Definition of No Negative Marking

Posted by Amit Goyal on May 13, 2013; 6:12am
URL: http://discussion-forum.276.s1.nabble.com/isi-2013-was-negative-marking-there-tp7580608p7580625.html

Any marking scheme can be thought of as a function from all possible outcome to scores:

m:{Attempted & Correct, Attempted & Wrong, Not Attempted} ---> R

For example, In ISI the marking scheme was:
m(Attempted & Correct) = 4
m(Attempted & Wrong) = 0
m(Not Attempted) = 1

Note that the above marking scheme is fair:
Expected Score from randomly selecting an answer = (1/4)(4) + (3/4)(0) =  1 =  Score from not attempting it

Consider now an alternative marking scheme
n:{Attempted & Correct, Attempted & Wrong, Not Attempted} ---> R
defined as follows
n(Attempted & Correct) = 3
n(Attempted & Wrong) = -1
n(Not Attempted) = 0

Note that n = m - 1 and is therefore the monotonic transformation of the marking scheme m. Also, it preserves the property that
Expected Score from randomly selecting an answer = (1/4)(3) + (3/4)(-1) =  0 =  Score from not attempting it

Therefore, n and m are equivalent. We have just shifted the origin.

Conclusion: If marking scheme n has "negative marking" then m also has negative marking. In fact, for all decision making purposes the two schemes should be treated as equivalent.