The claimant is (rightly) concerned that her ability doesn't work all the time. But that's a red herring. No ability works all the time, there's always some failure rate. All it does is change how you calculate what's needed to distinguish the ability from random chance. Having the claimant allowed to reject test subjects as unsuitable *during the test* is manipulating that threshold.
Here's an example:
Claim:I have a magic
[*] screwdriver that can unscrew slot-headed screws.
Protocol: As selection of slot headed screws are provided, screwed into a number of different blocks of wood. Each one is presented in turn and I have 10 minutes to unscrew the screw. However, I am allowed to reject a screw/block combination as unsuitable during the test, if I believe my magic screwdriver fails on that one.
Pass Criteria. Of those that I claim I have unscrewed, I have to have been correct for 9/10 of them. I have to have unscrewed at least 9.
See the problem? It's obvious I can pass this test, if there are sufficient blocks of wood. And if there are insufficient blocks, I can still claim that for the cases where I claimed I had unscrewed the screw, I was right 100% of the time -- presuming I'm not an idiot who cannot tell when a screw's been unscrewed
There are several ways of fixing this. One is to allow me to reject at most N screw/block combinations out of the pool of M that I attempt. But that's just a fancy way of changing the pass threshold. We could reduce the threshold to 7/10 or something. Reducing the threshold makes it much clearer how far away one is from random chance. With a forced choice design, the random chance calculation is easy to do.