I just found out that I could join MENSA with my LSAT score if I wanted. How was it determined that the LSAT correlates to a person’s IQ? Does the LSAT accurately test intelligence? Can I now introduce myself as “Star Was - Certified Genius” without being a complete asshole?
http://www.us.mensa.org/join_mensa/testscores.php3
The LSAT, the SAT, the ACT, the MCAT, the GRE, and similar exams are not tests of intelligence. They make no claims except that they are moderately good (not great, but moderately good) at predicting the grades of the prospective student at the level that he/she is applying for. In other words, the SAT and ACT are moderately good at predicting the freshman college grades for the students who take those tests, the LSAT is moderately good for predicting the first-year grades in law school for the students who take the LSAT, the MCAT is moderately good at predicting the first-year grades in medical school for those students who take the MCAT, and the GRE is moderately good at predicting the first-year grades in grad school for those students who take the GRE. They aren’t quite as good at predicting the second-year grades for the students. They are slightly less good at predicting the third-year grades for those students, etc. If you compare the success in their professions ten years down the road with the scores on the tests, the scores aren’t very good at predicting the success of the students who took the tests. They are even less good at predicting the success of the students twenty years later. They are still worse at predicting the success of the student thirty years later, etc.
In other words, all these tests tell you are a moderately good prediction of how well the student will do in the next year. The makers of the tests always emphasize that a combination of grades and test scores are a somewhat better (but not perfect, or even great) way of predicting how well the student will be doing in the next year. So what do any of these tests actually measure? No one knows. Presumably it’s a combination of how much one has learned in classes so far, how much one has learned out of class, how good one is at taking tests, and (assuming that such a thing exists) some native talent that can be called intelligence. There is no general agreement on what intelligence is and how it can be measured.
So why does MENSA take things like the LSAT for admission? Laziness. They could administer their own tests, but that’s expensive and hard to do.
Mensa does administer its own tests. They simply accept LSAT and other standardized test scores in lieu of taking its tests. It’s not laziness on the part of Mensa but rather their accepting that some people who want to join won’t want to bother taking the Mensa test, so they decided to accept other scores instead; they thereby get more people to join than otherwise might.
No standardized test measures IQ anyway. It’s just a benchmark by which the organization - a college, Mensa, law school, etc. - can go by to “measure” everyone on an even scale.
Mensa, like every other organization, cares most about one thing: getting new members. It’s to their interests to make the net as wide as possible while still maintaining some semblance of deniability to those who don’t get in.
A few years ago AARP - the former but no longer American Association of Retired Persons - defined down its entrance age requirement to 50. This was very risky because it may have alienated its core group of those 65+ without attracting the new group of baby boomers it was seeking.
Which is why I never joined Mensa. Why associate myself with a group whose standards were that low? 
Even if I.Q. tests actually measure something valid, it’s very dubious to claim that getting into Mensa makes you a “genius.” Mensa claims to accept the top 2% of the population in intelligence. That’s approximately everyone with an I.Q. over 130 or approximately everyone two standard deviations above the average in intelligence. Do you really think that 2% of the population are geniuses? A more common use of “genius” is to say that everyone with an I.Q. over 160 is a genius. This is four standard deviations above the average, so about one person in 31,000 is a genius. But, and this should be emphasized, there is no standard definition of the term “genius.” And there’s no possible way to standarize the definition. There is no dividing line in intelligence that groups people except completely arbitrarily. There’s not even any general consensus about whether the notion of intelligence makes sense.