Tyrrell_McAllister comments on Critiques of the heuristics and biases tradition - Less Wrong

18 Post author: lukeprog 18 March 2013 11:49PM

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Comment author: Benja 19 March 2013 09:23:00PM 2 points [-]

You'd think so, except that the rest of the paragraph doesn't seem to make much sense if this is just a typo, does it? "X and therefore Y" and "X and X is the cause of Y" must both have smaller probability than "X", just like "X and Y". It seems to me that this is a thinko rather than a typo -- somebody really thought that the conjunction X&Y must have higher probability (like, it's X AND Y so it's probability is that of X PLUS the probability of Y, or something), while "X and therefore Y" must have lower probability than X. Or something.

Alternatively, perhaps someone felt that ranking "X and Y" interpreted as "X and therefore Y" as more probable than "X" could be interpreted as "the conditional probability of Y given X is higher than the probability of X"? But that seems like an extreme stretch of the words.

Reading the original source might clarify things [i.e., Hertwig, Benz and Krauss (2008)] -- unfortunately I don't have the time right now, anyone?

(BTW, I've always wondered whether, given that the conjunction is on the list as an "alternative" choice, subjects interpret "X" by itself as "X but not Y". I've always thought someone would have done experiments to test that idea, but I haven't looked into the literature deeply enough to know.)

Comment author: Creutzer 20 March 2013 12:45:10AM 3 points [-]

(BTW, I've always wondered whether, given that the conjunction is on the list as an "alternative" choice, subjects interpret "X" by itself as "X but not Y". I've always thought someone would have done experiments to test that idea, but I haven't looked into the literature deeply enough to know.)

Actually, even though this explanation works for the oft-cited Linda case, it turns out that the locus classicus Kahneman & Tversky 1983 already contains several (versions of) experiments that yield conjunction-fallacy-type results but could not plausibly be interpreted in that way.

Comment author: Benja 20 March 2013 06:45:23AM 0 points [-]

Thanks!

Comment author: Tyrrell_McAllister 19 March 2013 10:13:35PM *  1 point [-]

You'd think so, except that the rest of the paragraph doesn't seem to make much sense if this is just a typo, does it? [...] Alternatively, perhaps someone felt that ranking "X and Y" interpreted as "X and therefore Y" as more probable than "X" could be interpreted as "the conditional probability of Y given X is higher than the probability of X"? But that seems like an extreme stretch of the words.

I think that this was the intended meaning. I was also confused by that paragraph at first, but I settled on the same interpretation as you give here. Granted, it means that the comparison should have been between Y and X&Y, not between X and X&Y.

(BTW, I've always wondered whether, given that the conjunction is on the list as an "alternative" choice, subjects interpret "X" by itself as "X but not Y". I've always thought someone would have done experiments to test that idea, but I haven't looked into the literature deeply enough to know.)

The link to Moro 2009 in AlexSchell's comment discusses possibilities like this.

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