Dr. Arthur Jensen:  I know very little about the testing of "general mental ability" at the very high end.  The only test of this type I have seen (years ago) was by Langdon, who sent it to me.  It undoubtedly shows reliable individual differences, but I have never come across any evidence of its statistical properties or its construct validity.   I have been under the possibly false impression that there has been little serious or professional research effort devoted to these types of tests.  I recently read an article on some of the characteristics of youths who are above the 99.9%ile which has some validity data, but these 320 subjects were identified by high scores on the SAT-M when they were 13 years old.( Lubinski, D..et al. (2001). Top 1 in 10,000: A 10-year follow-up of the profoundly gifted.  J. Applied Psychol., 86, 718-729. ) 
  
The one thing I'd be interested in knowing about any test that shows reliable individual difference in the range above the 99.9%ile of the general population is whether it is measuring individual differences in any variable that is significantly correlated with any external criteria of intellectual performance.  We already know that very high IQ is not a sufficient condition for exceptional achievement.  But is "IQ" beyond99.9\% ile even a necessary condition?   I suspect there is a linear relationship between IQ and certain external criteria all the way up to 99.9\% ile. but I have seen no evidence (one way or the other)  for any kind of criterion validity beyond that level.  Achievements have a very skewed or exponential distribution, as if it is a multiplicative function of some number of normally distributed "elemental" variables, each of which is necessary but not sufficient for high intellectual achievement.  These multiplicative variables (besides high IQ), whatever they are, may have quite different absolute levels and distributions in the general population. Above a certain IQ threshold, a  high standing on some of these other variables may be considerably more important achievement-wise than the difference between, say,  the 99.9th and 99.99th percentile of sheer intellectual ability, assuming such a difference  could be measured. 

Steve Coy: Do you believe it is possible, even in principle, to properly norm a high end test in the score regime where exceedingly few people are expected to exist in the population, take the test, or participate in its norming? 

Dr. Arthur Jensen: I think it possible in principle, but it would be a most difficult undertaking in practice because of the problem of screening enough people to find a large enough sample.  The studies of super-gifted school kids have had it relatively easy, because of the schools' identification of the gifted through their testing programs, special classes for high IQ pupils, etc. Probably the easiest way to find adults with IQs>175 would be to advertize for the cooperation of persons who had been identified as "gifted" while in school, then screen those who come forth. 

Steve Coy: Is it possible to quantify the self-selection effect, which has been proffered as an explanation for the observed high incidence of very high IQ scores on these tests, much higher than would be expected under the assumption that the testees were randomly selected from the general population? 

Dr. Arthur Jensen: This is a really tough one.  The interaction of  ability level with interests and lifestyle confounds selection.  I daresay you will find few Mensa or Mega members with few or no intellectual interests, for example, although there may be people out there in the population who are very bright but have few such interests.  There is also self-selection at the top end. How many Nobel Prize winners, or members of the National Academy of Sciences are in any of the high IQ societies?   I was struck by the fact that the Berkeley chapter of Mensa, with its many members, had only one member who was on the faculty of UC Berkeley, although I'm sure some large percentage of them could qualify if they wished to join.   And I know a Nobel Prize winner who was invited to join Mensa, but he had no interest in it and declined the invitation.  It has been my (untested) impression that if IQ and achievement could be correlated in the whole population, members of HI-IQ societies would ne among those who tend to lower the correlation, falling below the regression line (of achievement regressed on IQ).   Most conventional IQ tests have a general knowledge-achievement component which makes the test an amalgam of both ability and achievement and particularly skews the high end of the IQ  distribution. 

Steve Coy: Supposing the self-selection effect could be quantified, so that we can estimate the prior distribution from which testees are drawn, can we then somehow obtain a reasonable estimate of the conditional distribution for a given test describing the probability that a person with a given IQ/g will obtain a given score? (From that, appliying Bayes' theorem, we could invert the conditional probability to obtain the distibution of IQ/g corresponding to a given score.) 

Dr. Arthur Jensen: The problem with testing such propositions is that we don't have an absolute or ratio scale of ability, or even an interval scale, so we can't know if the units of measurement are equal throughout the full range of the scale.  This is partly why reaction times (to stimuli or cognitive tasks of varying complexity) has become interesting to me - we're operating with a true physical scale, which permits answers to questions about distribution parameters that can't be answered with conventional psychometric tests. Your Bayes' theorem idea is excellent, but I don't see how it would work (i.e.,  be statistically  tested)   unless some part of the distribution 
were "anchored" to a ratio scale or at least a true interval scale.  But I fear being too "off the top of my head" on this question.  It deserves more thought than I have time to give it at the moment. High-end tests constructed in terms of some reasonable criteria that would identify the kinds of people you want to bring together could be developed,  it seems to me, without concern about psychometric/statistical evidence about whether the test is part of the continuum of psychometric g as identified and scaled  in the general population.  We tend to select or friends and even good acquaintances on the basis of their general knowledge and understanding of things, as well as their interests and attitudes.  I could see joining a society in which members met certain criteria along these lines.  (Actually my only memberships are in the professional societies I'm more or less obligated to take part in, but I have no trouble in finding most of my good friends an acquaintances in these groups.)