I'm looking to infer items' values from only ranked lists of these items. I'm assuming that each item has some value, for which a higher value makes it more likely to appear first. This value can be on any scale (meaning, I don't need this value to be on any particular scale) as long as it can be compared to other items' values.
I have N items, and M ranked lists of these N items, where each ranked list contains a subset of N (anywhere from 2 to N items).
How can I infer these values--or at least, get some idea about a value's distribution?
(P.S.: I'm not sure if "order-statistics" is the right tag for this post.)