Negative scoring is subtracting a certain number of points from the total number of points for each incorrect answer .

 Usually even the discussion about negative points is not popular and unnecessarily emotionally coloured. Students reluctantly accept negative points. Most of them see it as an "unfair punishment", so many institutions don't use or even forbid using negative points for incorrect answers. The downside of negative points testing is that it takes longer than a test without negative points. Another one is the fact that except knowledge testing it includes some personality traits (e.g. risk propensity).

 
Is there anything that speaks in favour of negative points?
 
  Remember that random answers to MCQ, sometimes result in guessing the correct answer. If we correct that, the difference between "better" and "worse" prepared students becomes greater. Another characteristic of well prepared negative points system is that it actually awards students' partial knowledge. This is especially true of multiple response questions.   
  Almost the same effect of cancelling "random guesses" is achieved by result normalization after the test, without introducing unpopular negative points.
  In all three cases (no corrections, negative points or normalization) it is not the ranking of student results that normally changes, but the achieved range of points.
  
  Instead of conclusion

  It is important that students see the test as "fair" both as far as the questions and evaluation is concerned. Teachers should follow the feedback with the goal to insure a high quality test which truly reflects the student knowledge. 
  Negative points should probably be avoided, and random guessing cancellation taken care of by increasing minimum required score to pass the test (which we will talk about later)
  You should have good reason to introduce negative points. If you decide to do so, such examination should be well prepared and extensively explained to the students. 
  Negative answers should always be awarded points so that the total "random result" of the test is at least 0, it must not be negative (-1 etc.). 
  If negative points are applied, students should be advised that it is still, unlike popular belief, in their best interest to answer all the questions.