Liquid Democracy with Ranked Delegations

Abstract

Liquid democracy is a novel paradigm for collective decisionmaking that gives agents the choice between casting a direct vote or delegating their vote to another agent. We consider a generalization of the standard liquid democracy setting by allowing agents to specify multiple potential delegates, together with a preference ranking among them. This generalization increases the number of possible delegation paths and enables higher participation rates because fewer votes are lost due to delegation cycles or abstaining agents. In order to implement this generalization of liquid democracy, we need to find a principled way of choosing between multiple delegation paths. In this paper, we provide a thorough axiomatic analysis of the space of delegation rules, i.e., functions assigning a feasible delegation path to each delegating agent. In particular, we prove axiomatic characterizations as well as an impossibility result for delegation rules. We also analyze requirements on delegation rules that have been suggested by practitioners, and introduce novel rules with attractive properties. By performing an extensive experimental analysis on synthetic as well as real-world data, we compare delegation rules with respect to several quantitative criteria relating to the chosen paths and the resulting distribution of voting power. Our experiments reveal that delegation rules can be aligned on a spectrum reflecting an inherent trade-off between competing objectives.

Liquid Democracy with Ranked Delegations

“…As our model captures the delegation phase only, we need to adapt the axiom to our setting. In the full version of this paper (Brill et al 2021) we show that our version implies theirs, and, under a very mild assumption on the delegation rule, the two axioms are equivalent. Definition 11.…”

“…, |s|}). Proofs for results marked by (⋆) can be found in the full version of this paper (Brill et al 2021). Proposition 4 (⋆).…”

Who won? Winner Determination and Robustness in Liquid Democracy

“…First, there also exist different models of liquid democracy where the type of questions studied in this paper are relevant. For instance, instead of simply specifying multiple acceptable delegation options, it is sometimes assumed that each agent provides a preference relation over all acceptable delegation options [10,21]. Moreover, we could also assume that directly voting agents do not cast a simple plurality-like vote but provide us with a preference relation over alternatives.…”

“…While the basic ideas of liquid democracy can be traced back all the way to the 1800s [12], the start of the modern study of liquid democracy is often attributed to Ford [18] (for a more comprehensive review of the history of liquid democracy, see the work of Behrens [4]). Currently, liquid democracy is a very active area of research [10,14,19,23,24,25] (see also [4,9,17,24] for surveys). While many different liquid democracy models have been proposed our model closely follows that of Gölz et al [19].…”

“…Concerning the computational problems studied in this paper, to the best of our knowledge, the Winner Determination problem has neither been studied in our nor any other model of liquid democracy. However, the broader problem of finding delegations with "good" properties has attracted a significant amount of research [10,11,19,23]. For our bribery problems, there is one previous work by D'Angelo et al [14] analyzing bribery related problems in the context of liquid democracy using a model similar to ours.…”