Fine-Grained Liquid Democracy for Cumulative Ballots

TL;DR

This paper explores efficient methods for implementing fine-grained liquid democracy in cumulative ballot elections, addressing the challenges of transitive delegations and proposing computational solutions.

Contribution

It introduces a theoretical framework and algorithms for resolving transitive delegations in fine-grained liquid democracy with cumulative ballots.

Findings

Feasible resolution methods exist for various delegation rules.

Conditions for efficient computation of delegation resolutions are identified.

Mathematical programming techniques are effectively applied.

Abstract

We investigate efficient ways for the incorporation of liquid democracy into election settings in which voters submit cumulative ballots, i.e., when each voter is assigned a virtual coin that she can then distribute as she wishes among the available election options. In particular, we are interested in fine-grained liquid democracy, meaning that voters are able to designate a partial coin to a set of election options and delegate the decision on how to further split this partial coin among those election options to another voter of her choice. The fact that we wish such delegations to be transitive -- combined with our aim at fully respecting such delegations -- means that inconsistencies and cycles can occur, thus we set to find computationally-efficient ways of resolving voter delegations. To this aim we develop a theory based fixed-point theorems and mathematical programming techniques and we show that for various variants of definitions regarding how to resolve such transitive delegations, there is always a feasible resolution; and we identify under which conditions such solutions are efficiently computable.