skip to main content

Title: Liquid Democracy: An Algorithmic Perspective
We study liquid democracy, a collective decision making paradigm that allows voters to transitively delegate their votes, through an algorithmic lens. In our model, there are two alternatives, one correct and one incorrect, and we are interested in the probability that the majority opinion is correct. Our main question is whether there exist delegation mechanisms that are guaranteed to outperform direct voting, in the sense of being always at least as likely, and sometimes more likely, to make a correct decision. Even though we assume that voters can only delegate their votes to better-informed voters, we show that local delegation mechanisms, which only take the local neighborhood of each voter as input (and, arguably, capture the spirit of liquid democracy), cannot provide the foregoing guarantee. By contrast, we design a non-local delegation mechanism that does provably outperform direct voting under mild assumptions about voters.
Authors:
; ;
Award ID(s):
2007080 2024287 1733556
Publication Date:
NSF-PAR ID:
10250703
Journal Name:
Journal of Artificial Intelligence Research
Volume:
70
Page Range or eLocation-ID:
1223 to 1252
ISSN:
1076-9757
Sponsoring Org:
National Science Foundation
More Like this
  1. A boardroom election is an election with a small number of voters carried out with public communications. We present BVOT, a self-tallying boardroom voting protocol with ballot secrecy, fairness (no tally information is available before the polls close), and dispute-freeness (voters can observe that all voters correctly followed the protocol). BVOT works by using a multiparty threshold homomorphic encryption system in which each candidate is associated with a set of masked primes. Each voter engages in an oblivious transfer with an untrusted distributor: the voter selects the index of a prime associated with a candidate and receives the selected prime in masked form. The voter then casts their vote by encrypting their masked prime and broadcasting it to everyone. The distributor does not learn the voter's choice, and no one learns the mapping between primes and candidates until the audit phase. By hiding the mapping between primes and candidates, BVOT provides voters with insufficient information to carry out effective cheating. The threshold feature prevents anyone from computing any partial tally---until everyone has voted. Multiplying all votes, their decryption shares, and the unmasking factor yields a product of the primes each raised to the number of votes received. In contrast tomore »some existing boardroom voting protocols, BVOT does not rely on any zero-knowledge proof; instead, it uses oblivious transfer to assure ballot secrecy and correct vote casting. Also, BVOT can handle multiple candidates in one election. BVOT prevents cheating by hiding crucial information: an attempt to increase the tally of one candidate might increase the tally of another candidate. After all votes are cast, any party can tally the votes.« less
  2. We solve a long-standing challenge to the integrity of votes cast without the supervision of a voting booth: ``{\it improper influence},'' which typically refers to any combination of vote buying and voter coercion. Our approach allows each voter, or their trusted agents (which we call ``{\it hedgehogs}''), to {\it ``nullify''} (effectively cancel) their vote in a way that is unstoppable, irrevocable, and forever unattributable to the voter. In particular, our approach enhances security of online, remote, public-sector elections, for which there is a growing need and the threat of improper influence is most acute. We introduce the new approach, give detailed cryptographic protocols, show how it can be applied to several voting settings, and describe our implementation. The protocols compose a full voting system, which we call {\it {\votexx}}, including registration, voting, nullification, and tallying---using an anonymous communication system for registration, vote casting, and other communication in the system. We demonstrate how the technique can be applied to known systems, including where ballots can be mailed to voters and voters use codes on the ballot to cast their votes online. In comparison with previous proposals, our system makes fewer assumptions and protects against a strong adversary who learns all ofmore »the voter's keys. In {\votexx}, each voter has two public-private key pairs. Without revealing their private keys, each voter registers their public keys with the election authority. Each voter may share their keys with one or more hedgehogs. During nullification, the voter, or one or more of their hedgehogs, can interact through the anonymous communication system to nullify a vote by proving knowledge of one of the voter's private keys via a zero-knowledge proof without revealing the private key. We describe a fully decentralizable implementation of {\votexx}, including its public bulletin board, which could be implemented on a blockchain.« less
  3. The conventional (election) voting systems, e.g., representative democracy, have many limitations and often fail to serve the best interest of the people in a collective decision-making process. To address this issue, the concept of liquid democracy has been emerging as an alternative decision-making model to make better use of “the wisdom of crowds”. However, there is no known cryptographically secure e-voting implementation that supports liquid democracy. In this work, we propose a new voting concept called statement voting, which can be viewed as a natural extension of the conventional voting approaches. In the statement voting, instead of defining a concrete elec- tion candidate, each voter can define a statement in his/her ballot but leave the vote “undefined” during the voting phase. During the tally phase, the (conditional) actions expressed in the statement will be carried out to determine the final vote. We initiate the study of statement voting under the Universal Composability (UC) framework, and propose several construction frameworks together with their instantiations. As an application, we show how statement voting can be used to realize a UC-secure liquid democracy voting system. We remark that our statement voting can be extended to enable more complex voting and generic ledger-based non-interactivemore »multi-party computation. We believe that the statement voting concept opens a door for constructing a new class of e-voting schemes.« less
  4. We present Phrase-Verified Voting, a voter-verifiable remote voting system easily assembled from commercial off-the-shelf software for small private elections. The system is transparent and enables each voter to verify that the tally includes their ballot selection without requiring any understanding of cryptography. This system is an example of making voter verification usable. The paper describes the system and an experience with it in fall 2020, to vote remotely in promotion committees in a university. Each voter fills out a form in the cloud with their selection $V$ for each race and a two-word passphrase $P$. The system generates a verification prompt of the $(V,P)$ pairs and a tally of the votes, organized to help visualize how the votes add up. After the polls close, each voter verifies that this table lists their $(V,P)$ pair and that the tally is computed correctly. The system is especially appropriate for any small group making sensitive decisions. Because the system would not prevent a coercer from demanding that their victim use a specified passphrase, it is not designed for applications where such malfeasance would be likely or go undetected. Results from 43 voters show that the system performed effectively for its intended purpose, andmore »introduced users to the concept of voter-verified elections. Compared to the commonly-used alternatives of paper ballots or voting by email, voters found the system easier to use, and that it provided greater privacy and outcome integrity.« less
  5. U.S. elections rely heavily on computers such as voter registration databases, electronic pollbooks, voting machines, scanners, tabulators, and results reporting websites. These introduce digital threats to election outcomes. Risk-limiting audits (RLAs) mitigate threats to some of these systems by manually inspecting random samples of ballot cards. RLAs have a large chance of correcting wrong outcomes (by conducting a full manual tabulation of a trustworthy record of the votes), but can save labor when reported outcomes are correct. This efficiency is eroded when sampling cannot be targeted to ballot cards that contain the contest(s) under audit. If the sample is drawn from all cast cards, then RLA sample sizes scale like the reciprocal of the fraction of ballot cards that contain the contest(s) under audit. That fraction shrinks as the number of cards per ballot grows (i.e., when elections contain more contests) and as the fraction of ballots that contain the contest decreases (i.e., when a smaller percentage of voters are eligible to vote in the contest). States that conduct RLAs of contests on multi-card ballots or RLAs of small contests can dramatically reduce sample sizes by using information about which ballot cards contain which contests—by keeping track of card-style datamore »(CSD). For instance, CSD reduce the expected number of draws needed to audit a single countywide contest on a 4-card ballot by 75%. Similarly, CSD reduce the expected number of draws by 95% or more for an audit of two contests with the same margin on a 4-card ballot if one contest is on every ballot and the other is on 10% of ballots. In realistic examples, the savings can be several orders of magnitude.« less