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Say you have multiple advisors, each of which may have multiple domains of expertise.

You rank the advisors in each domain, starting at $1$ and proceeding through $2, 3,$ etc. Since an advisor can have expertise in multiple domains, advisor Alice might be ranked $4$ in domain $A$ and $7$ in domain $B$ where Bob is ranked $3$ in domain $A$ and $5$ in domain $C$, Charles is ranked $2$ in domain $A$ but has expertise in no other domains.

Say you wanted to invite your most important advisors to an event, but you could only accommodate a fraction of the total number. You would like to rank them on overall importance based on the domain importance rankings you have.

Is such a thing even plausible? We could take the simplifying assumption that all the domains were equally important.

shadow10
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scanny
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    Not really, no. Just given the ranking you can't tell whether the first- and second-ranked advisors in a field are almost equally good or whether the first-ranked advisor is far and away the best and all the rest are uniformly terrible. –  Jul 13 '14 at 07:28
  • Ah, very interesting. So what I'm thinking now is that maybe it would make sense to explore a richer characterization for the advisors than a simple ranking. So say you could roughly estimate the amount of positive financial impact each advisor could provide you in each domain; then I expect you could just total that impact and rank based on overall impact. Would that be the type of foundation required for a meaningful overall ranking? – scanny Jul 13 '14 at 07:34
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    @scanny yes, you can do that, but that generally requires more information (or assumptions). Ranks are typically used because you cannot quantify such things. If you can, then you should use the actual values (think temperature: its far better to know that A is 1000C and B is 50C than simply that A is hotter than B). Also, you need to be sure your "economic" metric captures the key aspects of what makes an advisor important. It seems counter to your first system, where each category is rated, which suggests that they are not necessarily reducible to a common number. –  Jul 14 '14 at 16:45
  • Ah, I see. That makes even more sense now. In this case, I'd say we use rankings because they are "gut-accessible", i.e. any of our practitioners could say "Alice is more important to us that Bob in domain A". At the same time, I think we could make meaningful estimates of the economic value each represents if we put our mind to it. So I'm inclined to use Rahul's and your reasoning to argue for investing in more careful measurements that could provide a foundation for "investment" decisions in particular advisors. Thank you both for your help! :) – scanny Jul 14 '14 at 22:44

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