A liquid democracy representation

Liquid democracy (also known as delegative democracy) is a hybrid system that exists between representative and direct democracy. Like in a representative democracy, voters can elect delegates that will vote on matters on their behalf. However, in liquid democracy a voter can override their representative’s choice at any time with a direct vote, as well as change their choice of representative, again at any time. These two possibilities make the system a hybrid, affording the voter more direct control of their choices.

In this series of posts we briefly describe three cryptographically secure voting schemes that support liquid democracy. As with any other secure voting scheme, these schemes can be judged in terms of the usual properties listed in the literature, including privacy and verifiability. In these post we will not review these thoroughly beyond stating that these schemes aim to support privacy and be end-to-end verifiable. This is what we would like for a standard voting system, the question is how to extend known techniques to support the particular requirements of liquid democracy.

The first scheme we propose can be seen below:


Mixnet/Mixnet scheme

As we said above, voters can elect delegates and also override their representative’s choice at any time with a direct vote. These votes are represented above by the double bordered boxes, the double border indicates that the votes are encrypted. Once the delegate votes are processed by a mixnet (with the usual anonymization and joint decryption), we obtain the tally totals for each delegate. We call these total delegate weights, as they tell us how much weight each delegate’s choice will carry when calculating the final tally. This is represented by the ‘X’ multiplication sign above, which means that the scheme works as if X copies of the delegate’s ballot are generated, giving the weighted delegate votes box.

On the other hand, we must also take into account those voters that choose to override their delegate’s choice casting a direct vote. These encrypted ballots are again processed by a mixnet to give us a partial tally corresponding to direct choices. The partial tallies corresponding to weighted delegate votes and direct votes are summed together to give the final tally, which is the election result. The line connecting the two input vote boxes labeled ‘invalidate duplicates’ represents the action of eliminating from the set of delegate ballots those that correspond to voters who voted directly. This implements the fact that direct votes override delegate votes. Note, finally, that delegate votes persist across elections, whereas a direct vote is tallied only for the specific matter it was casted on.

In summary, this scheme is a simple combination of two typical mixnet based schemes to yield a scheme that supports the mechanics of liquid democracy. The combination is implemented by summing tallies from an ongoing cross election delegate tally with per-election direct votes. Although there are a few more details, in theory this scheme inherits the privacy, and end-to-end verifiability properties of each of its two components. We continue in the next post.