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Liquid delegation: caps and cycles

Some voters hand their vote to someone they trust, and that person may hand it on. The paper proposes a cap so no delegate speaks for more than 1% of the population. This model shows what the cap and different cycle rules do to voting weight, and how often they change a close result.

Set up the electorate

Delegation cap Enforce the cap (paper proposal: 1% of the population per delegate)

When delegations form a loop Everyone in the loop votes directly; people delegating into it follow them Every vote that reaches the loop is lost

Extensions from the paper (off at their default settings)

Section 4.4.2 of the paper proposes delegation limited to topics and renewed every year. The defaults below leave both out, so the model tests only the cap and the loop rules unless you move them.

Delegate competence (off by default) Treat A as the correct answer and give delegates their own accuracy

The paper's section 4.4.2 proposes expertise verification for delegates. This approximates it: when on, "Share who prefer A" above is read as the chance an ordinary voter picks A, the correct option, and anyone who holds delegations picks it with the chance below. The results then also show how often each tally picks the correct option.

Random seed

A preset loads its settings and runs 300 trials straight away.

One trial

Run a trial to see the heaviest delegates and the tally.

Across many trials

Run 300 trials to see how often delegation changes the outcome.

Illustrative model, not a prediction. Each voter prefers A or B. A chosen share delegate instead of voting; each picks a delegate who may also be delegating, so chains form. A delegate's vote follows the delegate's own preference, so weight concentrates but expertise is not modeled. When a delegate is already at the cap, which delegators are turned away is decided by a random draw (a seeded shuffle), and they vote directly. The paper (section 4.4.2) proposes delegation limited to topics and renewed every year. Two optional sliders approximate that: a share of delegations that do not cover this vote's topic (those delegators vote directly), and a share that have lapsed without renewal (those people either vote directly or sit this vote out, and any vote that reaches someone who sat out is not cast). With both at their defaults, delegation covers every topic and never expires, so only the cap and the loop rules are tested. The paper's expertise verification for delegates is approximated by an optional accuracy model: A is the correct option, an ordinary voter picks it with the "Share who prefer A" chance, and anyone holding delegations picks it with their own chance. It does not model how expertise would be verified, topic by topic, or how voters would choose delegates by skill: delegators still pick a delegate as before. Outcome "differs" includes ties, and uncast votes count against the delegated tally. Try the same seed under different settings to compare like with like. Every rule on this page is a proposal, and CIP is not live.