My grading (at least when I do it myself, as on the midterm) is intended to be a bit bimodal. Bimodal at the level of each problem or problem part. Specifically, I try to give more than half the possible points to any answer that is basically correct; and I try to give fewer than half the possible points for any answer that is basically wrong. I have observed that this translates to less partial credit than many students are used to.
As a consequence of the above, you are likely to get a better score getting half the problems fully correct -- not even attempting half the problems -- than you will get by answering everything but getting no answer basically correct.
In the "extreme" version of this grading methodology, your score is simply the number of problems that you fully and correctly solve. I like this idea, in principle, but I have never found it to be feasible to really implement. I approximate it a bit more than many professors.
I grade this way because I like things to be right. I want students to know if they understand a problem. If you can't solve a problem, that doesn't bother me at all. Know that you can't solve it. Maybe in time you would get it. When you get it, you know it and feel happy.
One more comment. One student told me that he left some True/False questions blank because he was worried about getting negative points for wrong answers. Let me emphasize that I never give so many negative points for the wrong answer on a True/False question so as to be "punitive" about guessing: in a no-justification-needed True/False question, it will still be in your interest, statistically, to guess. The purpose of "taking off" for wrong answers in True/False questions is just to normalize scores so that "knowing nothing" doesn't give you an expected 50%. (After all, 50% isn't much worse than the median grade I often see on exams!) It will remain in your interest (statistically) to guess on True/False questions, but the expected score from guessing will be smaller.
In any case, for True/False questions with justifications, as on the midterm, I never give negative points for wrong answers because a student can't guess a convincing justification. The justification has to be present and correct to earn points for the problem.
Phil Rogaway