I've given those kinds of tests in my decision analysis and my probabilistic analysis courses (for the multiple choice questions). Four choices, logarithmic scoring rule, 100% on the correct answer gives 1 point, 25% on the correct answer gives zero points, and 0% on the correct answer gives negative infinity.

Some students *loved* it. Some hated it. Many hated it until they realized that e.g. they didn't need 90% of the points to get an A (I was generous on the points-to-grades part of grading).

I did have to be careful; minus infinity meant that on one question you could fail the class. I did have to be sure that it wasn't a mistake, that they actually meant to put a zero on the correct answer.

If you want to try, you might want to try the Brier scoring rule instead of the logarithmic; it has a similar flavor without the minus infinity hassle.

*20 points [-]