Re: Attempt at a Schema

["J. Barkley Rosser, Jr." <rosserjb@xxxxxxx>]

Goncalo,
     I must agree that, neat as it is, Lawson's schema
is probably too simple, although it is not bad.
     Let me remark on just two of your points.
     1)  I think you make this distinction within your subjectivist
category, but Bayesians can be divided into the "classical"
ones who actually accept the idea that there are objective
probability distributions that can be discovered.  Their view
involves focusing on the process by which with repeated trials
subjective priors will converge on objective posteriors, which
in effect assumes a frequentism of sorts, and the "radically
subjectivist" ones (e.g. Dale Poirier, perhaps these are
your "intuitionists"?)  who deny the existence of objective
probability distributions at all.
     2)  Well, I strongly disagree with your lumping of Keynes
and Lucas.  I have already noted that Keynes allowed for
multiple possible views of probability.  Indeed, he allowed for
a fifth case not mentioned in the quote I provided, that of just
straightforward objective probability, and he accepted the
rolling of dice as such a case.  So, he was neither strictly a
subjectivist nor an objectivist.  He accepted both.
     But, in the cases where he denies the existence of probability
distributions he strikes me as being an advocate of ontological uncertainty,
as I have already argued.  That he would argue, as you
note, that people might act "as if" they can do subjective Ramsey-
Savage calculations based on assumed probabilities is not the
same thing as saying that they should or that they will get reasonable
or useful results.  On p. 152 of the GT, Keynes says (in regard
to market valuation based on convention):
      "...it [the market valuation] cannot be uniquely correct, since
our existing knowledge does not provide a sufficient basis for
a calculated mathematical expectation."
       This is by no means the only such quotation in Keynes'
writings.
       As regards Lucas, well, I can see that you might argue
that he accepts that expectations are formed subject to
currently available information.  But, this is rather like the
division above between the different kinds of Bayesians.
Keynes is more willing to allow that no calculation may be
accurate or that sucessive estimations will converge on
any "objective truth."  But, Lucas clearly follows and accepts
Muth's formulation, which he quotes in his earliest papers
in which he used rational expectations.  Here is Lucas'
characterization of Muth's presentation in the very first paper
that Lucas ever wrote using rational expectations (from 1966)
"Optimal Investment with Rational Expectations," from
_Rational Expectations and Econometric Practice_, ed. by
Lucas and Thomas Sargent, 1981, University of Minnesota Press,
p. 61:
     [from footnote 2]
     "Muth (1961) defines a rational expectation as one with the
same mean values as the true future price, where both the
expected and actual prices are random variables."
      I do not see how you can stuff this kind of view into the same
category as any of Keynes' views, other than his case involving
rolling dice, and certainly not as detailed and articulated a
schema as you have put forth.
Barkley Rosser

-----Original Message-----
From: Goncalo Fonseca <fonseca@xxxxxxxxxxxxxxxxxx>
To: pkt@xxxxxxxxxxxxxxxx <pkt@xxxxxxxxxxxxxxxx>
Date: Tuesday, December 19, 2000 10:56 AM
Subject: Re: Attempt at a Schema


