Wednesday 12 March 2025
The quest for proportionality in voting systems has been a long-standing challenge in computer science and social choice theory. A recent paper delves into this topic, introducing a new axiom called Full Proportional Justified Representation (FPJR). This concept builds upon existing axioms like Proportional Justified Representation (PJR) and Extended Justified Representation (EJR), but offers a more nuanced understanding of proportionality.
Proportionality in voting systems is crucial because it ensures that the elected representatives accurately reflect the preferences of the voters. In other words, if a certain group or coalition of voters has a significant influence on the outcome, they should be represented proportionally in the elected body. This idea may seem simple, but it’s surprisingly difficult to achieve in practice.
The authors of this paper focus on approval-based voting systems, where voters express their preferences by approving candidates. They define FPJR as an axiom that requires any large coalition of voters to have a representative proportionate to its size. This means that if a group of voters has a significant influence on the outcome, they should be represented in the elected body.
One of the key contributions of this paper is the analysis of the relationship between FPJR and PJR+. While PJR+ ensures that any coalition of voters with a certain level of cohesion (i.e., agreeing on multiple candidates) is represented proportionally, FPJR takes it a step further by considering coalitions of varying levels of cohesion. This distinction is important because it acknowledges that not all coalitions are created equal.
The authors demonstrate that FPJR and PJR+ are incomparable axioms, meaning that a voting system can satisfy one but not the other. They provide an example where a voting system satisfies FPJR but violates PJR+, highlighting the limitations of each axiom.
The implications of this work are significant for the design of voting systems. By understanding the differences between FPJR and PJR+, designers can create more nuanced and proportional voting systems that accurately reflect the preferences of voters. This is particularly important in participatory budgeting, where citizens have a direct say in how public funds are allocated.
The paper’s findings also shed light on the challenges of achieving proportionality in approval-based voting systems. While existing axioms like PJR+ provide some guarantees of proportionality, they may not be sufficient to ensure that all coalitions of voters are represented accurately. FPJR offers a more comprehensive approach by considering coalitions of varying levels of cohesion.
Cite this article: “Advancing Proportionality in Voting Systems: The Case for Full Proportional Justified Representation”, The Science Archive, 2025.
Computer Science, Social Choice Theory, Voting Systems, Proportionality, Full Proportional Justified Representation, Proportional Justified Representation, Extended Justified Representation, Approval-Based Voting Systems, Coalition Formation, Participatory Budgeting
Reference: Yusuf Hakan Kalayci, Jiasen Liu, David Kempe, “Full Proportional Justified Representation” (2025).
