How to choose a good grading curve for yes/no exams? I teach a certain course where I think the best way to test knowledge is using yes/no questions. However, with a simple yes/no exam, a student can just answer randomly to  all questions and get, in expectation, a score of 50%, which is not very fair. I thought of several solutions, but each of them has a disadvantage:


Give a negative score to a wrong answer, such that the expected value of a student who answers randomly is 0. However, this rule made some students highly anxious, and I realized that this anxiety could unjustly harm their performance .
Ask the students to explain each answer. Award points only to correct answers with correct explanations. The problem is that it takes much more time to write and to grade, negating one of the main advantages of a multi-choice exam.
Give a grade of 0 to any student with less than 50% correct answers, and give twice the points for each answer above 50% (e.g, a student with 90% correct answers will receive 2·(90−50) = 80% score). However, I fear this might not be accepted by the university, which encourages additive scoring. E.g, students with 60% correct answers will complain that it is unfair to give them only 20% grade.


What is a good way to write an exam based on yes/no questions?
For this situation, I provide three answer options:

Yes.
No.
I don't know.

The grading rubric is:

Correct answer: +1
Incorrect answer: 0
I don't know: +0.5

That way, if the student really doesn't know, they are guaranteed the expectation of a random guess and you get feedback on holes in student knowledge, which can be used to take remedial action. If your aim is more effective student learning, this can be a good strategy.
I've tried to avoid negative marks for a couple of reasons:

Imagine two candidates who achieve the same final score in a negatively marked exam. One candidate answers only part of the paper, losing a few marks for wrong answers. The other answers almost all of the paper, getting far more correct but also getting several wrong and having marks deducted. Which one knows more?
The second problem is that the use of negative marking extends the theoretical range of marks for the exam. For example, if one mark is awarded for every correct answer and one deducted for each wrong answer, the theoretical range of the exam is - 100 to +100 per cent.

—
From the comments moved to chat: someone asked about a slightly different value for the “I don’t know” option. This is my response:
I tend not to use Yes/No questions, but multiple choice for some assessment. In those cases, I make the &quot;I don't know&quot; option worth 1/(N-1) where N is the number of other options. That way, if there are 3 other options, a random guess would expect to get 1/3 but the I don't know option gains 1/2 --- the expected value if the student can knock out one of the three options..