Unravelling multi-agent ranked delegations

TL;DR

This paper introduces a generalized multi-agent ranked delegation voting model extending liquid democracy, proposing six unravelling procedures and analyzing their properties, complexity, and axiomatic foundations.

Contribution

It presents a novel multi-agent ranked delegation model with multiple delegation options and backup rankings, along with six unravelling procedures and their theoretical analysis.

Findings

Six unravelling procedures are proposed and analyzed.

Algorithms and axiomatic properties are studied for different ballot types.

Computational complexity of unravelling procedures is characterized.

Abstract

We introduce a voting model with multi-agent ranked delegations. This model generalises liquid democracy in two aspects: first, an agent's delegation can use the votes of multiple other agents to determine their own -- for instance, an agent's vote may correspond to the majority outcome of the votes of a trusted group of agents; second, agents can submit a ranking over multiple delegations, so that a backup delegation can be used when their preferred delegations are involved in cycles. The main focus of this paper is the study of unravelling procedures that transform the delegation ballots received from the agents into a profile of direct votes, from which a winning alternative can then be determined by using a standard voting rule. We propose and study six such unravelling procedures, two based on optimisation and four using a greedy approach. We study both algorithmic and axiomatic properties, as well as related computational complexity problems of our unravelling procedures for different restrictions on the types of ballots that the agents can submit.