Pairwise Liquid Democracy

Brill, Markus; Talmon, Nimrod

doi:10.24963/ijcai.2018/19

Cited by 46 publications

(46 citation statements)

References 22 publications

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“…Another paper by Brill and Talmon (2018) considers liquid democracy in the setting of ordinal elections in which the electorate wishes to construct a complete ordering over alternatives, as opposed to deciding a binary issue as in this work. In this framework, each voter may specify a partial ordering over the alternatives and delegate to others in order to construct a complete ranking.…”

Section: Subsequent Related Workmentioning

confidence: 99%

Liquid Democracy: An Algorithmic Perspective

Kahng

Mackenzie

Procaccia

2021

jair

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We study liquid democracy, a collective decision making paradigm that allows voters to transitively delegate their votes, through an algorithmic lens. In our model, there are two alternatives, one correct and one incorrect, and we are interested in the probability that the majority opinion is correct. Our main question is whether there exist delegation mechanisms that are guaranteed to outperform direct voting, in the sense of being always at least as likely, and sometimes more likely, to make a correct decision. Even though we assume that voters can only delegate their votes to better-informed voters, we show that local delegation mechanisms, which only take the local neighborhood of each voter as input (and, arguably, capture the spirit of liquid democracy), cannot provide the foregoing guarantee. By contrast, we design a non-local delegation mechanism that does provably outperform direct voting under mild assumptions about voters.

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Section: Subsequent Related Workmentioning

confidence: 99%

Liquid Democracy: An Algorithmic Perspective

Kahng

Mackenzie

Procaccia

2021

jair

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“…In the work of Christoff and Grossi [CG17], the authors study the potential loss of a rationality constraint when voters should vote on different issues that are logically linked and for which they delegate to different proxies. In the continuation of this work, Brill and Talmon [BT18] considered an LD framework in which each voter should provide a linear order over possible candidates. To do so each voter may delegate different binary preference queries to different proxies.…”

Section: Related Workmentioning

confidence: 99%

The Convergence of Iterative Delegations in Liquid Democracy in a Social Network

Escoffier

Gilbert²,

Pass-Lanneau³

2019

Lecture Notes in Computer Science

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Liquid democracy is a collective decision making paradigm which lies between direct and representative democracy. One of its main features is that voters can delegate their votes in a transitive manner such that: A delegates to B and B delegates to C leads to A indirectly delegates to C. These delegations can be effectively empowered by implementing liquid democracy in a social network, so that voters can delegate their votes to any of their neighbors in the network. However, it is uncertain that such a delegation process will lead to a stable state where all voters are satisfied with the people representing them. We study the stability (w.r.t. voters preferences) of the delegation process in liquid democracy and model it as a game in which the players are the voters and the strategies are their possible delegations. We answer several questions on the equilibria of this process in any social network or in social networks that correspond to restricted types of graphs.We show that a Nash-equilibrium may not exist, and that it is even NP-complete to decide whether one exists or not. This holds even if the social network is a complete graph or a bounded degree graph. We further show that this existence problem is W[1]-hard w.r.t. the treewidth of the social network. Besides these hardness results, we demonstrate that an equilibrium always exists whatever the preferences of the voters iff the social network is a tree. We design a dynamic programming procedure to determine some desirable equilibria (e.g., minimizing the dissatisfaction of the voters) in polynomial time for tree social networks. Lastly, we study the convergence of delegation dynamics. Unfortunately, when an equilibrium exists, we show that a best response dynamics may not converge, even if the social network is a path or a complete graph.Aim of this paper. In this work, we tackle the problem of the stability of the delegation process in the LD setting. Indeed, it is likely that the preferences of voters over possible gurus will be motivated by different criteria and possibly contrary opinions. Hence, the iterative process where each voter chooses her delegate may end up in an unstable situation, i.e., a situation in which some voters would change their delegations. A striking example to illustrate this point is to consider an election where the voters could be positioned on the real line in a way that represents their right-wing left-wing political identity. If voters are ideologically close enough, each voter, starting from the left-side, could agree to delegate to her closest neighbor on her right. By transitivity, this would lead to all voters, including the extreme-left voters, having an extreme-right voter for guru. These unstable situations raise the questions: "Under what conditions do the iterative delegations of the voters always reach an equilibrium? Does such an equilibrium even exist? Can we determine equilibria that are more desirable than others?".We assume that voters are part of an SN represented by an undirected graph so that they can o...

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“…A major advantage of utilizing a unified framework, capturing many social choice settings at once, is that extensions and generalizations can be designed in a unified way, making them applicable to all such settings at once. One natural extension would be to incorporate proxy voting (Miller, 1969) and liquid democracy (Behrens, Kistner, Nitsche, & Swierczek, 2014;Brill & Talmon, 2018) to the model. Another natural extension would be to incorporate sybil resilience (Shahaf et al, 2018) to the model, making it applicable in situations in which not all agents participating in the process can be assumed to be genuine.…”

Section: Extensionsmentioning

confidence: 99%

Aggregation over Metric Spaces: Proposing and Voting in Elections, Budgeting, and Legislation

Bulteau¹,

Shahaf²,

Shapiro³

et al. 2021

jair

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We present a unifying framework encompassing a plethora of social choice settings. Viewing each social choice setting as voting in a suitable metric space, we offer a general model of social choice over metric spaces, in which—similarly to the spatial model of elections—each voter specifies an ideal element of the metric space. The ideal element acts as a vote, where each voter prefers elements that are closer to her ideal element. But it also acts as a proposal, thus making all participants equal not only as voters but also as proposers. We consider Condorcet aggregation and a continuum of solution concepts, ranging from minimizing the sum of distances to minimizing the maximum distance. We study applications of our abstract model to various social choice settings, including single-winner elections, committee elections, participatory budgeting, and participatory legislation. For each setting, we compare each solution concept to known voting rules and study various properties of the resulting voting rules. Our framework provides expressive aggregation for a broad range of social choice settings while remaining simple for voters; and may enable a unified and integrated implementation for all these settings, as well as unified extensions such as sybil-resiliency, proxy voting, and deliberative decision making. We study applications of our abstract model to various social choice settings, including single-winner elections, committee elections, participatory budgeting, and participatory legislation. For each setting, we compare each solution concept to known voting rules and study various properties of the resulting voting rules. Our framework provides expressive aggregation for a broad range of social choice settings while remaining simple for voters; and may enable a unified and integrated implementation for all these settings, as well as unified extensions such as sybil-resiliency, proxy voting, and deliberative decision making.

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Pairwise Liquid Democracy

Cited by 46 publications

References 22 publications

Liquid Democracy: An Algorithmic Perspective

Liquid Democracy: An Algorithmic Perspective

The Convergence of Iterative Delegations in Liquid Democracy in a Social Network

Aggregation over Metric Spaces: Proposing and Voting in Elections, Budgeting, and Legislation

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