Research Paper AAMAS 2020, May 9–13, Auckland, New Zealand Incentivising Participation in Liquid Democracy with Breadth-First Delegation∗ Grammateia Kotsialou Luke Riley Political Economy - King’s College London Informatics - King’s College London, Quant Network London, United Kingdom London, United Kingdom [email protected] luke.riley@{kcl.ac.uk,quant.network} ABSTRACT Party in Argentina and Partido de Internet in Spain have been ex- Liquid democracy allows members of an electorate to either directly perimenting with liquid democracy implementations. Additionally, vote over alternatives, or delegate their voting rights to someone the local governments of the London Southwark borough and the they trust. Most of the liquid democracy literature and implementa- Italian cities Turino and San Dona di Piave are working on integrat- tions allow each voter to nominate only one delegate per election. ing liquid democracy for community engagement processes (Boella However, if that delegate abstains, the voting rights assigned to et al. [2018]). In the technology domain, the online platform Liq- her are left unused. To minimise the number of unused delegations, uidFeedback uses a liquid democracy system where a user selects it has been suggested that each voter should declare a personal a single guru for different topics (Behrens et al. [2014]; Kling etal. ranking over voters she trusts. In this paper, we show that even if [2015]). Another prominent online example is GoogleVotes (Hardt personal rankings over voters are declared, the standard delegation and Lopes [2015]), where each user wishing to delegate can select method of liquid democracy remains problematic. More specifically, a ranking over other voters. we show that when personal rankings over voters are declared, it Regardless of the increasing interest in liquid democracy, there could be undesirable to receive delegated voting rights, which is exists outstanding theoretical issues. This work focuses on liquid contrary to what liquid democracy fundamentally relies on. To solve democracy systems where each individual wishing to delegate can this issue, we propose a new method to delegate voting rights in an select a ranking over other voters. In such systems, given the com- election, called breadth-first delegation. Additionally, the proposed mon interpretation that delegations of voting rights are multi-step 1 method prioritises assigning voting rights to individuals closely and transitive , we observe that: searching for a guru follows a connected to the voters who delegate. depth-first search in a graph that illustrates all delegation pref- erences within an electorate, e.g. nodes represent the voters and KEYWORDS directed edges the delegation choices for each voter. For this rea- son, we name this standard approach of delegating voting rights liquid democracy, social choice theory, economic mechanism design as depth-first delegation. Despite its common acceptance, we came ACM Reference Format: across an important disadvantage even for the majority rule with Grammateia Kotsialou and Luke Riley. 2020. Incentivising Participation binary issues. In particurlar, we show that when depth-first dele- in Liquid Democracy with Breadth-First Delegation. In Proc. of the 19th gation is used, it could be undesirable to receive the voting rights International Conference on Autonomous Agents and Multiagent Systems of someone else. At this point, we emphasize that disincentivising (AAMAS 2020), Auckland, New Zealand, May 9–13, 2020, IFAAMAS, 7 pages. voters to participate as gurus is in contrast to the ideology of liquid democracy due to the following. How can a liquid democracy sys- 1 INTRODUCTION tem flourish if voters may not be incentivised to receive delegated votes? Motivated by this, we propose a simple idea solution to this Liquid democracy is a middle ground between direct and repre- issue: a new rule for delegating voting rights, called the breadth- sentative democracy, as it allows each member of the electorate to first delegation, which guarantees that casting voters (those who do directly vote on a topic, or temporarily choose a representative by not delegate or abstain) weakly prefer to receive delegated voting delegating her voting rights to another voter. Therefore individuals rights, i.e. to participate as gurus. For these reasons, we consider who are either apathetic for an election, or trust the knowledge this work of a high societal importance and immediate applications. of another voter more than their own, can still have an impact on We outline this paper as follows: In the introduction we discuss the election result (through delegating). An individual who casts the latest applied and theoretical developments in liquid democracy a vote for themselves and for others is known as a guru (Christoff and give the preliminaries