[Jdm-society] Coherence and Correspondence (RE: On Samuelson "Letaxioms satisfy themselves")

[Deborah Frisch]

Dear Roberta,

I don't think this thread is primarily about ambiguity in the meaning of
coherence and correspondence.  I think the point is that coherence has been
given much more weight than correspondence in decision research.  It's been
assumed that one type of coherence (consistency with the axioms of expected
utility theory) is necessary for correspondence. [Some economists believe
that this type of coherence is sufficient for correspondence, but most
decision researchers do not.]

I actually think the meaning of both terms is pretty clear.  Coherence means
internal consistency among beliefs and/or preferences.  Chris points out
that there are many types of coherence including logical consistency,
obedience of the axioms of probability theory and expected utility theory,
regular (i.e., intertemporal) reliability and inter-rater (i.e.,
interpersonal) reliability.

To me, the meaning of correspondence as applied to decision making is very
clear - it means that "decision utility" corresponds to "experienced
utility."  Correspondence means that if I choose the apple over the orange,
I'll experience more utility from the apple than I would have from the
orange. My concept of correspondence is based on Kahneman and Tversky, not
Sen or Gigerenzer.

You write, "To me, nobody (even the most orthodox economist we can think of)
would  buy the idea that axioms (independence and continuity) ought to be
satisfied."

I think many members of this list and almost all economists believe that
independence and continuity ought to be satisfied, especially continuity.

Framing effects and preference reversals show that the principle of weak
ordering (transitivity + continuity) is empirically false.  (Oddly enough,
all of the variants of EU that have been developed in the last 25 years
(e.g., cumulative prospect theory) assume weak ordering.)

Framing effects call into question the normative status of "transitivity AND
continuity."  These axioms seem normatively compelling when you look at them
individually, but their joint implication is normatively unacceptable.  When
framing influences decision utility, weak ordering is descriptively
unjustified.  When framing affects experienced utility, weak ordering is
normatively unjustified.

Best,

Deb

Original Message ----- 
From: <rmuramatsu at uol.com.br>
To: "Chris Anderson" <chris.anderson at temple.edu>; "'Deborah Frisch'"
<dfrisch at pobox.com>
Cc: <jdm-society at mail.sjdm.org>
Sent: Tuesday, May 18, 2004 9:27 AM
Subject: Re: [Jdm-society] Coherence and Correspondence (RE: On Samuelson
"Letaxioms satisfy themselves")


> Dear all,
> I have the impression that a great deal of  this debate has to do with the
> conceptually ambiguous usage of coherence and correspondence. With this in
> mind, I am inclined to agree with Anderson that better definitions would
> help us to understand what is being argued. I can think of at least two
> completely different interpretations of "correspondence".
>
> For instance,  the economist Amartya  Sen ([1987], 1994) uses the notion
of
> correspondence to criticize the mainstream view of rationality as inner
> consistency of choices (underlying Samuelson's approach). In his view,
> correspondence is a necessary condition of rationality, but he admits that
> it may be not sufficient ). To him, "correspondence rationality- the
> correspondence of choice  with aims - must be a necessary condition of
> rationality...whether or not [it]has to be supplemented by [other]
> rationality requirements" (1994, pp.13-14, fn.8). It seems to me that
Sen's
> ideas can be rephrased in terms internalist criterion of rationality as
> coherence (e.g. Hausman, Thagard).
>
> Gigerenzer and his colaborators use the term "correspondence"quite
> differently. It refers to the "the fit between the structure of the
> heuristic and the structure of the environment" and in this sense it is an
> 'externalist' criterion.  This may be because Sen and Gigerenzer have
> different interpretations of what choice theory can (should) accomplish.
It
> seems to me that Sen wants to study  the outcomes of individual
> decision-making so as evaluate how one's choices satisfy her goals and
> ethical concerns. Gigerenzer and this ABC group embarks on a different
> task - they are interested in studying the rationality of cognitive
> mechanisms or heuristics productive of actual thinking and
decision-making.
>
> Even though I am very fond of Gigerenzer's work, I hesitate to agree with
> his conclusion that correspondence criterion can replace a consistency
> criterion. We are in need of a refined notion of coherence that comes to
> supplement the correspondence criterion if we are interested in a broad
> account of rational decision-making. Focusing only on correspondence does
> not allow us to address certain normative issues about human rationality.
> Besides that we would be downplaying the fact that individuals in the real
> world evaluate the rationality of their own and others' actions based on
> coherence (prerequisite for "proper" decisions). All this is to express my
> opinion that coherence is a necessary but not sufficient sufficient
> criterion.
>
> My final remark is about the SAA. To me, it mainly serves  rhetorical
> purposes (rather than descriptive ones). Then, it does not make sense to
> take it at face value (to interpret it literally).  What Samuelson tries
to
> do is to stress the (predictive) validity of his hypothesis. Based on his
> analytical treatment, one can predict that an individual that (optimally)
> satisfies her preferences exhibits a pattern of choice behavior
(logically)
> equivalent with satisfaction of axioms. That's all. For that reason, he
> rhetorically suggested us to "let them satisfy themselves".  Of course,
this
> point could be disputed. There is robust evidence that would call into
> question that preference satisfaction will lead "naturally' to axiom
> satisfaction and that many instances of actual choice behavior deviate
from
> redictions made by mainstream decision theory. With the above in mind, I
> tend to agree with Frisch's critical remarks. But I think Debra's
> exaggerates a bit when she says:  " you should satisfy your preferences
and
> leave axioms unsatisfied. Better them than you..." To me, nobody (even the
> most orthodox economist we can think of) would  buy the idea that axioms
> (independence and continuity) ought to be satisfied.
>
> Cheers,
> Roberta Muramatsu
> Erasmus University of Rotterdam
>
>