Estimation of the partial order on the basis of pairwise comparisons

The problem of estimation of the partial order on the basis of multiple pairwise comparisons in binary and multivalent form, with random errors, is investigated. The estimators are based on the idea of the nearest adjoining order (see Slater, 1961; Klukowski 2011). Two approaches are examined: comparisons indicating the direction of preference (binary) and comparisons indicating the difference of ranks (multivalent) - both with possibility of existence of incomparable elements. The properties of estimators and the optimization problems formulated in order to obtain them are similar to those for the case of complete relation. However, the assumptions about the distributions of comparison errors are different – they comprise the case of incomparable elements.