# Ranking on multiple variables

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.

• Are all the characteristics equally important? What scale(s) are they measured on? – tristan Nov 11 '15 at 8:39
• 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. – user93929 Nov 11 '15 at 9:37

• 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. – tristan Nov 11 '15 at 11:11