Using Social Choice Function for Multi Criteria Decision Making Problems

Abstract

This study comparatively examines the performance of social choice functions such as Borda, Copeland, Dodgson, and Kemeny in aggregating rankings in Multi-Criteria Decision Making (MCDM) problems. The analyses, conducted using a total of 500,000 datasets, observed that the aggregation results of different social choice functions were generally similar. Although the Borda and Copeland techniques are advantageous in terms of ease of application, they were found to be insufficient in obtaining a complete ranking, especially as the number of alternatives increases. This situation is also valid for the Dodgson and Kemeny techniques. The findings of the study indicate that these techniques provide consensus in the aggregation of rankings but fail to achieve a complete ranking. In 78% of the ranking aggregations using the techniques considered, a complete ranking could not be obtained. Additionally, it was determined that the average rate of achieving a complete ranking was higher in datasets with an even number of rankings compared to those with an odd number of rankings, specifically for the Copeland and Dodgson techniques. This study evaluates the effectiveness of social choice functions in aggregating MCDM problems and provides significant insights for future research.

Keywords

• aggregation techniques
• borda
• copeland
• dodgson
• kemeny
• multi criteria decision making
• social choice function