counterexamples to Causal Decision Theory. Philosophical Review,116(1),93-114.
②Lewis, D.(1976). Probabilities of conditionals and conditional probabilities. The Philosophical Review,85(3),
297-315.
③Egan, A.(2007). Some Counterexamples to Causal Decision Theory. Philosophical Review,116(1),93-114.
①Weirich, P.(1988). Hierarchical Maximization of Two Kinds of Expected Utility. Philosophy of Science,55(4),560-582.
②Gibbard, A., Harper, W. L.(1981). Counterfactuals and Two Kinds of Expected Utility. In R. S. William L.Harper, Glenn Pearce (Ed.), Ifs: conditionals, belief, decision, chance, and time (pp.153-190). Dordrecht: D.Reidel Publishing Company.
③Weirich, P.(1988). Hierarchical Maximization of Two Kinds of Expected Utility. Philosophy of Science,55(4),560-582.
④Harper, W.(1986). Mixed strategies and ratifiability in causal decision theory. Erkenntnis,24(1),25-36.
⑤Weirich, P.(1988). Hierarchical Maximization of Two Kinds of Expected Utility. Philosophy of Science,55(4),560-582.
①对这个问题感兴趣的读者请参见Lewis, D.(1973). Counterfactuals. Cambridge: Harvard University Press.
②Eells, E.(1984). Causal Decision Theory. PSA: Proceedings of the Biennial Meeting of the Philosophy ofScience Association, Vol.1984,2,177-200. p.178
①Reichenbach, H.(1959). Modern philosophy of science: Selected essays. London: Routledge and KeganPaul.Chapter3.pp.67-78
①Jeffrey, R. C.(1983). The logic of decision（Second Edition). Chicago: University of Chicago Press.p.16
②Jeffrey, R. C.(1983). The logic of decision（Second Edition). Chicago: University of Chicago Press.p.18
①本节的大部分内容来自于我已经发表过的一篇论文：论证据决策理论的困境与出路[J].哲学动态，2010,(6).
①Nozick, R.(1993). The Nature of Rationality. Princeton, New Jersey: Princeton University Press.p.43
②方钦.可能世界中的选择：纽康姆难题[J].社会科学战线,2006,(3).
③Nozick, R.(1993). The Nature of Rationality. Princeton, New Jersey: Princeton University Press.p.45
①Kahn, C. H.(1979). The art and thought of Heraclitus: An edition of the fragments with translation andcommentary. Cambridge; New York: Cambridge University Press.p.33
①Kahneman, D.,&Tversky, A.(1972). On prediction and judgment. Oregon Research Institute Bulletin,12(4),10.
①Kahneman, D.,&Tversky, A.(1973). On the Psychology of Prediction. Psychological review,80(4),237-251.
①Kahneman, D.,&Tversky, A.(1973). On the Psychology of Prediction. Psychological review,80(4),237-251.
②Kahneman, D.,&Tversky, A.(1973). On the Psychology of Prediction. Psychological review,80(4),237-251.
③Beach, L. R.(1966). Accuracy and Consistency in the Revision of Subjective Probabilities. IEEE Transactionson Human Factors in Electronics,7(1),29-37.
④李章吕.支持理论对标准概率理论的超越和发展[J].学术论坛,2010,(8).
①关于“恰当相符性”这一逻辑哲学中心问题的详细论述，请参见桂起权.当代数学哲学与逻辑哲学入门[M].上海:华东师范大学出版社,1991:97-116.
②李章吕.支持理论对标准概率理论的超越和发展[J].学术论坛,2010,(8),10-15.
①张昆仑.边际效用递减规律新探.现代财经:天津财经学院学报,2004,(4),8-10.
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②熊立文.贝叶斯决策理论与归纳逻辑[J].北京师范大学学报（社会科学版）,2005,(2).
①Savage, L. J.(1972). The foundations of statistics (2nd edition). New York: Dover Publications.pp.13-14.
