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Input: vector data x_1,...,x_n and a partial ranking function e..g r_p(x_1) > r_p(x_2).

Output: a "complete order function" r_c that projects the data onto 1D (e.g. r_c(x_1)=0.5, r_c(x_2)=0.3)?

Question: what's the standard model/algorithm to use? (e.g. parametric family of functions)

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Draw the partial ranking data as a directed graph, and then observe if the resulting graph really is linear? If it is linear, you can read the complete order off the graph, if it is not linear, such complete order (compatible with your ranking data) do not exist.

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