Rating elements via partial orders
What you're essentially asking is to find a total ordering of a graph of users whose partial orderings are results of querying a user for their relative rank. Your asymptotic complexity of the minimum necessary number of partial orders will relate to the Stirling number of the Second Kind mathworld.wolfram.com/StirlingNumberoftheSecondKind.html. To find this total ordering (re: "how do I map the partial order into my range?") you would topologically sort the graph you're describing. Note that for every vertex, $u\leq_p v\Rightarrow (u,v) \in E$, and the graph would be directed.