①Jeffrey, R. C.(1983). The Logic of Decision(2nd Edition). Chicago: University of Chicago Press.p.84
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge UniversityPress.pp.67-68
①Arnauld, A., Nicole, P.,&Buroker, J. V.(1996). Logic, or, The Art of Thinking: Containing, Besides CommonRules, Several New Observations Appropriate for Forming Judgment. New York: Cambridge University Press.pp.273-274
②Arnauld, A., Nicole, P.,&Buroker, J. V.(1996). Logic, or, The Art of Thinking: Containing, Besides CommonRules, Several New Observations Appropriate for Forming Judgment. New York: Cambridge University Press.pp.275-276
③关于这个问题的最著名讨论请参见Todhunter, I.(1865). History of the Mathematical Theory of Probabilityfrom the time of Pascal to that of Laplace. Cambridge; London: Macmillan and Co.. pp.7-21
①Jeffrey, R. C.(1992). Probability and the Art of Judgement. New York: Cambridge University Press.pp.213
②Bentham, J.(1823). An Introduction to the Principles of Morals and Legislation. London: Pickering.p.12
①de Finetti, B.([1937]1964). Foresight: Its logical laws, its subjective sources. In H. E. Kyburg&H. E. Smokler(Eds.), Studies in Subjective Probability (pp.53-118). New York: Wiley.
①James M. Joyce. The Foundations of Causal Decision Theory. New York: Cambridge University Press,1999.p.79
①Ramsey, F. P.(1931). Truth and probability. In R. B. Braithwaite (Ed.), The Foundations of Mathmatics andOther Logical Essays (pp.156-198). London: Routledge and Kegan Paul.pp.178-179
②Ramsey, F. P.(1931). Truth and probability. In R. B. Braithwaite (Ed.), The Foundations of Mathmatics andOther Logical Essays (pp.156-198). London: Routledge and Kegan Paul.p.179
③Ramsey, F. P.(1931). Truth and probability. In R. B. Braithwaite (Ed.), The Foundations of Mathmatics andOther Logical Essays (pp.156-198). London: Routledge and Kegan Paul.pp.179-180
①Ramsey, F. P.(1931). Truth and probability. In R. B. Braithwaite (Ed.), The Foundations of Mathmatics andOther Logical Essays (pp.156-198). London: Routledge and Kegan Paul.p.182
②Ramsey, F. P.(1931). Truth and probability. In R. B. Braithwaite (Ed.), The Foundations of Mathmatics andOther Logical Essays (pp.156-198). London: Routledge and Kegan Paul.p.180
④Leonard J. Savage. The Foundations of Statistics(2nd Edition). New York: Dover Publications, Inc.1972.[1stEdition,1954].p.21
②G rdenfors, P.,&Sahlin, N.-E.(1988). Decision, probability, and utility: selected readings. New York:Cambridge University Press.
①更多论述请参见Savage, L. J.(1972). The foundations of statistics (2nd edition). New York: DoverPublications.p.25
①Allais, M.(1953). Le comportement de l'homme rationnel devant le risque: Critique des postulats et axiomes del'école Américaine. Econometrica,21,503-546.
②对于阿莱斯悖论的经验证据，可以参见Kahneman, D.,&Tversky,A.(1979). Prospect theory:An analysis ofdecision under risk. Econometrica,47,263-291.
①Ellsberg, D.(1961). Risk, ambiguity, and the Savage axioms. The Quarterly Journal of Economics,75(4),643-669.
①Kahneman, D.,&Tversky, A.(1979). Prospect theory: An analysis of decision under risk. Econometrica,47,263-291.
①James M. Joyce. The Foundations of Causal Decision Theory. New York: Cambridge University Press,1999.p.115-116
①James M. Joyce. The Foundations of Causal Decision Theory. New York: Cambridge University Press,1999.p.115
③Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30.p.5
①Savage, L. J.(1972). The foundations of statistics (2nd edition). New York: Dover Publications.p.15
②Brecher, R., Brecher, E. M.,&Herzog, A.(1963). The Consumers Union Report on Smoking and the PublicInterest: Consumers Union, Mount Vernon, New York.p.69
①James M. Joyce. The Foundations of Causal Decision Theory. New York: Cambridge University Press,1999.pp.115-116
①Jeffrey, R. C.(1983). The Logic of Decision(2nd Edition). Chicago: University of Chicago Press.p.22
①Jeffrey, R. C.(1983). The Logic of Decision(2nd Edition). Chicago: University of Chicago Press.p.22
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge UniversityPress.pp.54-56
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.148
①Nozick, R.(1969). Newcomb's Problem and Two Principles of Choice. In N. Rescher (Ed.), Essays in honor ofCarl G. Hempel (pp.114-146). Dordrecht: Reidel.
①Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1).p.5
②Aristotle.(2004). Nicomachean Ethics (R. Crisp, Trans.). Cambridge: Cambridge University Press.p.105
②Gibbard, A., Harper, W.(1981). Counterfactuals and Two Kinds of Expected Utility. In W. Harper, R. Stalnaker&G. Pearce (Eds.), Ifs: conditionals, belief, decision, chance, and time (pp.153-190). Dordrecht: D. ReidelPublishing Company.
