## Comparison tables

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The two tables below show both simple and complex forms of the classic method of comparing small numbers of alternatives in terms of multiple properties (e.g. as used in many of the ‘best buy’ magazines). This particular version uses manual compilation, however there are software tools available, which would speed up the process.

An alternative option of a series of imaginary holidays appears on the left of the table, with a series of criteria along the top (happy kids, low cost, etc.) on which they are to be compared in order of importance to the decision maker (as indicated by the ‘weight’ to be attached to each criterion). The main body of the table contains raw and weighted scores for each alternative on each criterion. This comparison uses ratings from 1 to 5 (the ‘raw score’ columns), plus a numerical ‘weight’ for each criterion (also 1 to 5), so that weighted scores can in theory go from 1 (raw score = 1; weight=1) to 25 (raw score = 5; weight = 5).

 Options Happy Kids (weight=5) Low Cost (weight=3) Happy Adults (weight=2) Easy Travel (weight=1) Totals   Raw score Weighted score: x5 Raw score Weighted Score: x3 Raw score Weighted score: x2 Raw score Weighted score: x1 Sum of raw scores Sum of weighted score Walking Holiday 1 5 3 9 4 8 4 4 12 26 Cruise Holiday 2 10 1 3 2 4 3 3 8 20 Beach Holiday 4 20 1 3 3 6 2 2 10 31 Stay at home 1 5 5 15 2 4 5 5 13 29 Holiday Camp 5 25 1 3 1 2 2 2 9 32

During the final comparison, the ‘weighted value’ of a given option on a given criterion is the raw score for that option on that criterion, multiplied by the weight of that criterion. Thus, ‘beach holiday’ gets a raw score of ‘4’ on the ‘happy kids’ criterion. However as this criterion is highly valued (at 5) ‘beach holiday’ gets a weighted value of 20 (4 x 5).

It is clear that the ‘Total’ on the right shows ‘Stay at home’ would win on ‘raw scores’ (Sum of raw scores = 13) basis, but ‘Holiday camp’ wins once you allow for the different weight of each criterion (Sum of weighted scores = 32).

Nevertheless the results are still very sensitive to the exact values chosen. For instance, if the criterion ‘Low cost’ is given a weight of ‘4’ rather than ‘3’, ‘Stay at home’ would win instead (Sum of its weighted scores would be 34, whereas Holiday camp would only increase to 33). Such technicalities can make it quite difficult to see what going on unless one option is ‘head and shoulders’ above the rest. Sensitivity to slight changes also makes this an easy method to ‘rig’ so as to manufacture an impressive-looking self-objective case that seems to support an option that you happen to be in favour of!

The qualitative version presents essentially the same picture, but reduced to a scatter of ‘+’ and ‘-‘ signs, which amount, effectively, to a five-point scale: --, -, blank, +, ++:

 Happy kids (+++) Low cost (++) Happy adults (++) Easy travel (+) Walking Holiday - + ++ + Cruise Holiday - Beach Holiday + - + - Stay at home - ++ ++ Holiday Camp ++ - - -

To use this table begin by selecting the options that score best on the most important criterion. If there is only one (as above), it wins. If several tie, compare the tied options on the next most important criterion. Again, if there is only one, it wins, but if several are still tied, move on to the next criterion. And so on.

Less important criteria are only used to resolve ties. As this procedure is much easier and less obscure, the implications of working with such crude information are much simpler to grasp and discuss (and if necessary to allow for an even ignore).