Liquid democracy under vote correlation: On the fallacies of averaging and the excluded middle
2026-08-17 • Computer Science and Game Theory
Computer Science and Game Theory
AI summaryⓘ
The authors study liquid democracy where voters can either vote themselves or pass their vote to others before public information is revealed. They show that simply using one number to represent a voter's overall reliability is not enough because voters' accuracy depends on the specific information state. They propose and analyze three new ways to decide vote delegation that consider how reliable voters are in different situations, ensuring better outcomes. These methods provide guarantees that better reflect how voters perform depending on the public signal.
Liquid democracyVote delegationVoter competenceCommon-signal modelBinary signalsDo-no-harm principleDelegation mechanismsVote correlationGraph theoryMajority correctness
Authors
Seth Gilbert, Stefan Schmid, Santiago Schnell, Jakub Svoboda, Michelle Yeo
Abstract
Liquid democracy permits voters to vote directly or delegate their votes to others. Existing algorithmic analyses assign each voter a single scalar parameter, interpreted as an independent probability of voting for the ground truth. This representation is inadequate when delegation is fixed before public information changes different voters' reliability in different ways. In this work, we study a minimal common-signal model of this phenomenon. Delegation occurs before a public binary signal is realised, while voting occurs afterwards. Conditional on the signal, sink votes are independent, and each voter has a signal-specific competence; marginally, correctness events are correlated through the common signal. We show that delegation based on average competence is not a safe scalarisation: it can violate do-no-harm, and a beneficial delegation rule may send votes to voters with lower average competence. We present and analyse three novel delegation mechanisms for this setting. The first is a conservative intersection mechanism that delegates only to neighbours whose competence exceeds the delegator's by a prescribed margin in every signal state; the conservative intersection mechanism inherits all the guarantees of delegation in the scalar competence setting. The next mechanism is a confounded-set mechanism that enable the delegation to neighbours who are favoured in one state and worse by at most a prescribed tolerance in the other. For this mechanism, we prove expected-margin bounds, and identify the weight-dispersion and mechanism-concentration conditions needed to obtain majority-correctness guarantees. Finally, on bounded-in-degree graphs, a multi-round certified-path mechanism propagates nonnegative two-dimensional path certificates; it is acyclic, yields statewise terminal competence improvement, and gives uniform bounds on path length and terminal voting weight.