Weighting by ranking

The easiest way is weighting the criteria by ranks in either ascending or descending order. Ascending means that the most important criterion is given rank 1, the second criterion rank 2 etc. When ranking in descending order, rank 1 is given to the least important criterion etc. Once the ranks are assigned, the numerical weights corresponding to the ranks are derived in different ways:

• Rank sum: With n criteria, rank r receives the weight n-r+1
• Reciprocal rank: With n criteria, rank r receives the weight 1/r, its reciprocal value
• Rank exponent: With n criteria, rank r receives the weight (n-r+1)p. The exponent p is a parameter to control the distribution of the weights. If p=0 then all the criteria will receive the same weight. If p=1 then the weighting is as in "Rank sum". The higher the value of p, the steeper the weight distribution is.

Usually, individual weights are normalized for comparability's sake, By dividing the individual weights by the sum of all weights, the individual weights are converted to fractions between 0 and 1. The sum of all normalized weights is 1.

Advantages and disadvantages

Weighting by ranking is a popular method because it is easy. However, its explanatory power decreases quickly with an increasing number of criteria. The results of this approach should be interpreted cautiously and documented carefully. They may be used as a first approximation only.