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Liquid democracy is the principle of making collective decisions by lettingagents transitively delegate their votes. Despite its significant appeal, ithas become apparent that a weakness of liquid democracy is that a small subsetof agents may gain massive influence. To address this, we propose to change thecurrent practice by allowing agents to specify multiple delegation optionsinstead of just one. Much like in nature, where --- fluid mechanics teaches us--- liquid maintains an equal level in connected vessels, so do we seek tocontrol the flow of votes in a way that balances influence as much as possible.Specifically, we analyze the problem of choosing delegations to approximatelyminimize the maximum number of votes entrusted to any agent, by drawingconnections to the literature on confluent flow. We also introduce a randomgraph model for liquid democracy, and use it to demonstrate the benefits of ourapproach both theoretically and empirically.

The Fluid Mechanics of Liquid Democracy