A comparative analysis of methods for constructing weak orders from partial orders

Abstract

This paper compares three methods (sequel, cardinal, maximal) for constructing a weak order from a partial order on a finite set. The constructed weak orders include the partial order. To evaluate the methods, several different selection disciplines were used to stochastically generate partial orders from a fixed linear order. The error of a weak order which includes a generated partial order is a function of the number of ordered pairs added to the partial order to get the weak order which are the reverse of ordered pairs in the fixed linear order. In all cases, the sequel and cardinal mean errors were much lower than the maximal mean error. In most but not all cases, the cardinal mean error was lower than the sequel mean error.