①Jeffrey, R. C.(1983). The Logic of Decision(2nd Edition). Chicago: University of Chicago Press.P.84.
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.150
②Gibbard, A., Harper, W.(1981). Counterfactuals and Two Kinds of Expected Utility. In W. Harper, R. Stalnaker&G. Pearce (Eds.), Ifs: conditionals, belief, decision, chance, and time (pp.153-190). Dordrecht: D. ReidelPublishing Company.
①Heap, S. H., Hollis, M., Lyons, B.,&Sugden, R. etc.(1992). The Theory of Choice: A Critical Guide. Oxford:
Basil Blackwell. p.342.
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.154
①参见Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30.; Skyrms, B.(1980). Causal necessity: A Pragmatic Investigation of the Necessity of Laws. New Haven: Yale University Press.;Skyrms, B.(1984). Pragmatics and Empiricism. New Haven: Yale University Press.; Armendt, B.(1986). AFoundation for Causal Decision Theory. Topoi,5(1),3-19.
①Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30.p.13
②Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30.pp.11-14
①参见Huppes, P.(1970). A Probabilistic Theory of Causality. Amsterdam: North Holland Publishing Company..;Cartwright, N.(1979). Causal Laws and Effective Strategies. Nous,13(4),419-437.; Eells, E.(1991). Probabilisticcausality. New York: Cambridge University Press.; Hitchcock, C. R.(1993). A Generalized Probabilistic Theoryof Causal Relevance. Synthese,97(3),335-364.
①Skyrms, B.(1980). Causal necessity: A Pragmatic Investigation of the Necessity of Laws. New Haven: YaleUniversity Press. p.133.
②参见Lewis, D.(1980).ASubjectivist’s Guide to Objective Chance. In R. Jeffrey (Ed.), Studies in InductiveLogic and Probability (Vol.2, pp.263-294). Berkeley: University of California Press.; Lewis, D.(1994). Chanceand Credence: Humean Supervenience Debugged. Mind,103,473-490.; Skyrms, B.(1988). Conditional Chance.In J. Fetzer (Ed.), Probability and Causality: Essays in Honor of Wesley C. Salmon (pp.161-178). Dordrecht:Kluwer.; Gaifman, H.(1988). A theory of Higher Order Probabilities. In B. Skyrms (Ed.), Causality, Chance andChoice (pp.191-219). Dordrecht: Kluwer.
②参见Skyrms, B.(1984). Pragmatics and Empiricism. New Haven: Yale University Press.
③Stalnaker, R.(1981). Letter to David Lewis. In William Harper, Robert Stalnaker, and and Glenn Pearce (Ed.),Ifs: Conditionals, Belief, Decision, Chance, and Time (pp.151-152). Dordrecht: D. Reidel Publishing Company.
④Gibbard, A., Harper, W.(1981). Counterfactuals and Two Kinds of Expected Utility. In William Harper, RobertStalnaker, and Glenn Pearce (Ed.), Ifs: conditionals, belief, decision, chance, and time (pp.153-190). Dordrecht: D.Reidel Publishing Company.
①Stalnaker, R.(1968). A theory of conditionals. In N. Rescher (Ed.), Studies in logical theory (pp.98-112).Oxford: Blackwell.
①Lewis, D.(1979). Counterfactual Dependence and Time's Arrow. No s,13,455-476. pp.456-457.
②Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.179
②Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30. p.5.
③Harper, W.,&Skyrms, B.(1988). Causation in Decision, Belief Change, and Statistics (Vol.2). Dordrecht:Kluwer Academic Publishers.p.x.
③Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30.p.13
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.176
②Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30.p.11
③Sobel, J. H.(1994). Taking chances: essays on rational choice. New York: Cambridge University Press. p.161
①Eells, E.(1985). Levi's" The Wrong Box". The Journal of Philosophy,82(2),91-104. p.102
②Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.177
③Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.177
④Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge UniversityPress.pp.172-176
①Lewis, D.(1973). Counterfactuals. Cambridge: Harvard University Press. pp.71-83
②Lewis, D.(1981). Causal Decision Theory. Australasian Journal of Philosophy,59(1),5-30.p.23
①Gibbard, A., Harper, W.(1981). Counterfactuals and Two Kinds of Expected Utility. In W. Harper, R. Stalnaker&G. Pearce (Eds.), Ifs: conditionals, belief, decision, chance, and time (pp.153-190). Dordrecht: D. ReidelPublishing Company.p.189
①详细论述可以参见Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: CambridgeUniversity Press.pp.198-199
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge University Press.p.178
①Anderson, E.(1993). Value in Ethics and Economics. Cambridge: Harvard University Press.
