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1、TheoryofDecisionunderUncertaintyItzhakGilboaJuly2008Contents1Preface62MotivatingExamples93FreeWillandDeterminism113.1Canfreechoicebepredicted?..................113.2Istheworlddeterministic?....................123.3Isfreewillobservable?......................133.4Theproblem
2、offreewill.....................143.5Arationalillusion.........................193.6Freewillandthedecisionmatrix................214ThePrincipleofIndi?erence234.1Willacanonicalspacehelp?...................244.1.1Thecanonicalstatespace................244.1.2Di?cultieswithaun
3、iformprioron[0,1]........254.1.3Conclusion.........................264.2What’sspecialaboutthecoin?.................274.2.1Symmetry.........................274.2.2Smoothbeliefs......................285RelativeFrequencies315.1Thelawoflargenumbers.....................315.2Th
4、eproblemofinduction....................335.2.1Hume’scritique......................3315.2.2Goodman’sgrue-bleenparadox.............345.2.3Kolmogorovcomplexityanditsdependenceoflanguage365.2.4Grue-bleenagain.....................405.2.5Evolutionaryexplanations................
5、475.3Problemswiththefrequentistapproach.............516SubjectiveProbabilities566.1Lindathebankteller.......................566.2Pascal’swager...........................586.3Classicalvs.Bayesianstatistics.................606.3.1Basicde?nitions......................606.3.2
6、Thegamblerfallacy....................626.3.3Exchangeability......................636.3.4Con?denceisnotprobability...............666.3.5Classicalstatisticscanberidiculous...........686.3.6Di?erentmethodsfordi?erentgoals...........697ACaseStudy747.1Acharacterizationtheoremf
7、ormaximizationofutility....747.2Proof................................777.3Interpretations..........................807.3.1Afewde?nitions.....................807.3.2Ameta-scienti?cinterpretation.............867.3.3Anormativeinterpretation................897.3.4Adescriptive
8、interpretation...............917.4Limitations............................937.4.1Semi-orders.....
