Researchers expand voting fairness theory to include negative ballots

Traditional voting theory focuses on what candidates voters support. A new computer science paper extends that framework to account for a richer voting mechanism where citizens can also actively oppose candidates—a format increasingly common in online polls and digital platforms.

The problem#

Proportional committee selection typically treats all votes the same way: each voter indicates which candidates they approve of, and the goal is to fill a fixed number of seats while ensuring minority groups gain fair representation. But in practice, many voting systems—especially online ones—let people express disapproval as well. The challenge is defining what proportionality means when both support and opposition matter.

Two approaches to fairness#

The researchers propose two distinct ways to interpret negative votes. In one model, preventing a disapproved candidate's election is weighted equally with electing an approved one—both matter to the voter's satisfaction. In the alternative approach, approvals and disapprovals operate under separate fairness rules, each with its own representation guarantees.

Testing existing methods#

The team tested whether well-known voting algorithms could be adapted to handle these new settings. They examined variants of three established techniques: Phragmén's rule, Proportional Approval Voting (PAV), and the Method of Equal Shares (MES). The work tests whether these classical approaches—and modified versions of them—can satisfy new proportionality axioms designed for the negative-vote context.