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SUMMARY:Towards a more realistic subjective decision theory - Yang Liu (Ce
 ntre for the Study of Existential Risk)
DTSTART:20170222T130000Z
DTEND:20170222T143000Z
UID:TALK70722@talks.cam.ac.uk
CONTACT:31287
DESCRIPTION:In his seminal work “the Foundations of Statistics\,” Sava
 ge \nput forward a theory of subjective probabilities. The theory is based
  on \na well-developed axiomatic theory of rational decision making. In \n
 constructing his system\, additional problematic assumptions are however \
 nrequired. First\, there is a Boolean algebra of events on which \nsubject
 ive probabilities are defined. Savage's proof requires this \nalgebra to b
 e a σ-algebra. However\, on Savage's view\, one should not \nrequire the 
 probability to be σ-additive. He\, therefore\, finds the \ninsistence on 
 a σ-algebra peculiar and unsatisfactory. But he sees no \nway of avoiding
  it. Second\, the assignment of utilities requires the \nconstant act assu
 mption: for every given consequence there exists a \nconstant act which ha
 s that consequence in every state. This assumption \nis known to be highly
  counterintuitive. The paper on which this talk is \nbased includes two ma
 thematical results. The first\, and the more \ndifficult one\, shows that 
 the σ-algebra assumption can be dropped. The \nsecond states that\, as lo
 ng as utilities are assigned to finite gambles \nonly\, the constant act a
 ssumption can be replaced by the plausible\, much \nweaker assumption that
  there are at least two non-equivalent constant \nacts.\n\nIn this talk\, 
 I will first review Ramsey and Savage’s classical \ndecision-theoretic m
 odels. I will then discuss the notion of “idealized \nagents” in stand
 ard normative decision theory. I will argue that our \nsimplified system\,
  which is adequate for all the actual purposes for \nwhich the system is d
 esigned\, involves a more realistic notion of \nidealized agents. This wil
 l be followed by a brief outline of our new \ntechnique of tripartition tr
 ees which leads to the construction of \nquantitative probabilities in Sav
 age-style systems without the σ-algebra \nassumption.
LOCATION:Seminar Room 2\, Department of History and Philosophy of Science
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