A paired-comparison approach for fusing preference orderings from rank-ordered agents

• The paper faces the problem of the fusion of multi-agent preference orderings.
• The specificity of the problem is that the agents’ importance is expressed by a rank-ordering, instead of a set of weights.
• A novel paired comparison approach denominated OPCA is proposed and discussed.
• The description of the new algorithm is supported by practical examples.

The problem of aggregating multi-agent preference orderings has received considerable attention in many fields of research, such as multi-criteria decision aiding and social choice theory; nevertheless, the case in which the agents’ importance is expressed in the form of a rank-ordering, instead of a set of weights, has not been much debated. The aim of this article is to present a novel algorithm – denominated as “Ordered Paired-Comparisons Algorithm” (OPCA), which addresses this decision-making problem in a relatively simple and practical way. The OPCA is organized into three main phases: (i) turning multi-agent preference orderings into sets of paired comparisons, (ii) synthesizing the paired-comparison sets, and (iii) constructing a fused (or consensus) ordering. Particularly interesting is phase two, which introduces a new aggregation process based on a priority sequence, obtained from the agents’ importance rank-ordering. A detailed description of the new algorithm is supported by practical examples.