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On 7/27/2018 at 3:16 PM, DavidOdden said:

Because this is a man-made problem and it is contextually obvious that there is some hidden agenda (these are not literal information questions), assumption-denying is a good thing, if you want to use the full power of your rational mind.

It doesn't seem like there's any more agenda than you would have on many measures of cognitive performance. Sure, we should nail down better what it is you mean by "best answer". But even on pattern matching tests, where you have 7 items in a sequence and need to select the 8th item, there are best answers. You could say that technically any answer is correct, because the pattern is man-made. From what I can tell, most puzzles like this are developed with some specific conceptual common denominator or fundamental characteristic. I don't take it as any more serious than a crossword puzzle or logic puzzle.

I like how you draw out the ways we can ask what makes the best answer. But how would you explain psychological tests of cognitive performance? Those don't seem to take much effort to know what people mean by best answer. 

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It’s not the quantity of agenda that matters, it’s the extent to which a subject knows or complies with the proponent’s agenda that is important. If the task were to construct one answer for each series, and the task were posed in a different context (for instance, were posted on “howsmartareyou.com” or “freeintelligencetest.com”), I would infer that the author’s intent was to provide some metric of intelligence, and they would at least (eventually) provide “correct” vs. “incorrect” scoring in response to answers. The present circumstances are so different that I have to dismiss the slight similarity to an intelligence test, and instead infer that the matter of interest is something about how Objectivists form concepts by identifying similarities and omitting measures. Asking for a second answer and a justification really puts this in a different domain.

To the extent that cognitive tests work, they rely on well-established intent, where training starts (or started: I don’t know what the present state of affairs in education is) in elementary. As long as you at least passively have knowledge of that context, these tasks are not offensive, though I’m not persuaded that they measure what people think they measure. I don’t have any technical knowledge of research on “best answers”, just anecdotal knowledge coming from errors in ordinary-language quiz-composition.  So I do not know for what classes of questions there is empirically verified overwhelming agreement on the “best answer” when there is more than one answer. I nominate “√4 = 2” as a probable best answer, better than “√4 = -2”, likewise “√3 = 1.7” as better than “√3 = 1”. The second answer is “more correct” in an obvious sense, because numeric precision is more valuable than brevity (in solving numeric puzzles), though “1” is infinitely more valuable if your life depends on a rapid ballpark computation (“2” might be even better). The first best answer probably wins (if it is actually believed to be the best answer) primarily because the second doesn’t occur to most people (i.e. it’s the only answer), and secondarily because most people will construct a decision-making principle that favors positive numbers (so, “negative numbers are not very good”, “there are no actual negative lengths”…).

In other words, the key is correctly identifying context, to flesh out the unspoken rules of the game.


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  • 3 years later...

e)  Numbering the elements of the sequence 1, 2, 3, etc, the following works for 1 thru 6, but I don't know how to tweak it to include 7.

Pick a random permutation of the integers 1 through n.  What is the probability that you will get a permutation that includes a 3-cycle that either does not include 5 or 6, or includes 4, 5, and 6.  (It's OK to have two 3-cycles.)


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