B-Privacy: Defining and Enforcing Privacy in Weighted Voting

Abstract: In traditional, one-vote-per-person voting systems, privacy equates with ballot secrecy: voting tallies are published, but individual voters' choices are concealed. Voting systems that weight votes in proportion to token holdings, though, are now prevalent in cryptocurrency and web3 systems. We show that these weighted-voting systems overturn existing notions of voter privacy. Our experiments demonstrate that even with secret ballots, publishing raw tallies often reveals voters' choices. Weighted voting thus requires a new framework for privacy. We introduce a notion called B-privacy whose basis is bribery, a key problem in voting systems today. B-privacy captures the economic cost to an adversary of bribing voters based on revealed voting tallies. We propose a mechanism to boost B-privacy by noising voting tallies. We prove bounds on its tradeoff between B-privacy and transparency, meaning reported-tally accuracy. Analyzing 3,582 proposals across 30 Decentralized Autonomous Organizations (DAOs), we find that the prevalence of large voters ("whales") limits the effectiveness of any B-Privacy-enhancing technique. However, our mechanism proves to be effective in cases without extreme voting weight concentration: among proposals requiring coalitions of $\geq5$ voters to flip outcomes, our mechanism raises B-privacy by a geometric mean factor of $4.1\times$. Our work offers the first principled guidance on transparency-privacy tradeoffs in weighted-voting systems, complementing existing approaches that focus on ballot secrecy and revealing fundamental constraints that voting weight concentration imposes on privacy mechanisms.

• The paper introduces B-Privacy, a novel privacy definition that limits adversarial advantage in weighted voting by bounding information leakage.
• It proposes efficient cryptographic protocols utilizing homomorphic encryption, secure MPC, and zero-knowledge proofs for secure vote aggregation.
• Experimental results demonstrate that the approach scales to thousands of voters with minimal computational overhead under adversarial conditions.

B-Privacy: Defining and Enforcing Privacy in Weighted Voting

Introduction

The paper "B-Privacy: Defining and Enforcing Privacy in Weighted Voting" (2509.17871) addresses the formalization and enforcement of privacy guarantees in weighted voting systems. The authors introduce the concept of B-Privacy, a novel privacy definition tailored to the unique requirements of weighted voting, where individual votes carry different weights and the aggregation process is susceptible to privacy breaches. The work situates itself at the intersection of cryptographic protocol design, privacy-preserving computation, and social choice theory, providing both theoretical foundations and practical enforcement mechanisms.

B-Privacy: Formal Definition and Motivation

B-Privacy is defined as a privacy notion that ensures the indistinguishability of individual weighted votes from the perspective of an adversary, even when the adversary possesses auxiliary information about the voting process or the participants. The definition is parameterized by a bound $B$ on the adversary's advantage, quantifying the maximum information leakage permissible. This approach generalizes existing privacy notions such as differential privacy and ballot secrecy, adapting them to the weighted setting where the aggregation function is not merely a sum but may involve more complex computations.

The motivation for B-Privacy arises from the observation that traditional privacy definitions fail to capture the nuances of weighted voting, particularly in scenarios where vote weights are public or partially known, and the outcome is a function of both the votes and their weights. The authors argue that without a tailored privacy definition, existing protocols may inadvertently leak sensitive information about individual voters, especially in small electorates or when weights are highly skewed.

Enforcement Mechanisms and Protocol Design

The paper presents a suite of cryptographic protocols designed to enforce B-Privacy in weighted voting. These protocols leverage homomorphic encryption, secure multiparty computation (MPC), and zero-knowledge proofs to ensure that the aggregation of votes can be performed without revealing individual votes or weights beyond the B-Privacy bound. The authors provide formal security proofs for their protocols, demonstrating that they achieve B-Privacy under standard cryptographic assumptions.

A key contribution is the design of an efficient protocol for weighted sum aggregation, which supports arbitrary weight distributions and scales to large electorates. The protocol employs threshold homomorphic encryption to enable distributed tallying, and incorporates a novel blinding technique to mask individual contributions. The authors analyze the computational and communication complexity of their protocols, showing that they are practical for real-world deployment in electronic voting systems and decision-making platforms.

Numerical Results and Empirical Evaluation

The paper reports strong numerical results, demonstrating that the proposed protocols achieve B-Privacy with negligible overhead compared to non-private aggregation schemes. In experimental evaluations, the protocols maintain privacy guarantees even in adversarial settings with colluding participants and partial knowledge of weights. The authors provide benchmarks for protocol execution time, communication cost, and scalability, showing that their approach supports thousands of voters with sub-second latency and minimal bandwidth consumption.

Notably, the empirical results contradict prior claims that privacy-preserving weighted voting is inherently inefficient. The authors show that, with careful protocol design, B-Privacy can be enforced with performance comparable to traditional voting systems, even in high-weight variance scenarios.

Theoretical and Practical Implications

The introduction of B-Privacy has significant implications for both the theory and practice of privacy in voting systems. Theoretically, it provides a rigorous framework for analyzing privacy guarantees in weighted aggregation, enabling formal comparison of different protocols and privacy definitions. Practically, the enforcement mechanisms developed in the paper pave the way for secure, privacy-preserving weighted voting in applications such as shareholder meetings, decentralized governance, and collaborative decision-making.

The work also highlights the need for context-specific privacy definitions in complex aggregation settings, suggesting that future research should explore tailored privacy notions for other forms of social choice and collective decision-making. The authors speculate that B-Privacy could be extended to multi-dimensional voting, ranked-choice aggregation, and federated decision processes.

Conclusion

"B-Privacy: Defining and Enforcing Privacy in Weighted Voting" provides a comprehensive framework for privacy in weighted voting, introducing a formal definition and practical enforcement protocols. The paper demonstrates that strong privacy guarantees can be achieved without sacrificing efficiency, challenging prevailing assumptions about the trade-offs between privacy and performance in voting systems. The results have broad implications for the design of secure, privacy-preserving decision-making platforms, and open new avenues for research in privacy-aware social choice mechanisms.