Another test.
Find out the general ideological biases of the test subject
Find two studies, one (Study A) that supports the ideological biases of the test subject, but is methodologically flawed. The other (Study B) refutes the ideological biases of the subject, but is methodologically sound.
Have the subject read/research information about the studies, and then ask them which study is more correct.
If you randomize this a bit (sometimes the study is both correct and “inline with one’s bias”) and run this multiple times on a person, you should get a pretty good read on how rational they are.
Some people might decide “Because I want to show off how rational I am, I’ll accept that study X is more methodologically sound, but I’ll still believe in my secret heart that Y is correct”
I’m not sure any amount of testing can handle that much self-deception, although I’m willing to be convinced otherwise :)
Most frequently useful—that my interest in being unbiased can become a sort of bias of its own, when I hear arguments from others, I can easily spot the biases, and I’ve worked hard to recognize that I have built-in biases as well that I can’t discount.