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I have a list of items (in my case firms) and four characteristics, lets call them A,B,C, and D.

My goal is to rank the firms in my sample based on these characteristics and to find the the firms with the highest (lowest) characteristics A,B,C and D. How can this be done?

I guess this would be like a multivariate ranking or sorting procedure.

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  • $\begingroup$ Are all the characteristics equally important? What scale(s) are they measured on? $\endgroup$ – tristan Nov 11 '15 at 8:39
  • $\begingroup$ I guess all characteristics are equally important. The multiple characteristics are basic key figures, such as firm size, profitability,.. etc. So the characteristics have very different scales. $\endgroup$ – user93929 Nov 11 '15 at 9:37
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There are two options for establishing such a ranking. On the one hand you can define a ranking order, and rank the firms first according to A, then B, etc. On the other hand you can combine the scores of A..D to obtain a single score, which can then be ranked trivially.

I am assuming that you would be more interested in the latter. In order to combine the scores of A to D in a fair way it is important to ensure that they operate on the same scale. If the scores are not already operating on the same scale, then this can be established by normalising each score between 0 and 1 (divide all values for a specific score by the maximum of that score, assuming all scores are positive) or between -1 and 1 if the scores can take on negative values.

Once you have normalised the scores, you can combine them. This can be done trivially by simply taking the average of the score, or by specifying specific weights based on the importance of the score. If you have some historical data available with the correct rankings, then you could also consider to apply regression to this data in order to obtain the weights for each score.

I would start with a simple average of the combined scores, and then ranking. If that does not produce satisfactory results I would manually play a bit with the weights, and see if you can find a configuration that better suits your needs.

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  • $\begingroup$ This is a potentially valid answer. There are two things I would also suggest considering: 1) Instead of normalising the scores by scaling you might instead calculate the centiles for each firm on each characteristic (so that the best firms would score 0.9-1, say) and then combining these. It's hard to know whether this would give better or worse results, but it is something that came to mind. 2) Do you want to favour firms which are consistently good or are you happy for firms which excel on one characteristic only to go near the top of the ranking? If the first consider a $x^2$ term. $\endgroup$ – tristan Nov 11 '15 at 11:11
  • $\begingroup$ Also, if you want to be sure that the top firms are not awful at anything, consider using the geometric mean (i.e. doing the calculation on a log scale). $\endgroup$ – Ian Sudbery Nov 11 '15 at 12:07

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