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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.