of our model. In the next two sections, and Grossi [2017]). Liquid democracy has recently started gaining we define delegation graphs, delegation rules and two types ofpar- attention in a few domains which we discuss to show an overview ticipation. Afterwards, we formally introduce a new delegation rule of the general societal interest. In the political domain, local parties and compare this rule with the standard one. Finally, we conclude such as the Pirate Party in Germany, Demoex in Sweden, the Net this work with future research goals. ∗This work is supported by the EPSRC grant EP/P031811/1. Proc. of the 19th International Conference on Autonomous Agents and Multiagent Systems 1 (AAMAS 2020), B. An, N. Yorke-Smith, A. El Fallah Seghrouchni, G. Sukthankar (eds.), May We assume the following interpretation for the meaning of transitive delegations of 9–13, 2020, Auckland, New Zealand. © 2020 International Foundation for Autonomous voting rights: If a voter i delegates to a voter j, then i transfers to j the voting rights Agents and Multiagent Systems (www.ifaamas.org). All rights reserved. of herself and all the others that had been delegated to i. 638 Research Paper AAMAS 2020, May 9–13, Auckland, New Zealand 1.1 Related work x over alternative y.A preference relation over voters for voter i 2 V ≻V V 2 V There currently exists a lack of theoretical analysis on liquid democ- is denoted by i and is a binary relation on , i.e.: for i; x;y 2 ≻V racy. However, we summarise the main differences of our work to with i , x;y and x , y, the expression x i y indicates that voter the main undertaking so far. i strictly prefers to delegate her voting rights to voter x instead of As outlined by Brill ([2018]), one of the main ongoing issues in voter y. For both preference relations, we allow an index to identify liquid democracy is how to handle personal rankings over voters. ranking positions e.g. for any i 2 Vd , her m-th preferred voter is ≻V His work discusses possible solutions around this issue without denoted by i;m. giving a formalised model, which this paper does. For two election ≻W ≻W For a set W , consider a binary relation i . Then, i is: alternatives where one is the ground truth, Kahng et al. ([2018]) ¹ º 2 ≻W ≻W find that: (a) there is no decentralised liquid democracy delegation a complete iff for every pair x;y W either x i y or y i x rule that is guaranteed to outperform direct democracy and (b) holds, ¹ º 2 ≻W there is a centralised liquid democracy delegation rule that is guar- b antisymmetric iff for every pair x;y W , if x i y then ≻W anteed to outperform direct democracy as long as voters are not y i x does not hold, and ¹ º 2 ≻W ≻W completely misinformed or perfectly informed about the ground c transitive iff for all x;y; z W , if x i y and y i z, then truth. In comparison, our model can be used in a wider variety ≻W x i z. of elections, as it allows for multiple alternatives and no ground Both preference relations over alternatives and preference relations truth. Additionally our delegation rules can be used in a central or over voters are antisymmetric and transitive but not complete (we decentralised manner, thus the negative result (a) does not apply to do not enforce voters to rank every other member of the electorate our paper. The work of Christoff and Grossi ([2017]) focuses on the as we consider this an unrealistic scenario for large electorates). existence of delegation cycles and inconsistencies that can occur The set of all possible preference relations ≻A and ≻V , for any when there are several binary issues to be voted on with a different i i i 2 V, are denoted by R A and RV , respectively. A preference profile guru assigned for each issue. In comparison, we avoid delegation A RA A cycles by stating that a delegation chain (a path from a delegating over alternatives is a function P : E¹Vº ! 2 , where P ¹N º voter to their assigned guru) cannot include the same voter more returns a set of preference relations over alternatives (maximum than once. Furthermore, individual rationality issues between mul- one for each voter in N ). For example, given an electorate N = f g A¹ º f¹ ≻Aº ¹ ≻Aºg tiple elections is out of scope for this work. Last, Brill and Talmon i; j;k , a preference profile P N could return i; i ; j; j , ([2018]) introduce a special case of Christoff and Grossi’s model, meaning that agent i and j have been assigned a preference relation which allows a single voter to be assigned several gurus. However, over alternatives but k has not (as k either delegates or abstains). our model assigns one guru per voter. Therefore Brill and Talmon Similarly, we define as a preference profile over voters a function V ([2018]) does allow more fine-grained delegations than our model, P V : E¹Vº ! 2R , where P V ¹N º returns a set of preference i.e.