[Jdm-society] Re: Linda

[William Neace]

Another way to influence the conjuntion fallacy is to prime the cognitive
perspective from which the information is processed - conjunction errors
occur less when participants are asked to "think as a scientist" compared to
those who are asked to "think as a clinician" - although the effect is
rather small.  Nonetheless, there is emerging evidence that problem frame
(frequency vs. probability) is less important than making salient the
set-subset relationship implied by the problem.  That is, conjunction errors
can occur in substantial proportion with a frequency frame (Sloman et al.,
2003) and can be reduced substantially with a probability frame (Neace &
Edgell, 2004).  That is, cueing the proper problem representation can make
logical rules more compelling than nonextensional rules, thus swaying the
"tension" between the two reasoning processes toward the more "rational"
side.

References:

Sloman, S.A., Over, D., Slovak, L., & Stibel, J.M. (2003). Frequency
illusions and other fallacies. Organizational Behavior and Human Decision
Processes, 91, 296-309.

Neace, W.P. & Edgell, S.E. (2004). The Effects of Reasoning Mode, Problem
Format, and Response Mode on Conjunction Errors.  Working manuscript.

Regards,

Bill

William P. Neace, Ph.D.
Visiting Assistant Professor
Department of Psychology
Universilty of Hartford
200 Bloomfield Avenue
West Hartford, CT  06117
E-mail:  neace at hartford.edu
Phone: 860-768-5906
FAX:   860-768-5292

----- Original Message ----- 
From: "Deborah Frisch" <dfrisch at pobox.com>
To: <jdm-society at mail.sjdm.org>
Sent: Wednesday, February 16, 2005 12:15 PM
Subject: [Jdm-society] Linda/T&K83


> Tversky & Kahneman (1983) present interesting data relevant to the
> question of how easy it is to make the conjunction effect "disappear"
> (Gigerenzer, 1991).  One trick for making cognitive illusions disappear is
> to present subjects with arguments endorsing the normative and
> non-normative responses. This method was invented by MacCrimmon (1968) and
> applied by Slovic & Tversky (1974) to the sure-thing principle (which they
> called the "SIP" for Savage Independence Principle).  Another trick is to
> frame questions in terms of relative frequencies instead of subjective
> probability judgments.
>
>
>
> T&K83 used both methods.  The results were as follows:
>
> 1. Linda
>
>
>
> p. 299:   85% show conjunction effect
>
> p. 299    57% show conjunction effect when superordinate hypothesis is
> "Linda is a bank teller whether or not she is active in the feminist
> movement."
>
> p. 299:  65% endorse non-normative argument
>
> p. 300:  56% would prefer to bet on FB with $10 at stake
>
>
>
> 2. Risky choice (six-sided red and green die):
>
>
>
> p. 303:  88% show conjunction effect
>
> p. 304:  24% endorse non-normative argument
>
>
>
> 3. One or more heart attacks VS. over 55 and one or more heart attacks
>
>
>
> p. 308:  percentage frame: 65% show conjunction effect
>
> p. 309:  concrete sample frame:  25% show conjunction effect
>
>
>
> T&K summarize these result as follows:
>
> p. 309:  A contrast worthy of note exists between the effectiveness of
> extensional cues in the health-survey problem and the relative inefficacy
> of the methods used to combat the conjunction fallacy in the Linda problem
> (argument, betting, "whether or not").  The force of the conjunction rule
> is more readily appreciated when the conjunctions are defined by the
> intersection of concrete classes than by a combination of properties.
> Although classes and properties are equivalent from a logical standpoint,
> they give rise to different mental representations in which different
> relations and rules are transparent.  The formal equivalence of properties
> to classes is apparently not programmed into the lay mind.
>
>
>
> The last line of the article is:
>
> p. 313-314: A comprehensive account of human judgment must reflect the
> tension between compelling logical rules and seductive nonextensional
> intuitions.
>
>
>
> According to Amos and Danny, the reason I believe Linda is more likely to
> be a feminist bank teller than a bank teller is that the seductiveness of
> the representativeness heuristic is more compelling to me than the logical
> compellingness of the conjunction axiom.  The fact that Linda seems so
> darn much like a feminist bank teller and nothing at all like a bank
> teller tricks me into violating the constraints in a Venn diagram.
>
>
>
> You know, maybe they're right.  As a Bayesian, I have to acknowledge that
> possibility,  although I'm pretty sure I've got that Venn thing down pat.
> And the fact that 54% of subjects violate the conjunction rule even when
> you qualify it as "Linda is a bank teller whether or not she is active in
> the feminist movement" suggests there's something going on here aside from
> reliance on an imperfect heuristic.
>
>
>
> [The fact that 56% of subjects would prefer bet on FB rather than B when
> $10 is at stake and nothing social is at stake (since she's hypothetical)
> is strong evidence that something like the representativeness bias is
> real.]
>
>
>
> The condescension toward intuition and reification of formalism echoes the
> last line of Slovic & Tversky (1973, pp. 372-373).  Faux Savage (Amos?)
> says to Fake Allais (Slovic?) "I have observed that, in general, the
> deeper the understanding of the axiom, the greater the readiness to accept
> it.  Were it not for the cogency of the argument, I doubt that this would
> be the case."
>
>
>
> Allais deserved a response to this.  He could have told Savage that Allais
> and Ellsberg were the first decision scientists to understand Savage's
> independence axiom deeply enough to construct counterexamples to it and
> that they both adamantly believed that their examples challenged the
> normative status of the axiom as well as its descriptive validity.  He
> could have reminded Savage that Allais and Ellsberg presented quasi-formal
> analyses demonstrating that a rational agent might choose to violate the
> independence axiom.  He might have pointed out that there was independent
> evidence that both Allais (Nobel) and Ellsberg (Nixon) were very sharp
> cookies.
>
>
>
> Allais:  I have observed that, in general, the deeper the allegiance to
> formalism, the greater the resistance to acknowledging that many smart and
> knowledgeable people willingly, gleefully and proudly violate Savage's
> allegedly normative axioms.  Lopes (1996, p. 184) said it best:  "I can
> well attest that it is not a comfortable experience to stand with the
> collection of money pumps, Dutch book victims, and assorted ne'er-do-wells
> who feel no obligation to obey the axioms and theorems of expected utility
> theory."
>
>
>
> Were it not for the importance of this matter, I'd have given up on you
> Americans long ago and retired to Cannes.
>
>