Your program will, out of a sample of 100,000 Facebookers, identify 1,980 people as being DSX. Half of them (99% of 1,000 = 990) have DSX. Half of them (1% of 99,000 = 990) are not actually DSX.
The math is much more favorable for oracle programs which look for traits which are evenly split in the population. This is one reason why "An AI which reads your work and guesses your gender" works so amazingly well as a tech demo. (That program exists, incidentally, and is better than 80% accurate.) However, even supposing there were sufficient cues in a person's writing to tell whether they were e.g. left handed or not in the same fashion, a similar Oracle Of Lefties would be almost useless because you'd get too many misclassified righties in with your identified lefties.
On a related note, this is why a) you are not particularly recommended to get an HIV test if you're not at risk for AIDS and b) the first thing that will happen after an HIV+ result is scheduling another test.
On a totally different note, much of the worries of privacy experts with regards to Gaydar and similar programs don't require the AI to be functional to come to pass. "My sophisticated computer analysis says you're 83% likely to be a child molester." If you're already under suspicion, folks will not ordinarily say "Wait a second, lets see the study showing that this, in fact, actually works." They'll simply take the "expert"'s word at face value.
(See, for example, computer models of global warming. The big black box will spit out any answer you want from it -- want the answer that global warming is no problem at all? Turn off the "Assume that water vapor evaporation causes a vicious warming cycle" and, bam, you can crank your smokestack slider to the max and not have any problems. Yet folks don't routinely consider that prior to saying that "Global warming is a fact -- the UN reported that the scientists proved it.")