>
>Barkley,
>
>Well, I've had this in my head for a while, but I think its a pretty
>standard schema among philosophers and probability theorists.  (I can't
>point out a precise reference though).
>
>On your suggestions: yes, I forgot Bayes as the grandfather of all
>informational & subjective probabilities; I also forgot Carnap in logical
>relationism. Also, I realized afterwards that what I called "heterogeneous
>relationism" is more conventionally called "credal probability".
>"Intuitionism", I believe, is the term Good and Koopman prefer to use for
>themselves.
>
>I know it sounds odd to describe Arrow-Debreu as extreme intuitionism, but
>(generally) they do not bother with deriving probabilities and they do not
>impose any assumptions on people's state-preferences which makes them
>"comply" with basic axioms of probability.  It's a very amorphous theory.
Of
>course, Arrow-Debreu is sometimes applied in a way so that probabilities
are
>derivable (e.g. temporary equilibrium theory), but that is not a necessary
>implication.
>
>Its been a while since I read Lawson's piece, but I remember being quite
>dissatisfied with its categorization.
>
>On lumping Keynes and Lucas together: I absolutely insist on this.  Keynes
>and Lucas have effectively the SAME theory about how probability
assessments
>are made.  They both believe that if people share the same information,
they
>make the same probability estimates. The difference between them lies in
>their justification of this (structural model-uniformity for Lucas,
>I-don't-quite-know-what for Keynes) and in the assumptions of the
>information available to people (all info will "come out" for Lucas, most
>info does not exist, for Keynes).
>
>Is it overcomplicating?  Partly.  But I believe it is necessary because
>Keynes gets away with sounding "subjectivist", when really he is far less
>"human" than people think.  Lucas, in turn, gets condemned for sounding
>"objectivist", when he is quite a bit more "human" than that.
>
>We can certainly see the inhuman aspect of Keynes in his Treatise on
>Probability, e.g.:
>
>"In the sense important to logic, probability is not subjective. A
>proposition is not probable because we think it so. When once the facts are
>given which determine our knowledge, what is probable or improbable in
those
>circumstances has been fixed objectively, and is independent of our
>opinion." (Keynes, 1921: p.4)
>
>The often quoted passage from Keynes (1937, QJE), "there is no scientific
>basis on which to form any calculable probability", etc. is based again on
>this idea.  If info is missing, then, probability assessments cannot be
>made, etc.
>
>It is interesting to note that Keynes absorbed Ramsey's "subjectivist"
>criticism of his theory.  In the continuation of the 1937 passage (that
>PKers somehow never quote), he writes:
>
>"Nevertheless, the necessity for action and for decision compels us as
>practical men to do our best to overlook this awkward fact and to behave
>exactly as we should if we had behind us a good Benthamite calculation of a
>series of prospective advantages and disadvantages, each multiplied by its
>appropriate probability waiting to be summed." (Keynes, 1937)
>
>which sounds to me exactly like Ramsey-Savage subjective expected utility,
>i.e. numerical assessments are being implicitly made.
>
>It is for this reason that I don't like characterizing Keynesian
uncertainty
>as being "non-numerical".  Keynes gets numerical probabilities when
>information is there, and when information isn't there, he adopts Ramsey's
>resolution (which is numerical too).  Only when he speaks of "animal
>spirits" does some idea of the whimsical come in -- but that is not
>"connected" very well by him to his uncertainty theory.
>
>So, my purpose with this far-too-extensive schema is to try to set the
>limits of what a debate on Keynes's uncertainty theory should lie, but also
>to dangle the bait of "rational beliefs".
>
>Personally, I think subjective beliefs are the ultimate guides to action,
>but I also think that these beliefs ought to be "consistent" with the
>information and data available.   So, for me, the true source of the
problem
>is perhaps not how complicated the world is (i.e. the information
>available), but how this information is processed differently by people and
>the consequences of this. The same stock market data has led economists to
>believe it is a bubble, and many practitioners to believe a "new economy"
is
>in the offering.  Keynes's liquidity preference theory has aspects of this.
>Same data, different beliefs -- a dangerous combination for the stability o
f
>the economy.
>
>Cheers,
>
>Goncalo
>
>----- Original Message -----
>From: "J. Barkley Rosser, Jr." <rosserjb@xxxxxxx>
>To: "Goncalo Fonseca" <fonseca@xxxxxxxxxxxxxxxxxx>
>Cc: <pkt@xxxxxxxxxxxxxxxx>
>Sent: Monday, December 18, 2000 3:04 PM
>Subject: Re: Attempt at a Schema
>
>
>> Goncalo,
>>      Wow!  Is this your schema, or have you borrowed
>> it from someone else?
>>     Some picky points.  I think your characterization of
>> Arrow and Debreu is simply way off base.  I also don't
>> see any of the versions of Keynes being lumped in with
>> Lucas.  How do you get that one?  And, I think that one
>> should be careful about using the term "intuitionism," given
>> its special use in mathematical logic to refer to systems
>> that allow the existence of the "excluded middle."  Finally,
>> I am surprised that you did not bring up Bayes in the discussion
>> of subjectivism.  Clearly, he is the key figure.
>>       More generally, I think maybe you have overcomplicated
>> the discussion, interesting as your cases are.  A somewhat
>> simpler, and I think quite useful, categorization is due to
>> Tony Lawson in a 1988 piece in the JPKE, "Probability and
>> uncertainty in economic analysis," JPKE, 1988, vol. 11, no. 1,
>> pp. 38-65.  Especially on p. 48 he presents a neat little
>> diagram that provides four cases based on two distinctions.
>> The distinctions are subjective versus objective and
>> numerically measurable versus not numerically measurable.
>> He identifies Savage and Friedman as in the subjective but
>> numerable category and Keynes as in the subjective but
>> not numerable category (although I have already noted that
>> Keynes allowed for other cases as well as this one).  In
>> the objective numerable he puts Muth and Lucas and in the
>> objective non numerable he puts Knight.
>> Barkley
>
>
>