Incentivising Participation in Liquid Democracy with Breadth First Delegation
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Liquid democracy allows an agent to either vote directly over the available alternatives (candidates) of an election, or to delegate her voting rights to another agent (her guru) who can then vote on her behalf. In the academic literature and industrial applications of liquid democracy, each agent is usually allowed to nominate only one guru per election. However, if the nominated guru does not participate in the election, then the votes delegated to this guru will be wasted. To minimise the possibility of wasted votes, each agent can declare a personal ranking over her most desirable gurus, e.g, as in GoogleVotes. In this paper, we show that even if personal rankings over gurus are declared, the common delegation method of liquid democracy (which we call Depth First Delegation) remains problematic. More specifically, we show that if personal rankings over gurus are declared under the Depth First Delegation rule, there can be gurus who become worst off by receiving a delegated vote. To solve this issue, firstly we introduce a general framework for voting systems that allow delegation of voting rights. The key feature of this framework is the delegation rule function, which when instantiated details who receives each delegated vote. Secondly, we propose a delegation rule function instantiation that we call Breadth First Delegation. Given that personal rankings over gurus are declared, this is the first rule where every agent weakly prefers receiving a delegated vote.
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