①Adams, E.(1965). The logic of conditionals. Inquiry,8(1-4),166-197.
①对这个问题感兴趣的读者请参见Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York:Cambridge University Press.pp.224-242
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge UniversityPress.pp.82-84
①Joyce, J. M.(1999). The Foundations of Causal Decision Theory. New York: Cambridge UniversityPress.pp.181-251
①Egan, A.(2007). Some Counterexamples to Causal Decision Theory. Philosophical Review,116(1),93-114.
①Egan, A.(2007). Some Counterexamples to Causal Decision Theory. Philosophical Review,116(1),93-114.
②Lewis, D.(1976). Probabilities of conditionals and conditional probabilities. The Philosophical Review,85(3),
297-315.
③Egan, A.(2007). Some Counterexamples to Causal Decision Theory. Philosophical Review,116(1),93-114.
①Weirich, P.(1988). Hierarchical Maximization of Two Kinds of Expected Utility. Philosophy of Science,55(4),560-582.
②Gibbard, A., Harper, W. L.(1981). Counterfactuals and Two Kinds of Expected Utility. In R. S. William L.Harper, Glenn Pearce (Ed.), Ifs: conditionals, belief, decision, chance, and time (pp.153-190). Dordrecht: D.Reidel Publishing Company.
③Weirich, P.(1988). Hierarchical Maximization of Two Kinds of Expected Utility. Philosophy of Science,55(4),560-582.
④Harper, W.(1986). Mixed strategies and ratifiability in causal decision theory. Erkenntnis,24(1),25-36.
⑤Weirich, P.(1988). Hierarchical Maximization of Two Kinds of Expected Utility. Philosophy of Science,55(4),560-582.
①对这个问题感兴趣的读者请参见Lewis, D.(1973). Counterfactuals. Cambridge: Harvard University Press.
②Eells, E.(1984). Causal Decision Theory. PSA: Proceedings of the Biennial Meeting of the Philosophy ofScience Association, Vol.1984,2,177-200. p.178
①Reichenbach, H.(1959). Modern philosophy of science: Selected essays. London: Routledge and KeganPaul.Chapter3.pp.67-78
①Jeffrey, R. C.(1983). The logic of decision（Second Edition). Chicago: University of Chicago Press.p.16
②Jeffrey, R. C.(1983). The logic of decision（Second Edition). Chicago: University of Chicago Press.p.18
①本节的大部分内容来自于我已经发表过的一篇论文：论证据决策理论的困境与出路[J].哲学动态，2010,(6).
①Nozick, R.(1993). The Nature of Rationality. Princeton, New Jersey: Princeton University Press.p.43
②方钦.可能世界中的选择：纽康姆难题[J].社会科学战线,2006,(3).
③Nozick, R.(1993). The Nature of Rationality. Princeton, New Jersey: Princeton University Press.p.45
①Kahn, C. H.(1979). The art and thought of Heraclitus: An edition of the fragments with translation andcommentary. Cambridge; New York: Cambridge University Press.p.33
①Kahneman, D.,&Tversky, A.(1972). On prediction and judgment. Oregon Research Institute Bulletin,12(4),10.
①Kahneman, D.,&Tversky, A.(1973). On the Psychology of Prediction. Psychological review,80(4),237-251.
①Kahneman, D.,&Tversky, A.(1973). On the Psychology of Prediction. Psychological review,80(4),237-251.
②Kahneman, D.,&Tversky, A.(1973). On the Psychology of Prediction. Psychological review,80(4),237-251.
③Beach, L. R.(1966). Accuracy and Consistency in the Revision of Subjective Probabilities. IEEE Transactionson Human Factors in Electronics,7(1),29-37.
④李章吕.支持理论对标准概率理论的超越和发展[J].学术论坛,2010,(8).
①关于“恰当相符性”这一逻辑哲学中心问题的详细论述，请参见桂起权.当代数学哲学与逻辑哲学入门[M].上海:华东师范大学出版社,1991:97-116.
②李章吕.支持理论对标准概率理论的超越和发展[J].学术论坛,2010,(8),10-15.
①张昆仑.边际效用递减规律新探.现代财经:天津财经学院学报,2004,(4),8-10.
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