Re: The Conjunction Fallacy Fallacy [WAS Re: Anti-singularity spam.]

From: Eliezer S. Yudkowsky (
Date: Sun Aug 27 2006 - 22:54:55 MDT

Mark Waser wrote:
> Hi Jeff,
> Thanks for the rational reply. :-) <Please do me a favor and
> re-read my last paragraph way down below after skimming this>
>> You've missed something, Mark -- the example that started this
>> subthread of the argument (the feminist bank teller question and
>> the typical responses it gets) *is a canonical
>> heuristics-and-biases example*.
> No, I got that. Richard's point (and my reply to your point) is that
> that exact same example is *also* specifically used by the mental
> modeling folk to show that the experts in that field don't agree with
> the experts in the Bayesian field -- at least, as far as saying that
> human reasoning can be explained by or is even consistent with
> Bayesianism.

Mark, are you familiar with heuristics and biases *specifically*? That
is, have you read _Judgment Under Uncertainty_ or some other work that
contains the literal substring "heuristics and biases" on the front or
back cover?

Because I can't think of *anyone* in H&B who has ever claimed that human
thought is Bayesian. (No memory is available to my recall attempt, so I
infer that the frequency is low or zero.) Bayes is prescriptive, not
descriptive. I'm too young to remember a time from the distant past
when anyone thought that human thought actually followed
probability-theoretic inference rules. Today, "everyone knows" that
human thought isn't Bayesian - it is an elementary point on which the
whole field of heuristics and biases is based; if human thought operated
using Bayesian procedures, rather than a toolbox of heuristics, there
would be no systematic biases. Even allowing for the possibility of
occasional error, the errors would center around a Bayesian mean.

> Eliezer keeps saying "RTFM! (To name a specific M, "Judgment Under
> Uncertainty" would do him some good.)". Richard keeps saying "I
> understand that topic but IT IS NOT RELEVANT TO MY POINT".
> Try googling "feminist bank teller". The first entry you come up
> with is David Chart's "Inference to the Best Explanation,
> Bayesianism, and Feminist Bank Tellers". He also seems to a)
> understand Bayesianism, b) refer to and understand the experimental
> results, and c) not believe that Bayes is relevant to the human
> mental model.

I read the referenced paper, which seems quite ordinary except for the
implicit inference (from what the paper is arguing against) that someone
in the field of mental models is still seriously putting forth Bayesian
inference as a descriptive model of human reasoning. If so, they would
seem to be rather ignorant of heuristics and biases. Which is why Chart
is trying to remedy their ignorance, with an extremely basic example -
or so it appears.

Chart's paper is at:

Sample quote from the paper:

"Tversky and Kahneman give their own interpretation of the results. They
suggest that we use a 'representativeness heuristic', and that a
feminist bank teller seems more representative of Linda's background
than merely being a bank teller. Their interpretation obviously has a
close affinity to the interpretation I have provided, and on certain
theories of explanation, particularly unification models, it may turn
out to be the same interpretation.

In conclusion, then, this result suggests that, if the choice is between
Inference to the Best Explanation and Bayesianism, we use Inference to
the Best Explanation. We make mistakes which are to be expected on an
explanatory model of inference, but which are surprising and hard to
explain on a Bayesian model. Thus, according to Inference to the Best
Explanation, we should tentatively conclude that we use explanatory, not
Bayesian, inference."

In other words, Chart is proposing something compatible with the
standard explanation in heuristics and biases ("it may turn out to be
the same interpretation"). This is also my impression on reading
Chart's paper; what Chart is describing is very close to the standard
model in H&B, possibly identical with it (as Chart says), just described
a different way so as to render it applicable to an ongoing dispute in
the related field of mental models.

>> except insofar as Richard keeps seeming to think modeling is part
>> of the heuristics-and-biases subfield, which it isn't.
> Could you give an example of where Richard does this?

Actually, Richard's error is much worse; he thinks heuristics-and-biases
is a subfield of mental models.

E.g. Loosemore: 'These people (Chater and Oaksford, at least) know
everything there is to know about the entire field of human reasoning,
including the subfield that Yudkowsky refers to as "heuristics and biases".'

My unreliable impression is that there are at least an order of
magnitude more researchers working on heuristics and biases. H&B is a
large experimental field, while "mental models" is a comparatively
small, comparatively more theoretical field.

> I think that
> he's pretty clear that his point is that he believes that heuristics
> and biases (at least as performed by Bayesians)

"Bayesians" wouldn't use heuristics, they would use the inference rules
of probability theory. The notion of a Bayesian "performing" a
heuristic, or a bias, is nonsense.

The above sentence demonstrates (1) a severely erroneous picture of what
H&B is all about, which seems to have been (2) virally transmitted by
Loosemore to Waser, which is (3) why I'm considering banning Loosemore
from the list.

> I think that
> he's pretty clear that his point is that he believes that heuristics
> and biases (at least as performed by Bayesians) are not relevant
> since they are not the mental model which is actually employed by the
> sole example of General Intelligence - i.e. humans (in fact, that's
> pretty much a rephrasing of his point).

The whole above paragraph is wildly ignorant of what the H&B folks do:
use experiments to pin down a descriptive model of human reasoning which
very first point made in the field - "Wow! Human reasoning is not
Bayesian!" - by Ward Edwards in the 1960s, if I recall correctly.

I therefore doubt your assertion that:

> I *think* that I've read the majority of the relevant stuff.

This also seems rather unlikely given:

> I understand that you got mired in the back-water and opinions of the
> H&B folk.

H&B a backwater? Kahneman, one of the founders of the field, recently
won a Nobel Prize in Economics - for that particular work, mind you.
I've yet to see a paper on mental models mentioned in the mainstream
press, while you can find plenty of press articles about various
particular results in heuristics and biases. Not that I have anything
against the real researchers in the field of mental models; H&B is a
much larger field than AGI research, too. But Loosemore's concept that
the large experimental field of H&B is a subfield of the small and
relatively theoretical field of MM, is another example of his severe
ignorance. Your above comment seems to imply that you have been misled
by the implicit assumptions you picked up from Loosemore. Which is very
much the sort of thing I'm worried about.

> The h&b field claim to understand something. The mental modeling
> people contest that understanding.

Not in Chart's paper. Please provide references - though, mind you, my
working assumption at this point is that you are wholly ignorant of the
large field of heuristics and biases, working with mistaken assumptions
picked up from Loosemore, and therefore not capable of assessing what
would constitute a conflict between the two fields, as evidenced by your
misassessment of Chart's paper.

> Well now, I provided a direct reference to an article that clearly
> supports Richard (with all of the feminist bank teller experiments as
> it's experimental basis).

The referenced paper by Chart does not support Richard's explicit
assertion that the conjunction fallacy arose from a particular
misunderstanding by the research subjects (a possibility that was long
since refuted a million ways from Sunday, see the paper referenced in my
reply to Medina), nor Richard's rather huge implicit mistake in thinking
that heuristics-and-biases is a subset of the field of mental models, or
Richard's misconception that H&B holds that humans are using Bayesian
inference procedures subject to noise. In fact, if you read the paper
by Chart carefully, it contradicts-in-passing the later point.

> Eliezer *really* needs to do so. This is *not* an odd dispute. It
> is an ongoing, inter-field debate.

I am not aware of this being an ongoing inter-field dispute. References
please. (Bearing in mind that I strongly suggest you read up
*specifically on heuristics and biases* before you attempt to determine,
from your own knowledge, what is or is not an inter-field dispute.)

Eliezer S. Yudkowsky                
Research Fellow, Singularity Institute for Artificial Intelligence

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