Ranking Using the Copeland Score: A Comparison with the Hasse Diagram

Abstract

This study concerns the problem of ranking objects (chemicals, projects, databases, etc.) when a number of indicators are available for these objects that convey different comparative information. There is no unique way to rank these objects while taking all indicators into account. Using the concept of partially ordered sets and the social choice theory, the Copeland score ranking methodology was applied outside of its usual political environment (voting) to rank objects in the sciences. This method avoids the disadvantages of the Hasse diagram and the linear extension usually used to resolve this issue. The ranking methodology was assessed using eight data sets, each with different numbers of objects and indicators. The results showed that the Copeland method appears to be an effective and stable tool for ranking objects, yielding results comparable to those of an evaluation by a Hasse diagram. Also, it has the advantage of facilitating the analysis of large partially ordered sets, which were practically impossible to handle using existing methods.