I generously gave you a break in the calculation, in that I did not confound you by the use of the “declining population of subjects” and the “declining population of acceptable choices” after the first selection has been qualified: I did not consider the minute difference in the result to be worth the trouble and the argument.

Please note however, that the “declining remaining populations” aspect of the calculations plus your express identification of current membership as the subject group, is why I did not perceive your “Mensa doesn’t exist” recipe as suited to any situ other than the chance that every current member of Mensa is qualified for the top 2% of those qualified for Mensa. I MAY have been wrong – there is a chance that it also produces a suitable approximation of the likelihood of 100,000 randomly selected subjects all meeting the prerequisites for Mensa (save application and provision of proof, the qualifications) – so your ruse may have succeeded in further confusing this issue.

However, having not established proof of your IQ, I SHOULD treat you no differently than as if your WERE in fact randomly chosen. If you have indeed NOT taken the qualifying tests, and have no other evidence that you DO qualify, I SHOULD continue to treat you as randomly chosen. After all, Pew shows that the overwhelming majority of the top 20% of earners believe themselves to be in the top 2%. The majority of the top 60% feel sure that they are in the top 40%. Self-perception is not a precise qualification?

The odds that BOTH of you qualify would remain approximately .0004, as random choices.

However, I will agree that the methadology of “choosing” you is probably flawed, in that I have personally experienced your “wit and wisdom, etc.”, as you put it: I will even concede that you each demonstrate characteristics of participation in the “upper half” – the “right” half of the bell curve. So, let’s redo the numbers with that basic assumption (which I am rigorously not entitled to make):

Now the target is the top 4% of “your” membership class;
each of you has one chance in 25, of meeting the standard;
BOTH of you, given that generous initial treatment, would still be .04 x .04 = .0016 = (round it generously) 2 chances in 1000. (Again, neither population declining due to the initial choice.)

Does this address the issue adequately?

(BTW, I thank you for the first outright assertion that you DO possess the requisite IQ – I had failed to provoke that forthrightness previously.)

Were we to take this recent assertion as a given, only XRLQ remains an unknown, reverting the calculation to the .04 of “your membership class”, above. That is for BOTH. Straightforward? Any assertions forthcoming from XRLQ?

Or is there still fear and loathing of identification as a member of that despised “elite”?

Earlier, you said:

Since you and Patterico are separate cases, for BOTH of you to qualify is the PRODUCT of the probability that either could – or, as shown, .02 * .02 = .0004 = 1 in 10,000.

Uh, no. This might be the case if Xrlq and I were randomly chosen subjects. But we are not.

The chance of any three randomly chosen subjects having an IQ under 100 is .5 x .5 x .5. The chance of all three of us (you, me, and Xrlq) having IQs under 100 is quite low, approaching zero. (If there were a common-sense component of the IQ measurement, I’d put the chances somewhat higher due to your inclusion in the mix. Since there is not, I am confident that the chance is so minimal as to be negligible.)

Understand now? It’s not a math problem. It’s a logic problem. Your calculations for us should be different from your calculations for people whose IQs are just as likely to be below 100 as above. (Here is the best place for you to insert a cheap crack about our intellects.)

My example of calculating whether everyone in Mensa is likely to be a Mensa took your error to an extreme, to make a point. That calculation would be a rough approximation of whether 100,000 randomly chosen people would qualify. That would not be an appropriate calculation for the *members*. Nor would a calculation for two random people be appropriate for two people who already told you they would probably qualify (and based on your specific IQ qualifications, I would).

Now that I gave that example, you now appear to get it, having said that the 1 in 10,000 number is “the probability that both of two randomly chosen subjects would QUALIFY for membership.” But that’s different from what you said before, Conley. You didn’t say “randomly chosen subjects” — you said us. That’s where you messed up, whether you want to acknowledge it or not.

Maybe you just misspoke when you said you were calculating the odds for *us* rather than random members of the public — but if so, what was your point? You seemed to be using the low probability to question the veracity of our claims.

*wrongly – applies inappropriate or inapplicable algorithms
*inaccurately – applies even THOSE so sloppily as to render incorrect results for the chosen algorithm

There has appeared in the 8:59 PM post, a whole new paragraph (albeit equally wrong mathematically and logically). The “.0004 ” calculation shown in mine, is the probability that both of two randomly chosen subjects would QUALIFY for membership. If you know anyone who can help you check the calculation, I will wait – but it is relatively trivial math, so I remain confident.

The wholly separate question of whether you would CHOOSE to do so, would need first to ascertain your ability (which I do not denigrate), then determine whether you sought enlightenment in the company of intellectual peers, or sought peace with your neighbors. Choose either way, if you were qualified. No choice is available if you were not. But your argument is flawed by your assumptions regarding the prevalence of testing to have identified those qualified, the proximity of chapters which those who did qualify might join, even the cultural acceptance of intelligence (often derided as “book learning” although totally unrelated thereto) as useful.

Now, look around you: do you really feel “smarter” than the next 49 random people whom you see? If so, there may be merit to your contention that you would have that choice. There is no doubt that you are more learned, so perhaps we should restrict the sampling to your workplace peers? Still feel “smarter” than that “next 49″? Next, have you, as an adult, taken any standardised IQ tests? Were you provided the results? Were those in the area of 137, or higher (it does depend on the test, what the numbers mean, but that is a guideline to the qualification)? Moving on up to viable candidate.
Now, let us post you in, say the Sudan? Any positive answers to any of the above questions? How about China? Where IS the local chapter of MENSA?

In conclusion, ignorance and stupidity remain a plague upon all our houses. At least, though, ignorance IS curable.