Semi-Quantum, Auditable Voting: Minimal Entanglement to Undercut GS while Staying Verifiable

Bao and Halpern (2015) and Dickey & Casey (2023) show that quantum constitutions can violate quantum analogs of Arrow/GS by leveraging superposition, entanglement, and quantum notions of truthfulness. But fully quantum elections face practicality and auditability barriers. This project proposes “semi-quantum voting”: voters receive classical ballots plus ephemeral entangled tokens that are measured to instantiate correlations across specific pairwise comparisons; the tally and audit trail remain classical, augmented by statistical tests on measurement outcomes. We formalize “decoherence-robust truthfulness” (extending Dickey & Casey’s quantum incentive compatibility) and show that, below a noise threshold, profitable manipulation has probability o(1), separating this regime from classical GS impossibility. We also map social welfare functions to social choice functions in this hybrid domain and derive testable completeness conditions (closing a gap in how quantum SWFs are operationalized in practice). The novelty is an implementable bridge between quantum theory’s conceptual escapes and the accountability requirements of real elections (e.g., public audit logs, chain-of-custody), yielding concrete pilot designs that quantify precisely where quantum effects beat GS—and where they fail.

References:

1. Quantum Voting and Violation of Gibbard-Satterthwaite's Impossibility Theorem. Ethan Dickey, Aidan Casey (2023). arXiv.org.
2. Quantum Voting and Violation of Gibbard-Satterthwaite's Impossibility Theorem. Ethan Dickey, Aidan Casey (2023). arXiv.org.
3. Quantum voting and violation of Arrow's Impossibility Theorem. N. Bao, N. Y. Halpern (2015).