Laird's query and the Wason Card Test

I realized, after I posted the simpler answer in this thread, that I was guilty of the very thing which I brought up in this thread as studied in the Wason Card Test - performing a confirming test and failing to perform a disconfirming test. 

The answer I gave initially assumes only one correct answer, since I devised a set of rules which would give a single answer. However, those rules were far more specific than they needed to be. My simpler rule would also work, and would produce several potential answers, only one of which was offered as a choice. 

The first thing we can assume about the test is that there is some way to distinguish among the eight choices. There are several ways to do this, though. For example, only B contains only lines which are all vertical or horizontal, only G has more than four elements, etc.

To make further progress, we need to assume that any rule is relevant to the grid. My simple rule (only elements which are common to the final column and row) is all that is needed, in combination with the eight choices offered. I can't find another, simpler rule which would work. So our assumptions should end there.

However, despite the lack of necessity, our next assumption is that all the elements, in each position, are necessary to the rule. This makes the dots in the central position problematic. So I don't think that this final assumption can hold (unless someone comes up with a rule that satisfies the other assumptions and makes the dots necessary). Which means that my initial rules (and Chris') are wrong because they contain more assumptions than are necessary or justified. Yet I'm sure that anyone looking at the answers (including myself), finds the more complicated rules cleverer and more likely to be right.

It's a nice illustration of our cognitive biases leading us astray.

Linda

[Laird]

Hi Linda,

Thanks for your analysis. I agree that the assumption that all elements, in each position, are necessary to the rule is invalid and should be dropped. That said, I think that Chris's solution has something going for it that your (second) solution doesn't: it makes a precise, singular prediction. Yours allows for three possibilities, and it is only because only one of those possibilities is present in the multiple choices that we can arrive at a singular answer.

[Laird]

Oops. Sorry. I missed your point. You already acknowledged that your initial (and, presumably, that Chris's) method arrived at a singular solution. And you were claiming that your (initial) method was too specific. So, the tension, then, is between simplicity and specificity (/singularity). I guess the question as to which should take preference might be partly aesthetic? I don't know. But I do think that Chris's method is simpler than your initial method. Whether it is as simple as your second method could be debated...

Oops. Sorry. I missed your point. You already acknowledged that your initial (and, presumably, that Chris's) method arrived at a singular solution. And you were claiming that your (initial) method was too specific. So, the tension, then, is between simplicity and specificity (/singularity). I guess the question as to which should take preference might be partly aesthetic? I don't know. But I do think that Chris's method is simpler than your initial method. Whether it is as simple as your second method could be debated...

There is no tension between simplicity and specificity. Simplicity just refers to satisfying the minimum number of conditions which form the problem, and no more. Singularity was not one of those conditions, so satisfying singularity is unjustified in this case. In addition, we also know that any rules will be incomplete (per the problematic dots in the central position), so completeness is also off the table.

Every time you add an unnecessary condition to your explanation, you decrease the probability it is right. So the suggestions which involved arriving at a singular answer, and attempts to account for every pattern seen, are less likely to be right. There is no aesthetic justification (I hope) for accepting methods which are less likely to be right.

However, intuitively, it is hard not to see a set of rules which are highly specific as more likely to be right than ones which are not.

Linda

It's interesting that there are a variety of ways to arrive at the one answer. I like Ersby's way, as well (it's also why Chris' works).

It would be interesting to know what the maker of the question had in mind. 

Linda

[Laird]

There is no tension between simplicity and specificity. Simplicity just refers to satisfying the minimum number of conditions which form the problem, and no more. Singularity was not one of those conditions

Well, to be fair, there were no (explicit) conditions. The puzzle was simply presented graphically. The conditions are inferred. And it seems to me that "singularity" is a reasonable inference...

Well, to be fair, there were no (explicit) conditions. The puzzle was simply presented graphically. The conditions are inferred. And it seems to me that "singularity" is a reasonable inference...

You can infer, by the rules of multiple choice testing, that one of the offered answers is correct and the others are not. There isn’t anything about the presentation that limits the population of correct answers which weren’t offered, though.

However, now that I think about it, we don’t really know that only one of those answers was “correct” either. We weren’t given any feedback in that regard.

Linda