I am looking for an algorithm(s) that can compute a global ranking (partial ordering) given individual rankings, in some kind of principled manner.

I want to establish a partial-ordering of some projects, and had some users create their own partial orderings.

I've looked at these algorithms so far:

  • borda-0
  • borda-1
  • Dowdall

My problem is that these algorithms were not really designed to establish partial-ordering and are instead for choosing N winners. I haven't been able to find any widely-used algorithms for this purpose.

I looked at adapting STV to this purpose, but raw STV gives no instructions on how to resolve ties, and it's unclear to me what properties it would have when applied to partial ordering.

Is there a widely-used algorithm/family of algorithms for the problem?

up vote 4 down vote accepted

There is an entire area, rank aggregation (in your case, partial rank aggregation) which deals with these issues. You can take a look at Dwork et al., Rank aggregation revisited and Ailon, Aggregation of partial rankings, $p$-ratings and top-$m$ lists and the pointers therein. There are many other relevant papers online.

  • This is very helpful. Do you have any offhand recommendations of specific algorithms? Also, what are your views on beatpath? – BlackSheep Aug 9 at 22:56
  • Unfortunately I'm not much of an expert on the topic. – Yuval Filmus Aug 9 at 23:12

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