The beauty of item response theory is that you can infer both the test's parameters and the student's abilities. You can use EM or Gibbs sampling to estimate th

The beauty of item response theory is that you can infer both the test's parameters and the student's abilities. You can use EM or Gibbs sampling to estimate those parameters simultaneously, so there's no need to limit yourself to test difficulty or student ability. In your described scenario, who decides each question's difficulty? Are we sure the teacher or test author understand the true difficulty of their questions? This kind of grading scheme is marginally better than some super-naive approach, as we can't be sure the professor fully understands each question's difficulty.