Researchers from Universidad Carlos III de Madrid (UC3M), in collaboration with international experts, have published a scientific study on how to ensure that the selection of committees and expert groups is mathematically fair and proportional, preventing significant minorities from being excluded. These findings could find applications in the political sphere, the commercial sector, or group activity planning to ensure all group members feel represented.

Imagine that in your neighborhood association, a 10-person committee must be elected to make key decisions. If 30% of the voters share a similar vision, it would be logical for 3 of the 10 elected members to represent that viewpoint. While this seems like an intuitive concept, translating this "proportional fairness" notion into mathematical formulas and computer algorithms is an enormously complex challenge that this study successfully addresses.

In traditional "winner-takes-all" simple majority systems, a 51% majority can occupy 100% of the seats on a committee, silencing the remaining 49%. To avoid this scenario, a previous work proposed the concept of Justified Representation (JR). This rule establishes that if a group of voters is sufficiently large, it has a democratic right to have at least one of its preferred candidates included on the committee. That previous work also proposed Extended Justified Representation (EJR), a more demanding level that ensures large groups have multiple representatives.

The study recently published by the researchers in the journal Artificial Intelligence introduces an intermediate concept between JR and EJR: Proportional Justified Representation (PJR), which is the central innovation highlighted by the authors. The researchers discovered that the EJR rule was sometimes so rigid that it conflicted with other ideal democratic principles. The PJR proposal emerges as a more balanced and flexible tool. “It is more demanding than the basic rule, but it allows for mathematically perfect solutions that other systems would discard due to technicalities, ensuring that no significant group is left out of the picture,” explains one of the study's authors, Luis Sánchez Fernández, Professor in the Department of Telematics Engineering at UC3M.

This study does not stop at mathematical theory; it has several applications. According to the researchers, the developed axiom can be used to design fairer and more proportional electoral voting systems in the political arena; for the balanced selection of juries or expert committees; or even in recommendation systems, such as deciding which products to display in an online store or content platform, so that all customer profiles find options of interest.

This work is part of a relatively recent discipline (approximately 25 years old) called Computational Social Choice. “Computational social choice seeks to study voting systems as algorithms and examines all algorithmic and computational aspects of voting systems, including determining whether the voting system can be computed efficiently, its resistance to manipulation, and other aspects that must be studied from a scientific perspective,” explains Luis Sánchez Fernández.

Researchers from UC3M collaborated on this work with the Centro Universitario de la Defensa (the Naval Military Academy of Marín, Spain), Northwestern University (USA), the University of Applied Sciences St. Pölten (Austria), and the University of Warsaw (Poland).

Video: https://www.youtube.com/watch?v=R0rLeKwfvrU