Exploring the Resolution of Delegations in Liquid Democracy with Fractional Delegation
David Nicolaus Matthäus Holzwarth
B.Sc. thesis advised by Bryan Ford and Pramod Bhatotia
August 28, 2025
Abstract:
This thesis explores fractional delegation in Liquid Democracy, where voters
can split their vote among multiple delegates, aiming to reduce vote
concentration and improve representational fairness. We formalize the mode and
a method of resolving the final voting power of each participant. We then
present and evaluate three implementations of this method: using a solver for
systems of linear equations, a linear programming solver, and an iterative
implementation. We prove that, under well-formed conditions, delegation graphs
have a unique, power-conserving solution. A preprocessing pipeline ensures
graphs are resolvable by eliminating problematic cycles. Through evaluation on
synthetic, social, and real-world graphs, we find that the solver for systems
of linear equations is fastest in most cases, while the iterative
implementation struggles with certain graphs. Our findings demonstrate that
fractional delegation is both feasible and scalable, paving the way for more
expressive digital democratic systems.