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Re: [Phys-L] Inference Lab Design

I wrote:

In the game in question, there is a reward for answering quickly,
but you must not answer too quickly! You need to give the other
players time to make their first-stage inferences ... but then you
need to make your second- stage inference quicker than they do. So
this requires psychology as well as logic: you need to appraise
the capabilities of the other players.

On 08/19/2012 12:10 PM, John Mallinckrodt wrote:

Consider: These are supposedly "logicians" so it's almost impossible
to imagine any of them not instantaneously making the first stage
inference--i.e., recognizing the implication of seeing one black hat,
one white hat, and two raised hands. Thus, the moment one of them
makes the second stage inference (assuming only perhaps that it
wasn't worked it out in advance), there is no need for further

That parenthetical assumption is important. Thanks for documenting
it explicitly.

...... I'd say that it involves psychology in an almost trivial
if still interesting way, which is why I think this *would* be a good
example to use even in the first week of class.

I agree with most of that *except for the conclusion*. I reckon the
conclusion rests on some sketchy assumptions, including especially the
assumption that either all of the players or none of the players have
seen the problem before.

If Player A has seen the problem before but the others have not, it is
entirely foreseeable that he will finish both stage 1 and stage 2 before
the others have finished stage 1. It's not at all obvious to me what
strategy Player A should use to detect this situation and/or handle it
when it arises. If you know a suitable strategy, please explain.

As the proverb says:
Experience teaches you to recognize a mistake
when you've made it again.

I have personally made this mistake often enough to know rather well
what it looks like: I assign something that is intended to be a
reasoning exercise, only to find out that for half the class it is
merely a rote recall exercise, because they've seen it before. This
is a particularly prevalent problem in college-freshman classes and
in first-year graduate classes, especially at institutions that draw
students with a wide variety of backgrounds.

This is one of the reasons why it is hard to create a low-budget
"standardized" test of reasoning. We desperately need good tests, but
we should not imagine that it is trivial to administer a nontrivial